PRINCIPLES 

OF 

RADIO  COMMUNICATION 


WORKS   OF 
PROFESSOR  J.  H.  MORECROFT 

PUBLISHED   BY 

JOHN  WILEY  &  SONS,  Inc. 


Continuous  and  Alternating  Current  Machinery 

An  elementary  textbook  for  use  in  technical 
schools.  The  Wiley  Technical  Series,  J.  M.  Jame- 
son, Editor.  ix  +  466  pages.  5J  by  7|.  288  fig- 
ures. Cloth,  $2.75  net. 

Principles  of  Radio  Communication 

A  text  dealing  with  all  phases  of  the  radio  art. 
By  J.  H.  Morecroft,  Assisted  by  A.  Pinto  and 
W.  A.  Curry,  x  +  935  pages.  6  by  9.  788  figures. 
Cloth,  $7.50  net. 


BY 
J.  H.  MORECROFT  AND  F.  W.  HEHRE 

Continuous  Current  Circuits  and  Machinery 

For  students  in  Engineering  schools,  whatever  the 
branch  in  which  they  expect  to  specialize.  By 
J.  H.  Morecroft  and  F.  W.  Hehre,  Assistant 
Professor  of  Electrical  Engineering,  Columbia 
University,  viii  +  467  pages.  6  by  9.  377  figures. 
Cloth,  $4.00  net. 


PRINCIPLES 

OF 

RADIO  COMMUNICATION 


BY 

J.   II.   MORECROFT 

Professor  of  Electrical  Engineering,  Columbia  University 


ASSISTED    BY 

A.   PINTO 

Test  Engineer,  Otis  Elevator  Company,  Yonkers,  N.  Y. 

AND 

W.  A.  CURRY 

Instructor  in  Electrical  Engineering,  Columbia  University, 
Assistant  to  Chief  Electrical  Engineer,  New  York  Edison  Company 


NEW  YORK 

JOHN    WILEY    &    SONS,  Inc. 
LONDON:  CHAPMAN  &  HALL,  LIMITED 


Copyright,  1921 
BY  J.  H.  MORECROFT 


PRESS    Of 

/  BRAUNWORTH    «t    CO. 

BOOK    MANUFACTURER* 
•HOOKLYN.     N.    Y, 


PREFACE 


THE  student  desiring  to  familiarize  himself  with  the  theory  and  practice 
of  Radio  Communication  should  be  thoroughly  grounded  in  the  ordinary 
laws  of  continuous  and  alternating-current  circuits;  he  should  also  have 
a  clear  physical  conception  of  the  transient  conditions  continally  occurring 
in  such  circuits.  These  elementary  ideas  are  best  obtained  by  consider- 
ing the  electric  current  from  the  electron  view  point,  i.e.,  as  a  compara- 
tively slow  drift  of  innumerable  minute  negative  electric  charges,  which, 
at  the  same  time  they  are  drifting  through  the  substance  of  the  conductor, 
are  executing  haphazard  motions  with  very  high  velocities,  continually 
colliding  with  each  other  and  with  the  molecules  of  which  the  conductor 
is  composed. 

Due  to  the  extremely  high  frequencies  encountered  in  radio  practice 
it  is  necessary  to  expand  somewhat  one's  ideas  of  resistance,  inductance, 
and  capacity,  the  so-called  constants  of  the  electric  circuit.  As  a  result 
of  the  non-uniformity  of  current  distribution  the  resistance  of  a  conductor 
at  high  frequency  is  generally  much  higher  in  a  radio  circuit  than  it  is  at 
ordinary  engineering  frequencies;  due  to  non-penetration  of  magnetic 
flux  and  hysteretic  lag,  the  apparent  permeability  of  an  iron  core  is  much 
less  at  radio  frequencies  than  at  the  customary  sixty  cycles;  due  to  imper- 
fect polarization  of  dielectrics  the  apparent  specific  inductive  capacity 
of  an  insulator  may  be  much  decreased  at  radio  frequencies  and  the  heat- 
ing due  to  dielectric  losses  may  be  thousands  of  times  as  great  as  is  the  case 
in  ordinary  engineering  practice.  Furthermore,  due  to  the  unavoidable 
internal  capacity,  the  apparent  inductance  of  even  an  air  core  coil  may 
be  expected  to  vary  at  high  frequencies;  in  fact,  a  piece  of  apparatus 
which  is  physically  a  coil,  when  used  at  radio  frequencies,  may,  by  electric 
measurement,  be  found  a  condenser. 

All  of  the  effects  indicated  above  are  treated  in  the  early  chapters  of 
the  text,  not  in  as  comprehensive  manner  as  is  possible,  to  be  sure,  but 
with  sufficient  thoroughness  to  open  the  student's  eyes  to  the  possible 
peculiar  behavior  of  circuits  when  excited  by  the  very  high  frequencies 
of  radio  practice. 

Because  of  its  importance  to  the  radio  art  a  considerable  part  of  the 
text  is  given  over  to  the  theory  and  behavior  of  the  thermionic  three- 


vi  PREFACE 

electrode  tube;  at  the  time  this  material  was  compiled  there  was  no  com- 
prehensive treatment  of  the  subject  anywhere,  but  there  has  recently 
appeared  an  excellent  volume  on  Vacuum  Tubes  (by  H.  J.  Van  der  Bijl) 
which  every  student  of  radio  should  carefully  peruse.  It  is  hoped  that 
the  subject  matter  presented  in  this  text  may  supplement,  rather  than 
duplicate,  that  given  in  the  above  mentioned  volume;  the  actual  behavior 
of  tubes  in  typical  circuits  is  covered  in  this  text  in  a  more  thorough 
manner  than  has  been  attempted  in  other  texts,  and  practically  all  the 
theoretical  deductions  are  substantiated  by  experimental  data,  much 
of  which  has  been  obtained  in  the  author's  laboratory. 

A  chapter  has  been  devoted  to  each  important  phase  of  the  radio  art; 
there  is  also  incorporated  a  short  course  of  elementary  experiments  which 
may  well  be  carried  out  by  electrical  engineering  students  especially  inter- 
ested in  Radio.  For  those  desiring  to  specialize  in  Radio,  the  material 
given  in  the  body  of  the  text  will  furnish  ideas  for  unlimited  further 
experimentation . 

On  certain  parts  of  the  text  very  valuable  assistance  has  been  given 
by  the  author's  former  colleague,  Mr.  A.  Pinto,  and  by  Mr.  W.  A.  Curry, 
who  is  at  present  associated  with  him  in  radio  instruction;  due  credit 
is  given  to  them  on  the  title  page  of  the  text. 

J.  H.  M. 

COLUMBIA  UNIVERSITY, 
April,  1921. 


CONTENTS 


CHAPTER  I 
FUNDAMENTAL  IDEAS  AND  LAWS 

PAGES 

Electrons — Electric  fields — Induced  charges — Electric  current — Conductors 
and  insulators — Continuous  and  alternating  current — Wave  shape — 
Magnetic  fields — Units — Induced  e.m.f. — Self-induction — Coupling — 
Capacity — Oscillograph — Current  flow  in  inductive  and  condensive 
circuits — Time  constant — Alternating-current  flow  in  various  circuits — 
Effect  of  frequency — Transients  in  inductive  circuits — Resonance — 
Decrement — Decrement  from  resonance  curve — Parallel  circuits — Various 
types  of  coupling — Effect  of  neighboring  circuits  on  resistance  and  re- 
actance— Resonance  in  coupled  circuits — Resonance  in  electrically  long 
circuits 1-1 10 

CHAPTER  II 
RESISTANCE — INDUCTANCE — CAPACITY 

General  concept  of  resistance — Various  factors  affecting  resistance — Skin 
effect  and  its  elimination — Skin  effect  in  coils — Eddy  currents  in  iron 
cores — Characterisitics  of  iron  core  coils — Resistance  of  arc  and  spark — 
Resistance  of  an  antenna. 

Coefficient  of  self-induction — Self-induction  of  single  vertical  wire — Single 
horizontal  wire — Single  circular  turn — Single  layer  solenoid — Flat  spiral — 
Toroid — Single  layer  square  coil — Flat  square  coil — Multilayer  coil — 
Mutual  induction  of  two  single  turns — Coaxial  solenoids — Two-wire 
antenna — Two  concentric  coils — Two  coaxial  spirals. 

Capacity  in  general — Capacity  of  an  isolated  sphere — Parallel  circular  plates — 
Single  vertical  wire — Mutual  capacity  of  two  horizontal  wires — Multi- 
plate  condenser — Forms  of  condensers — Specific  inductive  capacity — 
Losses  on  condensers — Phase  difference  of  a  condenser — Internal  capacity 
coils — Natural  period  of  coils 111-178 

CHAPTER  III 
GENERAL  VIEW  OF  RADIO  COMMUNICATION 

Wave  motion  in  water — Electro-magnetic  waves — Velocity  of  propagation — • 
Different  types  of  waves — Spark  telegraphy — Continuous-wave  teleg- 
raphy— Radio  telephony — Receiving  station — Selectivity — Interference — 
Simultaneous  sending  and  receiving — Atmospheric  disturbance — Elimi- 

vii 


viii  CONTENTS 


nation  of  atmospheric  disturbance — Attentuation  of  waves — Day  and 
night  variation  in  signal  strength — Seasonal  variation — Amounts  of  power 
required — "Freak"  transmission .  179-201 


CHAPTER  IV 
LAWS  OF  OSCILLATING  CIRCUITS 

Condenser  discharge  through  inductance — Effect  of  condenser  leakage — 
Frequency — Wave-length — Voltage  and  current  relations — Damping  and 
decrement — Decay  of  current,  voltage  and  energy — Effect  of  spark  gap — 
Number  of  waves  in  a  train — Effective  value  of  damped  sine  wave  cur- 
rent— Effect  of  neighboring  circuits  upon  oscillatory  discharge — Coupled 
pendulums — Oscillations  in  coupled  circuits — Phases  and  amplitudes  of 
currents — Vector  diagram  of  currents  in  coupled  circuits — Frequency  of 
beats — Quenching  gap — Oscillatory  circuit  excited  by  continuous  vol- 
tage— Oscillatory  circuit  excited  by  application  of  alternating  voltage — 
Periodic  disturbances  in  oscillatory  circuit — Oscillatory  circuit  excited  by 
pulse — Impulse  excitation  of  parallel  resonant  circuit — Oscillatory  circuit 
excited  by  damped  sine  wave  and  resonance  curve  for  such  a  case 202-274 

CHAPTER  V 
SPARK  TELEGRAPHY 

Normal  transmission  equipment — Battery  and  coil — Alternators  for  radio 
transmitters — Transformers — Condensers — Resonance  conditions  in  audio 
frequency  circuit — Different  types  of  spark  gr.ps — Oscillation  trans- 
former— Energy  distribution  curves  of  a  transmitter  and  effect  of 
coupling — Adjustment  of  a  spark  transmitter — Elements  of  a  receiving 
set — Need  of  a  rectifier — Types  of  coupling — The  telephone  receiver — 
Crystal  rectifiers — Vacuum  tube  detector — Adjustment  of  receiving  set — 
Wave-lengths  and  ranges  of  transmission  in  spark  telegraphy — Arrange- 
ment of  apparatus  in  typical  transmitting  stations 275-3t>3 


CHAPTER  VI 

k 
VACUUM  TUBES  AND  THEIR  OPERATION  IN  TYPICAL  CIRCUITS 

Possibility  of  electron  emission — Theoretical  prediction  of  electron  evapora- 
tion— Electron  atmosphere — Power  required  to  produce  emission — Two- 
electrode  vacuum  tube — Fleming  valve — Space  charge  and  its  effects — 
Three-electrode  tube — Deforest  audion — Potential  distribution  in  three- 
electrode  tube — Uses  of  three-electrode  tube — Operating  limits  of  a 
tube — Effect  of  gas — lonization — Evacuation  of  a  tube — Detection  of 
gas  in  a  tube — Characteristic  curves  of  typical  three-electrode  tubes — 
Free  grid  potential — Equation  of  plate  current — Resistance  of  tube 
circuits — Capacity  of  input  circuit — Three-electrode  tube  as  detector — 
Action  of  grid  condenser — Triode  as  generator  of  alternating  current 
power — Output  and  efficiency — Heating  of  plates — Phase  relations  in  a 
triode — Possibility  of  self -excitation — Triode  as  detector  of  continuous 


CONTENTS  ix 


wave  signals — Analysis  of  typical  circuits  used  for  self -excitation  with 
conditions  necessary  for  oscillation — Starting  and  stopping  oscillations — 
Parasitic  frequencies — Circuits  used  with  triode  as  detector — Criterion 
for  oscillation  in  detector  tube — Peculiar  noises  in  autodyne  circuits — 
Regenerative  circuits  for  spark  signal  reception — Triodes  in  parallel — 
Alternating-current  power  supply  for  plate  circuit — Special  forms  oL 
tubes — Detailed  study  of  triode  as  power  converter — Triode  characteris- 
tics when  used  as  amplifier 364-577 

CHAPTER  VII 
CONTINUOUS- WAVE  TELEGRAPHY 

Advantages  of  continuous-wave  telegraphy — High-frequency  generators — 
Poulsen  arc — Elementary  theory  of  oscillating  arc — Types  of  oscillation 
of  arc — Commercial  form  of  arc — High-frequency  alternators — Alexan- 
derson  alternator — Goldschmidt  alternator — Frequency  transformers 
using  iron  cores — Marconi  multiple-gap  generator — Methods  of  signalin^ 
used  with  different  generators — Reception  of  continuous-wave  signals — 
Tone  wheel — Heterodyne — Effect  of  upper  harmonics  on  beat  reception — 
Arrangement  of  apparatus  in  continuous-wave  tube  transmitters 578-64^ 


CHAPTER  VIII 
RADIO  TELEPHONY 

Field  of  use — The  transmitter — The  receiver — Modulation  — The  microphone 
transmitter — Analysis  of  modulation— Percentage  modulation — Schemes 
for  modulation — The  vacuum  tube  in  radio  telephony — -Heising  scheme  of 
modulation  and  its  analysis — Alexanderson  scheme  of  modulation — 
Analysis  of  modulated  wave — Oscillating  tube  as  receiver — Effect  of 
decrements  upon  quality  of  speech — Multiplex  radio  telephony — Amounts 
of  power  used  and  distances  covered — Arrangement  of  apparatus  in  a 
commercial  set — Simultaneous  transmission  and  reception 646-693 


CHAPTER  IX 

ANTENNAE  AND  RADIATION 

Radiation  from  simple  antenna — Effects  of  moving  electric  and  magnetic 
fields — Open  and  closed  electric  systems — Fields  involved  in  radiation — 
Radiated  field  at  a  distance  from  the  antenna — Radiation  from  a  coil — 
Excitation  of  the  transmitting  antenna — Various  types  of  antennae  and 
their  characteristics — Relation  between  simple  antenna  and  coil  antenna — 
Antennae  for  air  ships — Underwater  antennae — Ground  antennae — Law 
of  radiation  from  an  antenna — Radiation  resistance — Current  in  receiving 
antenna — Merits  of  different  types  of  antenna? — Limitation  of  transmission 
formulae — Counterpoises — Antenna  resistance — Natural  wave-length  of 
an  antenna — Current  and  voltage  distribution  along  an  antenna  and 
effect  of  loading — Direction  finders — Reliability  of  direction  finders — 
Transient  effects  in  an  antenna 694-780 


x  CONTENTS 

CHAPTER  X 

WAVEMETERS  AND  THEIR  USE 

PAGES 

Frequency  and  wave-length — Principle  of  wavemeter — Extending  range  of  a 
wavemeter — Schemes  for  indicating  resonance — Classification  of  resonance 
indicators — Condenser  for  even  scale — Autodyne  wavemeter — Measuring 
the  wave-length  of  a  transmitter — Energy  distribution — Decrement 
determination  with  spark  transmitter — Determination  of  decrement  of 
wavemeter — Decremeter — Measurement  of  constants  of  an  antenna — 
Mutual  induction  and  coefficient  of  coupling  determination — An  im- 
provised wave-meter 781-823 

CHAPTER  XI 
AMPLIFIERS 

Amplifiers  in  general — Characteristics  of  triodes— Effect  of  plate  circuit 
resistance  and  reactance — Classification  of  amplifiers — Transformer-re- 
peating amplifiers — Construction  of  transformers  for  audio-frequency — 
Impedance  of  telephone  receivers — Connections  of  transformer-repeating 
amplifier  —  Transformer-repeating  amplifiers  for  high  frequencies — 
Resistance  amplifier — Proper  resistances  for  repeating — Grid  condenser 
and  leak — Inductance-repeating  amplifier — Filters  and  their  charac- 
teristics— Stability  of  amplifiers — Tube  noises — Arrangement  of  appa- 
ratus in  amplifiers 824-879 

CHAPTER  XII 
RADIO  EXPERIMENTS 

Resonance  curves — Buzzer-generator  and  crystal  detector  characteristics — 
Study  and  use  of  wavemeter — Setting  up  and  adjusting  a  spark  trans- 
mitter— Measurement  of  antenna  constants — Continuous  current  charac- 
teristics of  three-electrode  tube — Three-electrode  tube  as  detector  of 
damped  waves — Determination  of  tube  constants — Triode  as  power 
converter — Triode  as  source  of  power  in  self-exciting  circuit — Resistance 
measurements  at  high  frequency — Oscillating  triode  as  receiver  of 
continuous -wave  signals — Study  of  the  audio-frequency  amplifier — 
Study  of  radio-telephone  set 880-919 


PRINCIPLES 

OF 

RADIO  COMMUNICATION 


CHAPTER  I 
FUNDAMENTAL  IDEAS  AND  LAWS 

Nature  of  Electricity. — Everyone  is  more  or  less  familiar  with  elemen- 
tary experiments  having  to  do  with  electrically  charged  bodies.  Fur, 
if  rubbed  on  a  dry  day,  crackles  and  gives  off  minute  sparks;  a  glass  rod 
rubbed  with  a  cloth  becomes  electrified  and  will  attract  small  bits  of 
paper,  cotton,  etc. ;  due  to  wind  friction,  and  other  causes,  clouds  become 
intensely  electrified  and  are  able  to  break  down  the  insulating  strength 
of  the  air  and  produce  sparks  thousands  of  feet  long. 

In  what  way  does  an  electrified  body,  or  electrically  charged  body, 
differ  from  one  in  the  uncharged,  or  neutral,  state?  A  reasonable  answer 
to  this  question  is  found  in  the  modern  conception  of  the  constitution 
of  matter. 

Electrons. — It  has  been  firmly  established  that  every  atom  of  matter 
is  charged  with  minute  particles 1  of  negative  electricity,  so-called  electrons. 
An  electron,  when  detached  from  the  atom  of  matter  with  which  it  was 
associated,  shows  none  of  the  properties  of  ordinary  matter.  It  does  not 
react  chemically  with  other  electrons  to  produce  some  new  substance; 
moreover,  all  electrons  are  similar,  no  matter  from  what  type  of  atom 
they  have  been  extracted.  Thus  an  electron  from  the  hydrogen  atom 
acts  precisely  the  same  as  the  electrons  from  atoms  of  oxygen,  iron,  chlorine, 
or  any  other  substance.  It  seems  that  the  electron  is  nothing  but  electricity. 

1  It  may  seem  difficult  at  first  to  think  of  electricity  as  made  up  of  separate,  dis- 
crete, quantities  instead  of  a  continuous  distribution  of  electric  charge,  but  it  is  pointed 
out  that  according  to  modern  concept  energy  itself  is  always  present  as  a  certain  number 
of  unit  quantities;  that  is,  energy  itself  is  to  be  "  counted  "  in  terms  of  the  smallest 
possible  quantity,  called  a  "  quantum." 


2  FUNDAMENTAL   IDEAS   AND   LAWS  [CHAP.  I 

It  is  definite  in  amount,  always  being  exactly  the  same,  and  is  generally 
believed  to  be  the  smallest  possible  quantity  of  electricity,  i.e.,  electricity 
cannot  be  subdivided  into  quantities  smaller  than  the  electron. 

The  constants  of  the  electron  are:  Radius  =  2X10~13cm.;  mass  =  8.8 
X  10~28  grams;  charge  =  1.59  X  10~19  coulomb.1  The  mass  of  the  electron 
depends  upon  the  velocity  with  which  it  is  moving;  the  value  given 
here  holds  good  only  if  the  electron  is  traveling  at  velocities  considerably 
less  than  the  velocity  of  light,  say  less  than  109cm./sec. 

For  many  years  it  has  been  the  custom  for  physicists  to  speak  of 
positive  electricity  and  negative  electricity;  from  this  standpoint  the 
electron  is  negative  electricity.  All  electrons  are  the  same  kind,  or  polarity, 
hence  it  follows  that  the  electron  is  the  smallest  possible  quantity  of  negative 
electricity. 

Charged  Body. — From  the  electron  viewpoint  a  negatively  charged 
body  is  one  having  more  than  its  normal  number  of  electrons  and  a  posi- 
tively charged  body  is  one  having  less  than  its  normal  number  of  electrons. 
Let  the  circular  shape  in  Fig.  1  represent  an  atom 
of  hydrogen;2  the  small  circles  with  the  minus  sign 
in  them  represent  the  electrons  associated  with  the 
normal  hydrogen  atom.  The  normal  atom  is  not 
charged;  it  does  not  exert  any  attractive  or 
repulsive  force  on  the  other  atoms,  due  to  its  elec- 
trical state. 

The   structure  of  the  atom  itself,  whatever  it 
FIG.  1.  — Conventional  may  be,  is  always  charged  electrically  positive;    in 
model  of    a    simple,  the  normal  atom  there  are  enough  electrons  to  just 
neutral,  atom.  neutralize  the  positive   charge   of   the   atom   itself. 

The  normal   atom   acts   like    an   uncharged  body, 

therefore,  not  because  it  has  no  electrical  charge  associated  with  it,  but 
because  it  has  just  as  much  negative  charge  as  it  has  positive  charge,  and 
these  two  charges  neutralize  one  another  in  so  far  as  action  of  the  atom 
on  other  bodies  is  concerned. 

If  one  electron  is  removed  from  the  atom  by  some  means  or  other 
(represented  in  Fig.  2)  the  balance  between  positive  and  negative  charge 
is  destroyed;  an  excess  of  positive  charge  exists  on  the  atom  and  the  atom 
is  positively  charged.  The  electron  which  has  been  removed  from  the 
atom  constitutes  a  negative  charge.  If  the  electron  is  allowed  to  go  back 

irThe  student  who  is  particularly  interested  in  the  theoretical  and  experimental 
work  from  which  these  values  are  obtained  is  referred  to  "  Conduction  of  Electricity 
through  Gases,"  by  J.  J.  Thomson. 

2  In  recent  years  much  work  has  been  done  in  investigation  of  the  structure  of 
the  atom;  an  interesting  and  elementary  exposition  of  some  of  the  modern  views  is 
given  in  "  The  Nature  of  Matter  and  Electricity,"  by  Comstock  and  Troland. 


NATURE  OF  CHARGED  BODIES  3 

to  the  atom  the  balance  of  charge  is  restored  and  the  atom  is  again  un- 
charged, or  neutral. 

A  positively  charged  body,  therefore,  is  one  which  has  been  deprived 
of  some  of  its  normal  number  of  electrons;  a  negatively  charged  body  is 
one  which  has  acquired  more  than  its  normal  number  of  electrons.  Thus 
when  a  piece  of  sealing  wax  is  rubbed  with  dry  flannel  the  wax  becomes 
negatively  charged  and  the  flannel  becomes  positively  charged.  The 
friction  between  the  wax  and  the  flannel  must  have  rubbed  some  of  the 
electrons  off  the  flannel  molecules  and  left  them  on  the  surface  of  the  wax. 

The  extra  electrons  on  the  wax  are  attracted  by  the  deficient  mole- 
cules of  the  flannel  (positive  and  negative  charges  attract  each  other)  and 
if  the  flannel  and  wax  are  left  together  after  being  rubbed  they  soon  lose 
their  charges;  the  molecules  of  the  flannel  regain  their  proper  number  of 
electrons. 

Number  of  Electrons  Removable  from  an  Atom. — Although  there  may 
be  a  great  number  of  electrons  associated  with  an  atom  or  molecule  it 
is  generally  not  possible  to  remove  more  than  one;    in  a  body  which  is 
positively  charged  most  of  the  atoms  are 
neutral,  having  their    proper    complement 
of  electrons;    others  have  had  one  electron 
removed.     If  but  few  of  the  atoms  of  a 
body  have   had  an  electron  removed  the 
body  has  a  small  charge;  the  more  highly 
the   body   is    charged    the  more   deficient 
atoms  there  are  on  it. 

From  this  viewpoint  it  seems  that  the  FlG  2. -Conventional  model  of 
amount  of    charge    on    a    body  should    be       simple  atom  charged  positively, 
counted;    the  charge    consists    of    discrete       one  of  its  electrons  being  free, 
things.     Instead  of  saying  that  a  body  has 

a  certain  amount  of  negative  electricity  on  it,  we  might  more  reason- 
ably say  that  a  certain  number  of  electrons  have  been  deposited  on  it. 

Electric  Fields. — If  a  light  substance,  such  as  a  pith  ball,  is  touched 
to  a  charged  body,  it  becomes  charged  with  electricity  of  the  same  polarity 
as  that  on  the  body  itself;  as  like  charges  repel  one  another  the  pith  ball 
will  be  repelled  from  the  charged  body.  By  experimenting  it  may  be 
found  that  the  repulsive  force  between  the  pith  ball  and  the  original  charge 
exists  even  when  there  is  considerable  distance  between  the  two.  The 
space  surrounding  a  charged  body  is  evidently  under  some  kind  of  strain 
which  enables  it  to  act  upon  a  charged  body  with  a  force,  attractive  or 
repulsive,  according  to  the  relative  polarities  of  the  two  charges.  This 
space  surrounding  a  charged  body,  in  which  another  charged  body  is 
acted  upon  by  a  force  tending  to  move  it,  constitutes  an  electric  field, 
sometimes  called  an  electrostatic  field. 


4  FUNDAMENTAL  IDEAS  AND  LAW.S  [CHAP.  I 

Such  an  electric  field  surrounds  every  charged  body;  it  really  extends 
to  infinity  in  all  directions  from  the  charged  body,  but  as  the  force  becomes 
very  small  as  the  distance  is  increased  it  is  generally  considered  that  the 
electric  field  due  to  a  charge  extends  but  a  short  distance  from  the  charge. 
For  example,  the  field  due  to  a  piece  of  charged  sealing  wax  is  negligible 
at  a  point  a  few  feet  distant  from  the  wax,  so  we  say  that  the  field  of  this 
charge  extends  but  a  few  feet  from  the  wax.  On  the  other  hand  the 
electric  field  produced  by  a  large,  highly  charged,  wireless  antenna  may 
extend  several  thousand  feet  from  the  antenna. 

Electric  Fields  Represented  by  Lines.— In  diagrams  the  electric  field 
surrounding  a  charge  is  most  easily  depicted  by  drawing  lines  from  the 
charged  body  into  the  surrounding  space.  The  direction  of  the  lines, 
properly  drawn,  gives  the  direction  of  the  electric  force  and  the  relative 
,  closeness  of  the  lines  in  various  parts  of  the 

diagram  shows  the  relative  strengths  of  the  field 
at  these  points,  the  closer  the  lines  the  more 
intense  the  field.  A  line  of  force  originating 
on  a  positive  charge  is  properly  shown  end- 
ing on  an  equal  negative  charge.  In  diagrams 
it  is  not  always  convenient  to  represent  them; 
they  may  be  shown  as  discontinuous.  It  must 
not  be  supposed,  however,  that  the  electric 
force  itself  is  discontinuous;  it  always  con- 
FIG.  3.-Electric  field  around  tinues  from  a  Positive  charge  to  a  negative 
a  charged,  isolated,  sphere  charge. 

represented  by  radial  lines.          Fig.  3  shows  how  lines  may  be  used  to 

represent  the  electric  field;  it  shows  a  posi- 
tively charged  metal  ball  supposedly  far  enough  away  from  other  bodies 
to  be  considered  as  by  itself.  The  lines  of  force  originate  on  the  surface 
of  the  sphere  and  extend  as  radii  in  all  directions.  The  arrow  head  on 
the  lines  indicates  the  direction  in  which  a  positive  charge  would  be  urged 
if  placed  in  that  part  of  the  field. 

The  lines  are  closest  together  at  the  surface  of  the  sphere,  indicating 
that  the  force  is  greatest  at  this  point,  a  fact  easily  proved  experimentally. 
Although  the  lines  are  shown  as  discontinuous,  ending  in  uncharged  space, 
each  line  really  extends  in  some  direction  until  it  encounters  a  negative 
charge.  In  the  case  of  a  metallic  sphere,  suspended  in  the  air  distant 
from  other  bodies,  the  lines  should  all  be  shown  as  ending  on  the  earth's 
surface  as  suggested  in  Fig.  4.  Fig.  5  represents  the  electric  field  between 
two  parallel  metallic  plates,  one  of  which  has  been  charged  positively 
and  the  other  negatively.  Moreover,  as  all  the  lines  originating  on  the 
positive  plate  are  shown  as  ending  on  the  negative  plate,  it  shows  that 
the  two  plates  have  been  given  equal  charges,  The  field  is  properly 


ELECTRIC   FIELDS  5 

shown  as  very  intense  between  the  two  plates,  weaker  towards  the  edges, 

and  very  weak  in  the  space  not  directly  included  between  the  two  plates. 

Closed  and  Open  Electric  Systems. — In  Fig.  5  most  of  the  electric 

field  is  shown  directly  between  the  plates  on  which  the  charges  are  situated; 


FIG.  4. 


FIG.  5. 


FIG.  4. — Charged  body  near  the  earth  has  its  electric  field  radial  near  the  body,  all 
lines  of  force,  however,  bending  over  so  that  they  end  on  the  earth. 

FIG.  5. — Two  metallic  plates,  close  to  one  another,  one  charged  positively  and  the 
other  negatively,  have  an  intense  electric  field  between  the  plates,  and  weak  field 
elsewhere. 

such  distribution  of  lines  indicates  a  nearly  closed  electric  system.  The 
field  illustrated  in  Fig.  4  is  a  comparatively  open  one;  the  distinction 
between  open  and  closed  fields  is  not  a  very  sharp  one,  but  is  nevertheless 
a  very  important  one  for  the  radio  engineer. 


FIG.  6, — The  electric  field  around  a  charged  vertical  wire. 

Fig.  6  represents  a  vertical  wire  antenna,  such  as  Marconi  used  in 
tiis  early  experiments;  the  electric  field  when  the  antenna  is  charged  has 
the  form  shown.  If  the  antenna  is  bent  over  in  the  form  of  an  inverted 
L,  the  field  has  the  form  shown  in  Fig.  7.  With  the  antenna  in  this  form 


FUNDAMENTAL  IDEAS  AND   LAWS 


[CHAP.  I 


most  of  the  electric  field  is  evidently  included  directly  between  the  earth's 
surface  and  the  antenna  wire,  so  the  field  is  a  closed  one  as  contrasted 
with  that  of  Fig.  6,  which  is  regarded  as  an  open  field.  The  operating 
characteristics  of  the  two  antenna  shown  are  quite  different,  the  difference 
being  due  to  the  different  distribution  of  the  field  in  the  two  cases. 


FIG.  7. — The  electric  field  around  an  ordinary  antenna. 

Induced  Charges. — Suppose  a  charged  metal  ball  is  brought  close  to 
another  conducting  body,  as  a  metal  rod,  the  rod  being  uncharged.  Experi- 
ment shows  that  as  the  rod  is  brought  into  proximity  of  the  brass  ball 
the  rod  itself  becomes  charged  in  a  peculiar  way.  If  the  ball  is  positively 
charged  that  end  of  the  rod  nearer  to  it  becomes  charged  negatively  and 
the  farther  end  becomes  positively  charged  as  indicated  in  Fig.  8.  As 
a  whole  the  rod  is  not  charged,  there  being  as  much  negative  charge  as 


FIG.  8. — A  charged  body  inducing  charges  on  a  metal  rod. 

there  is  positive  charge.  These  charges  which  have  been  produced  on 
the  rod  through  the  action  of  the  charged  ball  are  called  induced  charges. 

Charges  induced  on  a  body  are  always  double  in  kind;  as  much  pos- 
itive charge  appears  as  does  negative.  However,  if  in  Fig.  8  a  wire  having 
one  end  connected  to  the  earth  is  touched  to  the  end  of  the  rod  marked 
C,  the  positive  charge  which  has  been  induced  at  this  end  of  the  rod  will 
run  off  to  the  earth,  and  when  the  wire  is  removed  there  will  be  left  of 
the  rod  only  the  negative  charge. 

Bound  and  Free  Charges. — In  the  case  considered  above  the  positive 
charge  runs  off  to  the  earth  because  there  is  no  force  tending  to  hold  it 
on  the  rod,  on  the  contraiy  it  is  being  repelled  by  the  positive  charge 
on  the  ball.  The  negative  charge  at  B  is  held  from  running  off  to  earth 


INDUCED    CHARGES  7 

by  the  attractive  force  of  the  positive  charge  on  the  ball.  The  negative 
charge  on  the  rod  is  called  a  bound  charge  and  the  positive  charge  which 
runs  away  if  given  the  opportunity  is  called  a  free  charge. 

An  illustration  of  the  way  in  which  this  method  of  producing  charges 
is  useful  in  radio  circuits  is  shown  in  Fig.  9.  The  charge  on  ball  A  is 
to  produce  a  charge  of  the  opposite  kind  on  the  conductor  F  through 
the  two  condensers  BC  and  DE.  When  A  comes  in  contact  with  B,  this 
becomes  positively  charged.  A  nega-  A  B  c  p  E 

tive  charge  appears  at  C  due  to  the 
inducing   action   of    5.     An   equal 

positive  charge   must  appear  at  D  +'  '—  +'  '~ 

and   this  must   induce   a   negative      FlG.  9. -A  charged  body  inducing  charges 
charge  on    E.     But    if    a    negative          On   conductor  F,  acting  through  two 
charge  appears  at  E  there  must  be          condensers, 
an   equal   positive   charge  induced 

on  F.  If  now  the  conductor  F  is  connected  to  the  ground  this  positive 
will  run  off  to  earth  and  there  will  be  left  on  the  conductor  EF  a 
negative  charge.  This  charge  will,  however,  be  bound  by  the  positive 
charge  on  D;  if  B  is  now  grounded  (connected  to  earth)  its  charge  will 
run  off  and  so  the  negative  charge  on  C  becomes  free.  This  free  charge 
on  C  will  combine  with  the  positive  charge  on  D  and  neutralize  it,  thus 
leaving  on  the  conductor  EF  a  free  negative  charge. 

Induced  Charges  from  the  Electron  Viewpoint. — As  will  be  explained 
later,  the  electrons  in  a  metallic  conductor  are  more  or  less  free  to  pass 
from  one  atom  of  the  substance  to  another;  they  are  continually  moving 
around  the  complex  molecular  structure  of  atoms  comprising  the  metal. 
When  the  rod  of  Fig.  8  is  brought  into  the  neighborhood  of  the  charged 
ball  the  electric  field  due  to  the  charge  on  the  ball  acts  on  the  free  elec- 
trons of  the  rod,  attracting  them.  Hence  the  free  electrons  of  the  rod 
tend  to  congregate  at  that  end  of  the  rod  which  is  nearest  to  the  ball; 
they  constitute  the  negative  charge  at  this  end  of  the  rod. 

But  if  the  rod  was  uncharged  before  coming  into  the  influence  of  thf 
charged  ball  there  must  be  just  enough  electrons  on  it  to  neutralize  the 
positive  charges  of  the  atoms.  If  more  than  a  proper  portion  of  the  elec- 
trons gather  at  one  end  of  the  rod  there  must  necessarily  be  a  shortage 
of  them  at  the  other  end.  This  shortage  of  electrons  at  the  end  C  of  the 
rod  constitutes  the  positive  charge  at  this  end. 

When  the  end  C  is  grounded,  the  positive  atoms  of  the  rod  cannot 
leave  the  rod  and  go  into  the  earth,  but  electrons  from  the  earth  can  run 
up  into  the  rod  and  they  do  so,  being  attracted  by  the  deficient  atoms  at 
C.  These  electrons  from  the  earth  appear  in  sufficient  quantity  to  make 
the  atoms  at  C  neutral.  When  the  wire  connecting  the  rod  to  the  earth 
is  removed  and  the  charged  ball  is  also  removed  the  rod  has  on  it  a  free 


8  FUNDAMENTAL  IDEAS  AND  LAWS  [CHAP.  I 

negative  charge,  the  quantity  of  charge  being  equal  to  the  number  of 
electrons  which  came  from  the  earth  into  the  rod. 

An  Essential  Difference  between  Positive  and  Negative  Charge. — As 
before  stated,  the  electrons  from  all  substances  are  the  same;  the  elec- 
trons have  none  of  these  qualities  by  which  we  distinguish  and  classify 
matter.  It  is  possible  to  have  electrons  in  space  entirely  devoid  of  matter; 
a  negative  charge  can  exist  in  a  perfect  vacuum. 

The  question  may  be  raised — How  can  it  be  a  perfect  vacuum  if  there 
are  electrons  present?  By  a  vacuum  we  mean  a  space  in  which  there  is 
no  material  substance,  solids  which  can  be  bodily  removed,  liquids  which 
can  be  poured  out,  or  gases  which  can  be  pumped  out.  A  glass  vessel 
which  has  been  evacuated  as  perfectly  as  modern  pumping  methods  can 
accomplish  may  nevertheless  be  filled  with  millions  of  electrons. 

From  our  conception  of  the  positive  charge,  however,  it  is  evident  that  a 
positive  charge  must  always  be  associated  with  matter,  in  fact  the  smallest 
positive  charge  is  an  atom  of  hydrogen  from  which  an  electron  has  been 
removed.  If  in  a  glass  bulb  supposedly  evacuated  it  can  be  shown  that 
under  some  circumstances  positive  charges  exist  the  vacuum  is  only 
partial;  to  the  same  extent  that  positive  charges  occur  in  the  supposedly 
vacuous  space,  must  matter  of  some  kind  (generally  gas)  be  present. 

The  Electric  Current. — The  electric  current  is  more  familiar  to  every- 
one than  the  electric  charge.  The  current  manifests  itself  in  various 
ways,  by  generating  heat  and  light,  by  producing  mechanical  forces  such 
as  those  required  to  ring  a  doorbell  or  pull  a  subway  train,  by  producing 
chemical  changes  such  as  occur  in  the  production  of  aluminum,  or  electro- 
plating, by  producing  death  if  it  flows  through  a  living  organism  with 
sufficient  intensity,  etc. 

Older  conceptions  of  the  electric  current  made  it  a  peculiar  fluid  of 
some  kind,  others  made  it  consist  of  two  fluids  with  different  properties. 
From  the  electron  standpoint  the  conception  of  the  electric  current  is 
easy  to  comprehend  and  enables  one  to  give  a  fairly  logical  explanation 
of  the  various  actions  of  the  current. 

Nature  of  the  Electric  Current.  An  Electron  in  Motion  Constitutes 
an  Electric  Current. — The  amount  of  electricity  on  one  electron  is  so  small 
that  the  current  produced  by  one  electron  in  motion  would  not  be  detect- 
able by  the  finest  current-measuring  instrument,  even  the  most  sensitive. 
To  produce  currents  of  the  magnitude  occurring  in  every-day  experi- 
ence requires  the  motion  of  electrons  measured  in  billions  of  billions  per 
second. 

An  ordinary  incandescent  lamp  requires  a  current  of  about  one  ampere; 
such  a  current  requires  that  about  1019  electrons  flow  past  any  point  in 
the  circuit  each  second.  This  large  number  per  second  might  be  brought 
about  by  a  comparatively  few  electrons  moving  rapidly  or  by  a  great 


NATURE  OF  ELECTRIC  CURRENT  9 

many  moving  more  slowly.  Contrary  to  what  one  would  naturally  think 
the  progressive  movement  of  the  electrons  is  very  slow.  To  produce  a  current 
of  one  ampere  in  a  copper  wire  one  millimeter  in  diameter  requires  that  the 
average  velocity  of  the  electrons  be  only  .01  cm.  per  second,  if  we  accept 
the  assumption  that  there  are  as  many  free  electrons  as  there  are  atoms. 

Although  the  progressive  motion  of  the  electrons  is  very  slow,  as 
indicated  above,  it  must  not  be  thought  that  the  actual  velocity  of  the 
electrons  is  small.  If  we  assume  the  "  equi-partition  of  energy  "  idea 
of  thermo-dynamics  and  thus  calculate  the  average  velocity  of  the  electrons 
in  a  copper  wire,  at  ordinary  temperature,  we  obtain  a  result  of  about 
6X106  cm.  per  second.  That  is,  even  when  no  current  is  flowing  in  the 
wire  the  electrons  have  a  haphazard  motion,  due  to  the  thermal  agita- 
tion of  the  atoms  (or  molecules),  which  give  them,  on  the  average,  a  velocity 
of  about  35  miles  per  second. 

Now  when  current  flows  the  required  progressive  velocity  of  the 
electrons  is  only  a  fraction  of  a  centimeter  per  second;  with  a  current 
so  large  that  the  copper  wire  is  heated  to  the  melting-point  the  velocity 
of  drift  of  the  electrons  is  less  than  1  cm.  per  second.  Thus  an  accurate 
concept  of  the  electric  current  in  a  conductor  shows  it  to  be  an  inappreciable 
"  drift  "  of  the  electrons  which  have,  due  to  temperature  effects,  hetero- 
geneous velocities  millions  of  times  as  great  as  the  velocity  of  drift. 

The  reason  for  the  slow  progressive  motion  of  the  electrons  is  to  be  seen 
in  the  tremendous  number  of  collisions  they  have  with  the  molecules  of 
the  substance.  A  given  electron,  acted  upon  by  the  potential  gradient 
in  the  wire  carrying  current,  accelerates  very  rapidly  and  would  acquire 
tremendous  velocities  if  it  did  not  continually  collide  with  the  more  massive 
molecules;  the  mean  free  path  of  the  free  electrons  in  a  copper  wire  is 
so  small  that,  between  successive  collisions,  the  electron  falls  through  a 
very  small  potential  difference  and  hence  gains  a  velocity  (along  the  con- 
ductor) due  to  the  current,  which  is  extremely  small. 

Suppose  that  we  wanted  to  measure  the  rate  of  flow  of  people  past  a 
given  point  in  a  large  city;  the  unit  of  flow  might  be  100,000  persons  per 
hour.  At  any  time  there  will  be  people  going  in  all  directions,  some 
uptown,  some  downtown,  and  some  crosstown.  In  the  morning  a  million 
people  pass  a  certain  point  where  the  flow  is  to  be  ascertained.  If  200,000 
move  in  the  uptown  direction  and  800,000  move  downtown,  the  net  flow 
is  600,000  people.  If  this  number  of  people  pass  in  one  hour  the  flow  is 
6  units  downtown.  At  noon  time  again  a  million  people  pass  the  same 
place  let  us  suppose;  400,000  move  uptown  400,000  move  downtown  and 
150,000  move  crosstown  west  and  50,000  move  crosstown  east.  The  net 
flow  is  now  100,000  people  west  and  if  this  number  pass  in  one  hour  the 
flow  is  one  unit  west.  Some  of  the  people  would  be  moving  rapidly  and 
others  going  more  slowly  and  some  might,  at  times,  be  standing  still. 


10  FUNDAMENTAL  IDEAS   AND  LAWS  [CHAP.  I 

The  picture  suggested  by  the  above  traffic  analysis  probably  gives 
one  a  reasonable  idea  of  the  motion  of  electrons  in  a  conductor  carrying 
current;  it  is  of  course  too  simple,  because  of  the  immense  number  of 
electrons  in  a  conductor  and  the  tremendous  number  of  collisions  occur- 
ring between  the  electrons.  When  a  conductor  is  carrying  no  current 
the  motion  of  the  electrons  resembles  that  of  the  individuals  in  a  stationary 
crowd;  there  is  a  deal  of  agitation  among  the  electrons,  but  they,  on 
the  whole,  show  no  progress  along  the  conductor. 

Electromotive  '  Force. — Suppose  a  copper  rod,  having  in  itself  the 
heterogeneously  moving  electrons  suggested  above,  is  connected  at  its 
two  ends  to  a  battery  as  shown  in  Fig.  10.  The  end  A  of  the  rod  becomes 
positive  with  respect  to  end  B  and  the  electrons,  instead  of  moving  back- 
wards and  forwards  to  the  same  extent,  progress  slowly  towards  A.  When 
they  arrive  at  A  they  leave  the  copper  rod,  move  down  the  connecting 

Conducting  Rod 


©  ©  ©  © 

©  ©  © 


Direction  of  Electron  Drift 


Battery 
FIG.  10. — Electric  current  caused  by  flow  of  free  electrons. 

wire,  through  the  battery,  through  the  other  connecting  wire,  and  so 
back  to  the  rod.  As  long  as  the  circuit  remains  closed  as  shown  the  elec- 
trons will  continue  to  move  around  the  circuit,  bounding  backward, 
forward,  and  across  the  conductor,  but  on  the  whole  progressing  grad- 
ually around  the  circuit;  this  progression  of  the  electrons  constitutes  the 
electric  current.  The  cause  of  the  flow  is  the  battery;  it  holds  one  end 
of  the  rod  positive  with  respect  to  the  other  and  so  maintains  the  flow 
of  electrons.  The  maintenance  of  this  difference  of  electric  pressure  (or 
difference  of  potential)  across  the  rod  is  due  to  chemical  changes  going 
on  inside  the  battery. 

A  piece  of  apparatus  which  has  the  ability  to  maintain  one  of  its  ter- 
minals at  a  higher  potential  than  the  other,  even  though  current  is  allowed 
to  flow  through  it,  is  said  to  develop  an  electromotive  force.  As  sources 
of  electromotive  force  for  the  production  of  currents  on  a  commercial 
scale  we  have  only  the  ordinary  battery  and  the  electric  generator.  The 
battery  depends  upon  chemical  action  for  maintaining  its  difference  of 
potential  and  the  generator  depends  upon  the  conductors  of  its  armature 
being  driven  through  the  magnetic  field  produced  by  its  field  poles. 


ELECTROMOTIVE   FORCE  AND   POTENTIAL  DIFFERENCE         11 

Electromotive  Force  and  Difference  of  Potential. — It  is  well  to  dis- 
tinguish between  electromotive  force  and  difference  of  potential.  Thus 
two  brass  balls,  one  charged  positively  and  the  other  negatively,  have  a 
difference  of  potential  between  them  and  they  will,  if  connected  by  a  wire, 
cause  a  momentary  flow  of  current  through  the  connecting  wire;  when 
sufficient  electrons  have  passed  from  the  negatively  charged  ball  to  neu- 
tralize the  positive  charge  on  the  other  the  current  will  cease.  There 
is  no  action  taking  place  which  tends  to  maintain  the  difference  of  potential 
between  the  two  balls;  such  a  combination  does  not  generate  an  electro^ 
motive  force  (hereafter  abbreviated  e.m.f.). 

In  the  case  of  the  battery  or  generator,  however,  when  the  two  ter- 
minals are  connected  by  a  wire  a  current  flows  and  continues  to  flow  until 
the  battery  is  worn  out  or  the  generator  is  stopped;  such  devices  develop 
or  generate  an  e.m.f.  These  ideas  are  depicted  in  Fig.  11. 


Current  Mai 


FIG.  11. — Illustrating  difference  between  electromotive  force  and  potential  difference. 

Direction  of  Flow  of  Current. — It  has  been  accepted  as  convention 
that  in  a  wire  connecting  the  poles  of  a  battery  the  current  flow  is  from 
the  positive  pole  of  the  battery  to  the  negative.  But  by  reference  to  Fig. 
10  it  is  evident  that  in  the  connecting  wire  the  electrons  flow  from  the 
negative  pole  of  the  battery  to  the  positive.  Hence  it  must  be  remembered 
that  although  we  shall  talk  of  the  current  flowing  from  the  positive  terminal 
to  the  negative  terminal  of  a  battery  or  generator  the  electrons  (which 
really  are  the  current)  are  flowing  in  the  opposite  direction.  In  dealing 
with  currents  through  vacua  the  motion  of  the  electrons  themselves  is 
generally  had  in  mind  and  we  often  say  that  the  electron  current  flows 
from  the  negative  to  the  positive  terminal  of  the  vacuum  tube.  Although 
this  sounds  anomalous  it  is  a  correct  statement  of  the  facts. 

Conductors  and  Insulators. — Roughly  speaking  a  conductor  is  a  body 
which  readily  permits  the  passage  of  an  electric  current  and  an  insulator 
is  a  body  which  offers  a  very  high  resistance  to  the  passage  of  the  current. 
There  is  no  sharp  distinction  between  conductors  and  insulators,  how- 
ever; a  material  which  for  some  cases  would  be  regarded  as  an  insulator 
would,  in  other  circumstances,  be  regarded  as  a  conductor.  Also  a  sub- 
stance which  is  a  good  insulator  at  low  temperatures  may  be  a  fair  con- 
ductor at  high  temperatures. 

Glass  is  the  most  striking  illustration  of  this  change  of  character  with 


12  FUNDAMENTAL  IDEAS  AND  LAWS  [CHAP.  I 

change  of  temperature;  at  ordinary  temperature  it  ranks  high  with  the 
very  best  insulators,  but  if  it  is  heated  in  some  way  to  a  red  heat  it  becomes 
a  fair  conductor  and  will  permit  the  passage  of  enough  current  to  melt 
itself. 

Difference  between  Conductors  and  Insulators  from  the  Electron 
Viewpoint. — When  a  conductor  is  carrying  an  electric  current  the  elec- 
trons throughout  the  substance  of  the  conductor  are  moving  gradually 
along  through  the  substance  of  the  conductor.  Now  in  a  solid  body, 
such  as  a  metallic  conductor,  the  atoms  or  molecules  comprising  the  sub- 
stance are  practically  fixed  in  position.  They  are  not  actually  stationary 
in  space  at  ordinary  temperature  of  course;  as  a  matter  of  fact  the  atoms 
have  an  irregular  to-and-fro  motion  similar  to  that  of  the  electron.  But 
there  cannot  be  a  progressive  motion  of  the  atoms  as  there  may  be  of  the  elec- 
trons. The  reason  for  this  is  more  or  less  evident.  Suppose  a  copper  wire 
is  fastened  to  the  terminals  of  a  battery  and  that  current  is  flowing  as 
indicated  in  Fig.  10.  The  electrons  move  all  the  way  around  the  circuit 
through  the  wire,  connections,  solution  in  the  battery,  etc. 

As  the  atoms  of  copper  are  charged  positively  after  an  electron  has 
left  them  it  might  seem  that  as  the  electrons  move  from  B  to  A  through 
the  wire  the  atoms  would  move  from  A  to  B,  then  into  and  through  the 
battery  and  so  back  to  the  wire.  But  the  atoms  are  the  real  substance 
of  the  wire,  and  hence  if  the  atoms  should  progress  one  way  or  the  other 
it  would  result  in  the  copper  itself  being  carried  from  one  end  of  the  wire 
to  the  other  and  then  through  the  battery.  This  state  of  affairs  is  not 
possible  in  solid  bodies  like  metals,  it  would  result  in  the  mixing  of  metals 
wherever  a  current  left  one  metal  and  went  into  another. 

In  chemical  solutions,  e.g.,  copper  sulphate  in  water,  the  salt  mole- 
cule breaks,  up  into  two  parts,  one  of  which  has  one  electron  more  than 
its  proper  number,  the  other  part  lacking  one  electron.  The  two  parts 
of  the  molecule  are  called  ions;  the  metallic  ion  (in  above  case,  copper) 
lacks  one  electron  and  so  is  charged  positively.  If  now  a  current  is  passed 
through  such  a  solution  the  metallic  ion  does  move  through  the  solution 
and  is  carried  from  the  solution  to  one  of  the  wires  by  which  the  current 
is  lead  into  the  solution.  Here  the  copper  itself  is  transported  by  the 
current  and  we  have  the  process  of  electro-plating. 

From  what  has  been  said  it  follows  that  if  the  molecules  of  a  body 
cling  to  the  electrons  so  tightly  that  none  of  them  are  free  to  move  away 
from  the  molecule  there  can  be  no  current  in  such  a  substance.  As  long 
as  the  molecule  keeps  all  its  electrons  it  remains  electrically  neutral,  and 
so  has  no  tendency  to  move  when  in  an  electric  field.  This  is  the  essential 
difference  between  insulators  and  conductors;  in  the  one  the  electrons 
cannot  move  from  the  atom  or  molecule  and  in  the  other  the  electrons 
are  perfectly  free  to  leave  the  atom. 


INSULATORS  AND   CONDUCTORS  13 

Disruptive  Strength  of  an  Insulator. — With  the  above  idea  in  mind 
the  possibility  of  break-down  of  an  insulator,  due  to  high  voltage,  becomes 
apparent.  For  low  voltage  the  force  tending  to  move  the  electron  is 
not  sufficient  to  break  it  loose  from  its  atom.  But  it  is  reasonable  to 
believe  that,  if  the  voltage  gradient  is  made  sufficiently  high,  any  .atom 
can  be  forced  to  let  go  of  one  electron,  and  such  is  the  case.  Such  fine 
insulators  as  glass  and  mica  break  down  and  carry  current  when  a  great 
enough  voltage  is  employed. 

Effect  of  Temperature  on  the  Disruptive  Strength  of  an  Insulator. — 
Imagine  a  good  insulator  heated  by  some  outside  source  of  power.  The 
rise  in  temperature  increases  the  to-and-fro  motion  of  its  molecules  with 
the  result  that  the  collisions  between  the  various  molecules  become  more 
frequent  and  violent  as  the  temperature  is  raised.  As  these  collisions 
occur  the  resulting  disturbances  in  the  molecular  structure  tend  to  weaken 
the  hold  of  the  molecule  on  its  electrons.  Hence  if  an  electric  force  is 
impressed  and  maintained  as  an  insulator  is  heated  the  combination  of 
electric  force  and  weaking  of  the  molecular  holding  power  will  result  in 
some  electrons  leaving  their  molecules;  the  electric  force  then  urges  them 
along  through  the  substance  of  the  insulator  with  the  result  that  a  small 
current  occurs.  This  would  be  interpreted  by  the  man  testing  the  insu- 
lator as  a  weakening  of  the  insulating  power  of  the  substance. 

Generally  the  partial  breakdown  of  an  insulator  as  described  above 
is  rapidly  followed  by  the  giving  away  of  the  insulator  completely;  as 
current,  even  though  small,  flows  through  the  insulator  it  generates  more 
heat  thus  still  further  decreasing  the  disruptive  strength. 

This  effect  of  temperature  upon  the  disruptive  strength  of  an  insulator 
is  very  important  to  the  radio  engineer.  A  glass  or  mica  condenser,  prop- 
erly designed  to  operate  in  a  radio  circuit  at  15,000  volts  may,  by  improper 
use,  be  broken  down  when  operating  at  only  5000  volts.  Condensers 
heat  up,  when  being  used,  due  to  various  causes;  in  normal  operation 
the  condenser  is  excited  only  a  small  fraction  of  the  time  as  the  sending 
key  is  opened  and  closed.  In  the  intervals  when  the  key  is  open  the 
cause  of  the  heating  is  removed  and  the  condenser  has  a  chance  to  cool 
off;  this  alternate  heating  and  cooling  results  in  a  certain  mean  temper- 
ature at  which  temperature  the  condenser  has  sufficient  disruptive  strength 
to  withstand  the  voltage  employed. 

If  now  the  normal  operating  voltage  is  put  on  the  condenser  and 
maintained  continuously,  the  heating  action  is  much  greater  than  when 
the  voltage  is  applied  intermittently  (normal  operation)  and  in  a  short 
time  the  dielectric  is  likely  to  puncture.  Condensers  which  are  designed 
for  operation  at  a  certain  voltage  with  spark  telegraphy  (intermittent 
excitation)  will  nearly  always  fail  if  operated  at  the  same  voltage  for 
undamped  wave  signaling  (continuous  excitation). 


14 


FUNDAiMENTAL   IDEAS  AND   LAWS 


[CHAP.  I 


Resistance. — In  a  conductor  where  the  electrons  are  free  to  leave  the 
atom  their  progressive  motion  is  hindered  by  collisions  with  the  atoms 
of  the  substance.  This  hindrance  to  their  free  progress  constitutes  the 
electrical  resistance  of  the  conductor.  It  differs,  as  might  well  be  expected, 
in  different  metals,  and  it  varies  with  the  temperature.  As  the  temper- 
ature of  a  metal  increases  the  agitation  of  its  atoms  or  molecules  increases 
and  this  results  in  more  hindrance  to  the  progressive  motion  of  the 
electrons  because  of  the  more  frequent  collisions  between  the  electrons 
and  the  atoms. 

The  increase  in  number  of  collisions  between  the  electrons  and  atoms 
with  increase  in  the  flow  of  electrons  (more  current)  gives  the  atoms 
themselves  an  increased  agitation,  which  really  means  a  higher  temper- 
ature; this  accounts  for  the  well-known  fact  that  when  a  conductor 
carries  current  it  always  heats  to  some  extent  and  heats  more  with  large 
than  with  small  currents. 

Continuous  Current  and  Alternating  Current. — If  the  electrons  in  a 
conductor  continually  progress  in  the  same  direction  the  flow  is  called 
a  continuous  current,  or  direct  current.  Such  is  the  current  supplied  by 
an  ordinary  battery. 

If  the  battery  is  connected  to  the  conductor  first  in  one  direction 
and  then  in  the  reversed  direction,  by  some  sort  of  a  commutator,  Fig. 
12,  the  progressive  motion  of  the  electrons  will  reverse  with  every  reversal 
of  the  battery  connection.  If  this  reversal  of  flow 
takes  place  at  regular,  short,  periods  of  time  the 
alternate  ebb  and  flow  of  the  electrons  constitute 
an  alternating  current.  In  ordinary  power  circuits 
supplied  with  alternating  current  this  reversal  takes 
place  about  60  times  per  second;  the  alternating 


Battery 


Alternating  Current 

FIG.  12. — A  battery  in 
combination  with  a 
rotating  commuta- 
tor may  produce  an 
alternating  current. 


FIG.  13. — The  lamp  will  burn  even  though  there  is  a  perfect 
insulator  in  series  with  the  circuit. 


currents  used  in  radio  circuits  reverse  much  more  rapidly,  perhaps  a 
million  times  per  second. 

Possibility  of  Alternating  Current  Flowing  in  a  Circuit  in  Series  with 
which  there  is  a  Perfect  Insulator. — Suppose  a  circuit  connected  as  indi- 
cated in  Fig.  13;  B  is  a  source  of  alternating  e.m.f.  and  A  consists  of  two 


CONTINUOUS  AND  ALTERNATING  CURRENTS 


15 


metal  plates  separated  by  paraffined  paper  or  mica.  The  disruptive 
strength  of  the  insulator  is  such  that  for  any  voltage  that  B  can  give  the 
insulation  is  perfect.  A  small  incandescent  lamp  is  inserted  in  the  cir- 
cuit to  detect  the  current  which  may  be  flowing.  The  lamp  will  bum 
as  soon  as  machine  B  is  excited.  Now  if  the  lamp  and  condenser  (the 
combination  of  two  conducting  plates  and  separating  insulator)  is  con- 
nected to  a  battery  which  gives  about  the  same  voltage  as  machine  B 
gives,  the  lamp  will  not  burn,  showing  that  there  is  no  current  in  the 
circuit.  Hence  this  circuit  which  is  open  for  continuous  current  (i.e., 
it  will  not  pass  current)  does  permit  the  flow  of  alternating  current. 

The  alternating  current  is  possible  because  of  the  number  of  electrons 
required  to  charge  the  condenser.  As  the  voltage  of  the  alternator  reverses 
in  direction  the  condenser  charges  first  in  one  direction  and  then  in  the 
other;  this  alternating  charge  and  discharge  requires  the  alternating  flow 
of  electrons  throughout  the  whole  circuit. 

A  simple  analogy  is  shown  in  Fig.  14.  Suppose  a  cylindrical  chamber 
A,  divided  in  the  middle  by  a  thin  rubber  diaphragm  B}  connected  to  a 


FIG.  14, — Hydraulic  analogue  of  an  alternating  current  circuit  containing  a  condenser. 

reciprocating  action,  valveless,  pump  C.  As  the  pump  works  back  and 
forth,  water  will  circulate  back  and  forth  in  the  connecting  pipes,  con- 
tituting  an  alternating  current  flow  of  water.  The  diaphragm  B  will 
bend  first  in  one  direction  and  then  in  the  other  as  the  water  reverses 
its  flow. 

Now  suppose  that  a  centrifugal  action  pump  be  substituted  for  the 
reciprocating  pump  (Fig.  15).  This  type  of  pump  tends  to  force  water 
always  in  the  same  direction.  If  the  pump  is  so  connected  as  to  force 
water  into  the  bottom  of  A  and  suck  it  out  of  the  top  of  A,  the  flow  of 
water  will  last  long  enough  to  stretch  the  diaphragm  into  some  such 
position  as  B',  and  then  the  flow  will  cease.  At  this  position  of  the  dia- 
phragm the  backward  pressure  of  the  stretched  rubber  will  be  just  great 
enough  to  balance  the  pressure  generated  by  the  pump.  In  this  water 
system  the  water  would  flow  while  the  diaphragm  was  being  displaced 


16 


FUNDAMENTAL  IDEAS  AND  LAWS 


[CHAP.  I' 


from  its  normal  central  position  to  position  B',  and  then  the  flow  would 
cease  because  the  pump  would  not  be  able  to  further  displace  the  dia- 
phragm. 

The  water  system  corresponds  very  closely  to  the  electrical  circuit 
having  a  condenser  in  series  with  it  and  excited  by  a  continuous  e.m.f.; 
in  ",uch  a  circuit  the  current  flows  long  enough  to  charge  the  condenser 
to  such  an  extent  that  its  back  pressure  (pressure  tending  to  discharge 
the  condenser)  is  just  equal  to  the  impressed  e.m.f.  and  then  the  current 
ceases.  It  is  to  be  remembered,  however,  that  if  the  pressure  is  alternat- 
ing there  will  be  a  flow  in  the  system  all  the  time,  the  current  being  an 
alternating  one. 

In  electric  circuits,  therefore,  it  is  possible  to  send  an  alternating 
current  through  a  circuit  in  which  continuous  current  cannot  flow.  Such 


FIG.  15. — Hydraulic  analogue  of  a  direct  current  circuit  containing  a  condenser. 

use  of  a  condenser  occurs  frequently  in  radio;  the  condenser  so  used  is 
called  a  stopping  or  "  blocking  "  condenser. 

The  Electric  Generator. — Except  for  very  small  sets  and  emergency 
outfits  the  power  for  a  radio  set  is  obtained  from  a  generator  of  either 
the  continuous  or  alternating-current  type.  The  continuous-current  gen- 
erator is  equipped  with  a  commutator  and  supplies  a  continuous  e.m.f.; 
that  is,  the  e.m.f.  impressed  on  the  connected  circuit  is  always  in  the 
same  direction  and  practically  constant  in  value.  There  are  slight  pul- 
sations in  the  value  of  the  voltage,  perhaps  a  fraction  of  1  per  cent,  at 
the  frequency  of  commutation;  this  frequency  is  in  the  neighborhood 
of  1000  cycles  per  second.  Although  these  pulsations  are  so  small,  they 
have  a  deal  of  importance  in  certain  radio  sets  using  vacuum  tubes  for 
the  generation  of  high-frequency  currents. 

The  alternating-current  generator  (or  simply  alternator)  has  no  com- 
mutator, but  generally  has  slip  rings  on  which  its  brushes  make  contact. 
The  e.m.f.  furnished  by  such  a  machine  alternates  in  direction  many  times 
per  second;  for  radio  use  the  generators  ordinarily  employed  give  several 
hundred  complete  reversals  of  voltage  per  second. 


WAVE  FORMS  AND  EFFECTIVE  VALUES 


17 


The  number  of  complete  reversals  per  second  is  called  the  frequency  of 
the  generator;  thus  a  500-cycle  generator  is  one  giving  500  complete 
reversals  of  e.m.f.  per  second. 

Wave  Shape  and  Effective  Values. — The  form  of  voltage  wave  gen- 
erated by  a  well-designed  alternator  is  such  that  it  can  be  closely  repre- 
sented by  a  sine  curve  as  shown  in  Fig.  16.  Expressed  in  the  form  of 
an  equation, 

e  =  Em  sin  o>  t (1) 

where 

e  =  the  value  of  voltage  at  any  instant  of  time ; 
Em  =  ihe  maximum  value  of  the  voltage  generated; 
co  =  2irf,  /  being  the  frequency  of  the  voltage. 

The  same  units  are  used  for  measuring  alternating  voltage  and  cur- 
rent as  are  used  for  continuous  voltage  and  current.  But  as  the  voltage 


Form  of  alternating  cmf. 
FIG.  16. — Sine  wave  of  e.m.f. 

and  current  of  an  alternating  current  circuit  are  continually  changing 
in  value  and  reversing  in  direction,  some  value  intermediate  to  the  maxi- 
mum and  minimum  value  must  be  chosen  as  the  unit.  It  is  shown  in 
all  elementary  texts  on  alternating  currents  that  when  the  current  flows 
according  to  the  law  of  a  sine  curve  the  alternating  current  will  produce 
heat  at  the  same  rate  as  one  ampere  continuous  current  if  the  maximum 
value  of  the  alternating  current  is  1.41  amperes. 

To  get  the  value  of  that  continuous  current  which  will  give  the  same 
heating  effect  as  a  certain  alternating  current,  therefore,  we  take  .707 
of  the  maximum  value  of  the  alternating  current.  That  value  of  con- 
tinuous current  which  will  produce  the  same  heating  effect  as  the  alter- 
nating current  in  question  is  called  the  effective  value  of  the  alternating 
current.  It  is  approximately  .7  of  the  maximum  value. 

In  the  same  way  the  effective  value  of  an  alternating  e.m.f.  (sine 
wave  shape  assumed)  is  .707  of  its  maximum  value.  Thus,  if  a  sine  wave 


18  FUNDAMENTAL  IDEAS  AND  LAWS  CHAP.  I 

of  voltage  has  a  maximum  value  of  141  volts  its  effective  value  (or  equiva- 
lent continuous  voltage  as  far  as  producing  heating  is  concerned)  is  100 
volts. 

Magnetic  Field. — The  action  of  the  magnet  is  familiar  to  everyone. 
If  a  piece  of  iron  is  placed  in  the  vicinity  of  the  magnet  a  force  of  attrac- 
tion is  set  up  between  the  two  and  the  piece  of  iron  will,  if  free  to  move, 
be  drawn  to  the  magnet. 

All  the  region  surrounding  a  magnet,  in  which  the  magnet  is  able  to 
exert  a  force  on  pieces  of  magnetic  material,  is  said  to  be  rilled  with  the 
field  of  the  magnet.  Thus  the  magnetic  field  is  exactly  analogous  to  the 
electric  field  surrounding  an  electrically  charged  body. 

The  magnetic  field  is  represented  by  lines  in  just  the  same  way  as 
the  electric  field;  the  direction  of  the  lines  indicates  the  way  in  which 
the  north  pole  of  a  compass  would  be  urged  if  placed  at  that  point  of 
the  field,  and  the  proximity  of  the  lines  to  each  other  serves  to  show  the 
relative  intensity  of  the  magnetic  force  at  various  points  of  the  field. 

Magnetic  Field  Set  Up  by  an  Electric  Current.— The  field  of  the  per- 
manent steel  magnet  is  interesting  historically,  but  it  plays  very  little 
part  in  the  electrical  engineering  of  to-day.  When  an  electric  current 
flows  through  a  conductor  a  magnetic  field  is  set  up  around  that  con- 
ductor; such  a  field  is  frequently  called  an  electro-magnetic  field.  The 
magnetic  fields  used  in  modern  apparatus  are  practically  all  of  this  type. 

The  strength  of  a  magnetic  field  set  up  by  an  electric  current  depends 
upon  the  strength  of  the  current,  in  general  being  directly  proportional 
to  the  current  strength.  The  direct  proportionality  holds  good  for  mag- 
netic fields  without  iron;  use  of  iron  in  the  magnetic  circuit  makes  the 
relation  between  current  and  strength  of  field  a  complex  one. 

Ampere-Turns. — When  the  magnetic  field  is  produced  by  a  coil  of 
several  turns  its  intensity  is  much  greater  than  if  only  one  turn  were 
used.  The  magnetizing  effect  of  a  current  depends  not  only  on  the  strength 
of  current,  but  also  on  the  number  of  turns  through  which  the  current 
flows.  In  fact  the  magnetizing  effect  of  a  coil  is  proportional  to  the  prod- 
uct of  the  current  strength  and  the  number  of  turns  in  the  coil;  this 
product  is  called  the  ampere-turns  of  the  coil.  If  a  coil  consists  of  one 
turn  and  is  carrying  a  current  of  one  ampere  it  has  one  ampere-turn;  a 
coil  of  twenty  turns  carrying  2.7  amperes  has  fifty-four  ampere-turns. 

Direction  of  the  Magnetic  Field  Produced  by  a  Current. — The  direc- 
tion of  magnetic  field  around  a  conductor  carrying  a  current  may  be 
easily  determined  by  the  application  of  the  following  rule.  Imagine  the 
conductor  grasped  in  the  right  hand,  fingers  around  the  conductor,  with 
the  extended  thumb  pointing  along  the  conductor  in  the  direction  in  which 
the  current  is  flowing;  the  fingers  then  point  in  the  direction  of  the  mag- 
netic field.  This  is  illustrated  in  Fig.  17;  it  is  to  be  remembered  that 


MAGNETIC   FIELD   PRODUCED   BY  ELECTRIC   CURRENT         19 

this  rule  assumes  the  commonly  accepted  direction  of  flow  of  current;  in 
Fig.  17  the  electrons  are  flowing  in  the  opposite  direction  to  that  marked 
current. 

As  follows  at  once  from  the  rule  given  above  the  direction  of  mag- 
netic field  reverses  when  the  current  reverses.  If  an  alternating  current 
is  passed  through  a  wire  or  coil  the  magnetic  field  produced  will  also  be 
an  alternating  one,  having  the  same  frequency  as  the  current,  and  revers- 
ing simultaneously  with  the  current! 


FIG.  17. — Direction  of  the  magnetic  field  produced  by  a  current. 

Iron  in  the  Magnetic  Field. — In  most  electrical  apparatus  depending 
on  the  magnetic  field  for  its  operation  the  field  is  produced  by  currents 
flowing  in  coils.  But  the  coils  are  usually  fitted  with  iron  cores  so  that 
the  magnetic  circuit  consists  partly  of  iron  and  partly  of  air.  The  reason 
for  the  use  of  iron  in  magnetic  fields  of  electrical  devices  lies  in  its  high 
permeability,  i.e.,  the  relatively  high  flux  density  produced  by  a  given 
coil  in  iron  compared  to  what  it  would  produce  if  only  air  were  used  in 
the  magnetic  circuit. 

The  magnetic  permeability  of  a  substance  is  the  ratio  of  the  flux  den- 
sity produced  in  this  substance  by  a  certain  magnetomotive  force  (mag- 
netizing force)  compared  to  the  flux  density  the  same  magnetomotive 
force  would  produce  in  air. 

For  most  substances  the  permeability  has  a  value  of  unity;  nickel, 
cobalt,  and  iron  are  the  notable  exceptions.  Of  these  three  iron  is  by 
all  means  the  most  important,  not  alone  because  of  its  comparative  cheap- 
ness (and  hence  utility  for  electrical  apparatus),  but  because  of  the  high 
value  of  the  permeability.  For  good  magnetic  iron  it  may  be  as  high  as 
several  thousand;  that  is,  if  a  given  coil  produces  500  lines  of  flux  with 
a  magnetic  path  of  air  it  will  produce  perhaps  a  million  lines  of  flux  if 
iron  is  used  for  the  whole  magnetic  circuit. 

1  This  statement  is  strictly  accurate  only  for  the  magnetic  field  in  the  immediate 
neighborhood  of  the  conductor;  for  more  distant  points  the  magnetic  field  reverses 
somewhat  later  than  the  current.  This  idea  is  taken  up  more  in  detail  on  p.  700. 


20  FUNDAMENTAL  IDEAS  AND  LAWS  [CHAP.  I 

When  the  magnetic  circuit  of  a  device  is  made  up  partly  of  air  and 
partly  of  iron,  the  flux  produced  by  a  given  coil  is  intermediate  to  thab 
which  would  be  produced  in  a  complete  iron  path,  and  that  which  would 
be  produced  in  a  complete  air  path.  The  shorter  the  part  of  the  path 
through  air  compared  to  that  through  iron  the  higher  will  be  the  flux 
induced.  The  permeability  of  iron  varies  greatly  with  the  treatment  it 
received  during  manufacture;  also  for  a  given  specimen  it  varies  greatly 
with  the  magnetizing  force  used.  This  point  will  be  taken  up  in  more 
detail  in  the  next  chapter,  under  the  head  of  self  induction  and  its  vari- 
ations. 

Units  of  Current,  E.M.F.,  Resistance,  etc. — The  unit  of  current  is  the 
ampere;  it  is  that  flow  of  electrons  which  will  deposit  1.118  milli- 
grams of  silver  per  second  from  a  silver  nitrate  solution  in  a  standard 
voltameter. 

The  unit  of  e.m.f.  is  the  volt;  it  is  generally  defined  in  terms  of  the 
voltage  of  a  standard  Weston  cell,  which  gives  an  e.m.f.  of  1.0183  volts. 
The  volt  is  therefore  defined  as  1.0000/1.0183  of  the  voltage  generated 
by  a  standard  Weston  cell. 

The  unit  of  resistance  is  the  ohm;  it  is  really  defined  already  1  when 
the  ampere  and  the  volt  have  been  defined  because  the  three  units  are 
directly  connected  by  Ohm's  law.  However,  it  is  also  defined  as  the 
resistance  of  a  column  of  pure  mercury  weighing  14.4521  grains  at  0° 
Centigrade  and  having  a  height  of  106.3  cm.,  the  cross-section  being 
uniform. 

The  unit  of  quantity  is  the  coulomb;  it  is  the  quantity  of  electricity 
transported  by  a  current  of  one  ampere  flowing  for  one  second.  Another 
way  of  defining  it  is  in  terms  of  electrons;  it  is  the  amount  of  electricity 
contained  on  6.28X1018  electrons. 

The  unit  of  work  is  the  joule;  it  is  the  amount  of  energy  required  to 
transport  one  coulomb  of  electricity  through  an  opposing  potential  dif- 
ference of  one  volt.  It  is  also  the  amount  of  work  done  in  one  second 
by  a  current  of  one  ampere  flowing  against  a  pressure  of  one  volt. 

The  unit  of  power  is  the  watt;  it  is  the  rate  at  which  work  is  done 
by  a  current  of  one  ampere  flowing  against  a  pressure  of  one  volt.  It 
is  therefore  a  rate  of  work  equal  to  one  joule  per  second. 

Resistance  of  a  Conductor. — The  resistance  of  a  circuit  depends  first 
of  all  on  the  kind  of  material  used  in  making  up  the  circuit;  it  depends 
upon  the  length  of  conductor  used  in  making  the  circuit  and  upon  the 
cross-sectional  area  of  the  conductor.  This  relation  may  be  expressed 
by  the  equation, 

R  =  Pl/a, (2) 

1  The  ohm  and  the  ampere  are  really  the  two  fundamental  units  of  th-3  practical 
system.  See  American  Handbook  for  Electrical  Engineers,  p.  1773. 


RESISTANCE  AND  ITS  VARIATIONS 


21 


where  p  =  the  specific  resistance  of  the  material  used; 
Z=the  length  of  the  conductor; 
a=the  cross-sectional  area  of  the  conductor. 

When  the  length  of  the  conductor  is  one  cm.  and  the  area  is  one  sq. 
cm.  the  value  of  R  is  the  specific  resistance  per  cm.3,  and  when  the -con- 
ductor has  a  length  of  one  foot  and  an  area  of  one  circular  mil  the  value 
of  R  is  the  specific  resistance  per  mil-foot.  In  engineering  the  latter 
specification  is  more  frequently  used. 

The  specific  resistance  of  some  of  the  more  common  conductors  is 
given  in  the  accompanying  table: 

SPECIFIC  RESISTANCE  OF  COMMON  METALS,  ALLOYS,  AND  SOLUTIONS 


Substance. 

Composition. 

Microhms  per  Cm3, 
at  0°  C. 

Temperature  Coefficient 
Referred  to  O°  C. 

Advance  
Aluminum 

Copper-nickel 
Pure 

48.8 
2  62 

.000018 

00423 

Brass  

66  Cu+34Zn 

6.29 

.00158 

Calido    

Ni-fCr+Fe 

100 

00034 

Carbon 

Lamp  filament 

4000 

-  0003 

Constantan  
Copper 

60Cu+40Ni 
Standard 

49. 
1  589 

.00000 
00427 

Copper  
German  Silver 

Electrolytic 
18Ni+Cu+Zn 

1.56 
33  1 

.00428 
00031 

la  la  soft 

Cu+Ni 

47  1 

00000 

Iron  
Iron  .  . 

Pure 
Hard  steel 

8.85 
45 

.00625 
00161 

Manganin 

Cu-f-Mn+Ni 

{40. 

{.  00001 

Nickel 

Electrolytic 

170. 
6  93 

i  .00004 
00618 

Silver  
Tungsten 

Electrolytic 
Hard 

1.47 
5  42 

.00400 
0051 

Per  Cent  Solution. 

Ohms  per  Cm.3 

H2SO4                    > 

5 

- 

4  80 

—  012 

KOH  

10 
20 
30 
50 
70 
20 

2.55 
1.53 
1.35 
1.85 

4.68 
2.01 

.013 
.014 
.016 
.019 
.026 
-  020 

HC1  

20 

1  31 

-  015 

HNO3 

20 

1  41 

-  014 

NaCl  

2 

37. 

-  023 

5 

10 
20 

14.9 
8.2 
5.1 

.022 
.021 
.022 

Practically  all  solutions  have  a  minimum  resistance  with  a  density  of  solution  between 
20  and  30  per  cent. 


22  FUNDAMENTAL  IDEAS   AND  LAWS  [CHAP.  I 

The  resistance  of  a  metal  varies  with  the  temperature,  in  general  being 
directly  proportional  to  the  absolute  temperature.  This  relation  is 
approximately  expressed  for  all  pure  metals  by  the  equation, 

Rt=R0(l+af), (3) 

where 

Rt  =  ihe  resistance  at  t  degrees  Centigrade; 
.Ro  =  the  resistance  at  0  degrees  Centigrade; 
2  =  the  temperature  at  which  the  resistance  is  desired; 
a  =  the  temperature  coefficient  of  resistance. 

The  value  of  a  is  very  nearly  .004  for  all  pure  metals,  for  copper  it 
has  been  decided  to  take  a  as  .00427,  at  0°  C. 

A  statement  which  gives  the  above  rule  in  words  is  as  follows — the 
resistance  of  a  pure  metal  increases  approximately  1  per  cent  for  each  2.5° 
rise  in  temperature  above  0°  C. 

The  resistance  of  a  field  coil  of  a  generator  which  has  a  resistance 
of  25  ohms  at  ordinary  temperature  might  have  a  resistance  of  30  ohms 
after  the  machine  had  been  operating  a  few  hours;  the  rise  would  be  due 
to  the  heating  of  the  coil.  A  tungsten  lamp  has  a  resistance  when  hot 
about  twelve  times  as  much  as  the  resistance  it  has  at  room  temperature. 

In  certain  materials  the  resistance  may  show  considerable  departure 
from  the  rule  given  above,  thus  in  carbon  an  increase  in  temperature 
brings  about  a  decrease  in  resistance.  In  a  certain  alloy  of  nickel  and 
copper  there  is  practically  no  change  in  resistance  with  ordinary  temper- 
ature changes. 

There  are  very  strange  resistance  changes  in  certain  substances,  e.g., 
a  large  change  in  resistance  takes  place  in  selenium,  according  to  the  amount 
of  illumination  it  receives;  bismuth  shows  a  large  change  in  resistance, 
as  it  is  introduced  into  a  magnetic  field  and  is  sometimes  used  to  measure 
the  strength  of  magnetic  field  by  the  determination  of  its  resistance. 

The  resistance  of  a  salt  or  acid  solution  such  as  we  have  in  primary 
or  secondary  batteries  depends  among  other  things  upon  the  strength 
of  the  solution.  This  .variation  does  not  follow  a  simple  law;  there  is 
a  certain  strength  of  solution  which  gives  minimum  resistance.  For  sul- 
phuric acid  solution  such  as  is  used  in  lead  storage  batteries  the  mixture 
which  gives  minimum  resistance  is  made  up  with  30  per  cent  (by  weight) 
acid. 

The  effect  of  temperature  of  the  resistance  of  electrolytes  is  to  give 
a  decrease  of  resistance  with  an  increase  of  temperature.  The  resistance 
decrease  is  about  2  per  cent  per  degree  Centigrade. 

In  case  a  circuit  is  carrying  an  alternating  current  the  resistance  may 
show  all  sorts  of  variations;  it  may  be  changed  by  bringing  a  piece  of  iron, 
or  another  circuit,  into  its  magnetic  field,  by  varying  the  frequency  or 


INDUCED  ELECTROMOTIVE  FORCE  23 

strength  of  current.  These  changes  of  resistance  in  so  far  as  they  have 
importance  in  radio  work  will  be  considered  in  the  next  chapter. 

Induced  Electromotive  Force.  —  When  current  passes  through  a  coil 
of  wire  it  sets  up  a  magnetic  field  in  the  coil  and  the  strength  of  this  field 
varies  as  the  current  varies.  Now  it  is  a  fundamental  law  of  the  electric 
circuit  that  when  the  strength  of  magnetic  field  through  a  coil  is  varied 
an  e.m.f.  is  induced  in  the  coil;  this  law,  which  was  discovered  by  Faraday, 
is  called  the  law  of  induced  e.m.f.  The  application  of  this  law  underlies 
the  design  and  operation  of  nearly  all  electrical  machinery  and  circuits. 

Magnitude  of  Induced  E.M.F.  —  The  magnitude  of  the  induced  voltage 
depends  upon  the  rapidity  with  which  the  magnetic  field  is  changing  and 
upon  the  number  of  turns  in  the  coil,  it  being  directly  proportional  to 
each  of  these  factors.  It  is  written 


in  which 

e  =  the  voltage  induced  at  any  instant  of  time  ; 
N  =  the  number  of  turns  in  the  coil  ; 
6  =  the  flux  through  the  coil. 

The  minus  sign  is  necessary  because  of  the  relation  between  the  direction 
of  the  induced  e.m.f.  and  the  change  in  magnetic  field,  i.e.,  increase  or 
decrease. 

Direction  of  Induced  E.M.F.  —  The  change  of  flux  is  of  course  produced 
by  a  change  of  current;  if  the  flux  is  decreasing  it  must  be  that  the  cur- 
rent in  the  coil  is  decreasing.  The  direction  of  the  induced  e.m.f.  is  always 
such  as  to  prevent  the  change  of  current  which  is  producing  the  induced 
voltage.  Hence  when  the  current  (or 
flux)  is  decreasing,  the  direction  of  / 

the  induced  e.m.f.  is  such   as  to  pre- 
vent the  decrease  of  current. 

Suppose  a  circuit  arranged  as  shown 
in  Fig.  18;  A  is  the  battery,  B  is  a 
coil,  C  is  a  switch,  across  which  is 
connected  a  resistance  D.  With  the 


_dLA       Iwwwwl 


switch  closed  current  will  flow  in  the     FIG.  18. — Opening  the  switch  will  re- 
direction of  the  arrow  and  will  be  fixed  duce  the  current  in  the  circuit 
in  magnitude   by  the  voltage   of   the 

battery  and  the  resistance  of  the  coil.  The  resistance  D  will  play  no 
part  in  fixing  the  value  of  the  current,  because  with  the  switch  closed 
this  resistance  is  cut  out  of  the  circuit,  or  short-circuited. 

A  certain  flux  $,  will  be  set  up  in  the  coil,  the  value  of  this  flux  being 
fixed  by  the  current.     If  now  the  switch  is  opened  the  current  must  change 


24 


FUNDAMENTAL  IDEAS  AND   LAWS 


[CHAP.  I 


to  some  lower  value  because  of  the  added  resistance  D.  This  lower  cur- 
rent will  produce  a  lower  flux  </>2.  While  the  flux  is  changing  from  <£i 
to  <j>2  an  e.m.f.  will  be  set  up  in  the  coil  B  and  the  direction  of  the  e.m.f. 
will  be  the  same  as  the  battery  e.m.f.,  i.e.,  it  will  assist  the  battery  e.m.f. 
in  tending  to  maintain  the  current  at  its  original  value. 

In  Fig.  19  the  switch  is  supposed  to  be  closed  until  time  A  and  here 
it  is  opened.  The  flux  will  decrease  from  the  value  AE  to  BF,  the  time 
taken  for  the  change  being  that  shown  on  the  diagram  between  A  and  B. 
The  decreasing  flux  generates  a  voltage  in  the  coil  shown  by  the  curved 
line  A  IB,  and  this  is  in  the  same  direction  as  the  battery  voltage,  hence 
the  total  voltage  acting  in  the  circuit  during  the  time  A-B  is  shown  by 
the  curved  line  GJH. 


Curve  of  flux 


'       Total  emf.  acting    I 

^in  circuit     \    02   Ijvj 


Battery  emf. 


Induced  emC.  due  to 
decreasing  flux 


Induced  emf.  due  to 
increasing  flux 


FIG.  19. — Curves  showing  direction  of  induced  e.m.f. 's  when  current  is  increasing  and 

when  decreasing. 

When  the  switch  is  closed  again  at  time  C  the  flux  increases  from  </>2 
to  <£i ;  the  induced  voltage  is  now  in  the  opposite  direction  and  is  shown 
by  the  curved  line  C  KD;  it  results  in  a  total  circuit  voltage  less  than 
the  batteiy  voltage,  as  shown  by  the  curved  line  MNO.  (The  shape 
of  the  induced  voltage  will  not  be  exactly  that  shown  by  the  lines  of 
Fig.  19;  these  curves  are  only  approximate  indications  of  the  actual  form 
of  the  induced  voltage.  The  exact  form  will  depend  upon  the  sparking 
taking  place  at  the  switch,  etc.) 

Summarizing  the  facts  brought  out  by  Fig.  19  and  its  explanation  we 
have  the  proposition  that  when  the  current  in  an  inductive  circuit  is 
decreasing  the  induced  voltage  acts  to  increase  the  total  voltage  of  the 
circuit,  when  the  current  is  increasing  the  induced  voltage  is  in  such  a 
direction  that  the  total  voltage  acting  in  the  circuit  is  decreased. 

Illustrating  the  above  ideas  there  is  a  certain  circuit  used  in  radio 
in  which  a  continuous  voltage  of  1200  volts  is  applied  through  a  coil  to 
the  plate  of  a  vacuum  tube;  as  the  current  in  this  circuit  pulsates,  alter- 
nately increasing  and  decreasing  from  its  normal  value,  the  induced  volt- 


SELF  INDUCTION  OF  A  CIRCUIT  25 

age  in  the  coil  has  a  maximum  value  of  1100  volts.  When  the  current 
is  increasing  this  induced  voltage  acts  in  the  opposite  direction  to  that 
of  the  generator  furnishing  the  1200  volts,  so  that  the  total  voltage  effect- 
ive in  maintaining  current  through  the  resistance  of  the  circuit  is  only 
100  volts.  When  the  current  is  decreasing  the  induced  voltage  assists 
the  generator  voltage  and  the  total  effective  voltage  in  the  circuit  is  2300 
volts.  The  effect  of  induced  voltage  in  this  special  circuit  is  to  produce 
a  pulsating  voltage,  between  100  volts  and  2300  volts,  although  there  is 
in  the  circuit  a  generator  to  supply  the  current  which  furnishes  a  contin- 
uous voltage  of  1200  volts. 

This  voltage  set  up  in  a  coil  by  the  changing  flux  in  the  coil  (the  flux 
being  caused  by  current  in  the  coil  itself)  is  called  the  e.m.f.  of  self-induc- 
tion. 

Coefficient  of  Self-induction. — Instead  of  expressing  the  magnitude 
of  the  induced  voltage  in  a  coil  in  the  form  given  by  Eq.  (4)  we  may  write 

Tdi  /rx 

e=-Ldi> (5) 

in  which 

i  =  the  current  in  the  coil ; 

e  =  the  instantaneous  value  of  the  induced  voltage,  due  to 

the  changing  current,  i, 
L  —  the  coefficient  of  self-induction. 

The  coefficient  of  self-induction  of  a  coil  varies  with  the  square  l  of 
the  number  of  turns  in  the  coil  and-  inversely  as  the  reluctance  of  its  mag- 
netic circuit. 

If  a  given  air  core  coil  has  an  L  of  two  units  and  the  number  of  turns 
is  doubled,  the  value  of  L  is  increased  four  times  so  it  becomes  eight  units. 
If  the  magnetic  circuit  is  changed  from  air  to  iron,  the  permeability  of 
which  is  1500,  the  L  will  be  further  increased  1500  times  and  so  becomes 
12,000  units.  This  increase  is  due  to  the  iron  decreasing  the  reluctance 
of  the  magnetic  circuit  1500  times.  If  the  iron  core  does  not  completely 
close  the  magnetic  circuit,  so  that  part  of  the  magnetic  path  is  still  through 
air,  the  value  of  L  is  not  increased  to  the  extent  stated  above.  For  example, 
if  the  path  through  iron  is  15  inches  and  the  air  part  of  the  path  is  .01  inch 
long,  then  the  value  of  L  is  increased  750  times,  instead  of  1500  times  as 
stated. 

The  great  increase  in  L  produced  by  the  use  of  iron  for  the  magnetic 
circuit  explains  the  almost  universal  use  of  iron  cores  (completely  closed 

1  This  law  holds  good  for  any  shape  of  coil  if  the  magnetic  circuit  is  a  closed  iron 
core,  but  for  an  air-core  coil  the  law  is  approximate  only ;  it  is  more  nearly  true  as  the 
turns  of  the  coil  are  placed  closer  together. 


26  FUNDAMENTAL   IDEAS   AND   LAWS  [CHAP.  I 

when  possible)  in  coils  which  perform  their  function  owing  to  the  value 
of  their  self-induction. 

The  unit  of  self-induction  is  defined  by  Eq.  (5);  if  a  rate  of  current 
change  of  one  ampere  per  second  gives  an  induced  voltage  of  one  volt,  the 
coil  has  a  self-induction  of  one  unit.  This  unit  is  called  the  henry;  the 
henry  is,  however,  too  large  a  unit  for  most  of  the  coils  used  in  radio 
work,  so  that  subdivisions  of  the  henry  are  used.  The  milli-henry  is  one 
thousandth  of  a  henry  and  the  micro-henry  is  the  millionth  part  of  a 
henry.  Sometimes  a  still  smaller  unit  is  used,  the  centimeter,  which  is 
the  billionth  part  of  the  henry.  It  may  seem  strange  that  the  unit  of 
[length "is  also  the  unit  of  self-induction,  but  such  is  the  fact;  the  deriva- 
tion of  the  dimensions  of  the  various  units  is  outside  the  scope  of  this 
text.  The  coils  used  in  "  tuning  "  radio  circuits  vary  from  a  few  micro- 
henries to  several  millihenries,  according  to  the  frequency  of  the  current 
being  used. 

Energy  Stored  in  a  Magnetic  Field. — It  requires  work  to  set  up  a 
magnetic  field  just  the  same  as  it  requires  work  to  set  into  motion  a  heavy 
body.  The  greater  the  self-induction  of  a  coil  the  greater  is  the  work 
required  to  start  current  flowing  in  the  coil ;  similarly  the  greater  the  mass 
of  a  body  the  greater  is  the  work  required  to  start  it  in  motion. 

The  amount  of  work  required  to  give  a  mass  m,  a  velocity  v,  is  measured 
by  \mv2,  as  shown  in  all  texts  on  mechanics. 

The  amount  of  work  required  to  set  up,  in  a  coil  of  self-induction  L, 
the  magnetic  field  caused  by  a  current  /  is, 

Energy,  or  work  =  | L/2 (6) 

where  L  is  measured  in  henries  and  /  is  measured  in  amperes  and  the 
energy  is  measured  in  joules. 

The  field  coil  of  a  large  generator  may  have  many  joules  of  energy 
stored  in  its  magnetic  field;  in  radio  circuits  the  amount  of  energy  in 
the  coils  of  a  transmitting  set  is  variable  because  the  current  is  variable. 
The  maximum  value  of  the  energy  in  the  coils  of  the  ordinary  transmitter 
is  about  one  joule  per  kilowatt  capacity  of  the  set. 

Mutual  Induction. — When  the  flux  through  a  coil  varies  an  e.rn.f. 
is  set  up  in  it;  if  the  flux  is  produced  by  current  in  the  coil  itself  the  e.m.f. 
is  spoken  of  as  the  e.m.f.  of  self-induction,  but  if  the  flux  is  due  to  some 
other  coil,  in  proximity  to  the  one  in  which  the  voltage  is  being  induced, 
the  e.m.f.  is  spoken  of  as  the  e.m.f.  of  mutual  induction.  The  voltage 
induced  in  the  second  coil  is  proportional  to  the  rate  of  current  change 
in  the  first  coil  (the  one  producing  the  flux)  and  the  mutual  induction 
of  the  two  coils.  The  relation  is  expressed  in  the  form  of  an  equation 


MUTUAL  INDUCTION  AND   MAGNETIC   COUPLING 


27 


where  €2  =  voltage  induced  in  the  second  coil; 
ii  =  current  in  the  first  coil ; 
M  =  the  coefficient  of  mutual  induction  of  the  two  coils. 

If  e  and  i  are  measured  in  volts  and  amperes  respectively,  then  M  is 
measured  in  henries,  the  same  unit  as  is  used  for  L.  For  smaller  values 
of  M  the  same  fractional  parts  of  the  henry  are  used  as  are  used  for  L. 
M  depends  for  its  value  upon  the  number  of  turns  in  each  of  the  coils 
and  upon  their  relative  position;  as  the  number  of  turns  in  either  coil 
is  decreased  the  value  of  M  is  correspondingly  decreased  and  as  the  dis- 
tance between  the  two  coils  is  increased  the  value  of  M  is  again  decreased. 
M  may  also  be  decreased  by  properly  orienting  the  two  coils  with  respect 
to  one  another.  Imagine  two  cylindrical  coils,  shown  in  plan  as  rect- 
angles in  Fig.  20;  M  will  have  a  relatively  high  value  for  the  position 


Position   a  Position   b  Position    c 

FIG.  20.  —  Variation  of  mutual  inductance  between  two  coils. 

shown  in  a  and  will  have  a  smaller  value  for  either  position  b  or  position  c. 
The  scheme  of  rotating  one  of  the  two  coils  to  diminish  M  has  the  advan- 
tage over  the  other  method  that  it  is  compact  and  so  permits  the  design 
of  a  set  to  be  kept  to  smaller  dimensions,  a  very  important  point  if  the 
sets  are  to  be  portable. 

Coefficient  of  Coupling.  —  If  all  the  flux  produced  by  one  coil  threads 
with  all  the  turns  of  the  other,  the  coils  are  said  to  have  100  per  cent 
coupling;  if  but  a  small  fraction  of  the  flux  produced  by  the  first  coil 
threads  the  turns  of  the  second,  the  coupling  is  weak.  Also  if  all  the 
flux  of  the  first  coil  links  with  but  a  few  turns  of  the  second,  the  coupling 
is  again  weak. 

The  coefficient  of  coupling1  between  the  two  circuits  is  given  by  the 
relation 

k-     M  (7) 

~ 


where  k  —  coefficient  of  coupling,  always  less  than  unity; 
M  =  mutual  induction  between  the  two  circuits; 
LI  =  the  total  self-induction  of  the  first  circuit; 
L2  =  the  total  self-induction  of  the  second  circuit. 
1  A  more  detailed  discussion  of  coefficient  of  coupling  is  given  on  p.  79. 


28  FUNDAMENTAL  IDEAS   AND   LAWS  [CHAP.  I 

M,  Li,  and  Z/2  must  all  be  expressed  in  the  same  units. 

As  examples  of  the  proper  use  of  Eq.  (7)  in  determining  A-,  Fig.  21 
is  given;  it  is  to  be  especially  noted  that  if  there  are  two  or  more  coils 
in  series  and  only  one  of  them  is  used  to  couple  the  two  circuits  the  total 
L  of  the  circuit  must  be  used  and  not  the  L  only  of  that  coil  used  for  the 
coupling.  Thus  if  two  circuits  are  coupled  to  a  certain  extent  by  two 
coils  in  a  certain  position  with  respect  to  one  another  and  another  coil 
is  added  in  series  with  one  of  these,  leaving  the  two  original  coils  exactly 
as  they  were,  the  coefficient  of  coupling  of  the  two  circuits  has  been  lessened. 

Practical  Uses  of  Mutual  Induction. — Whenever  energy  is  to  be  trans- 
ferred from  one  circuit  to  another,  insulated  from  the  first,  the  transfer 
generally  occurs  across  a  mutual  electric  or  magnetic  field,  and  generally 
this  transfer  utilizes  a  mutual  magnetic  field.  That  is,  the  energy  flows 
from  one  circuit  to  the  other  because  of  the  mutual  induction  of  the  two 
circuits.  In  a  radio  transmitting  set  mutual  induction  is  used  between 


oo 

U, 


L, 


M 


000 


La=4.0 
0.25  L 2=2.0   .M  =0.1  Lc=16    1^=20      M=5.0 

K     ,       5-° 

^(4.0+  2.4X16+  20) 

FIG.  21. — Examples  of  coefficient  of  coupling. 

the  two  coils  of  the  power  transformer  where  the  coupling  is  about  90  per 
cent;  in  the  high-frequency  oscillation  transformer  the  coupling  is  about 
20  per  cent;  in  the  coupler  of  the  receiving  set  the  antenna  is  coupled  to 
the  local  tuned  circuit  with  a  coupling  of  perhaps  2  to  10  per  cent. 

Effect  of  a  Short-circuited  Coil  on  the  Self-induction  of  a  Neighbor- 
ing Coil. — Suppose  a  coil  A  has  a  certain  self-induction  by  itself;  it  will 
be  found  that  if  another  coil  B  is  brought  close  to  A ,  and  in  such  a  position 
that  M  is  not  zero,  the  effective  L  of  coil  A  is  decreased,  if  the  second 
coil  is  connected  to  form  a  closed  circuit  so  that  current  can  flow  in  it. 
The  amount  of  decrease  in  L  depends  upom  the  coupling  between  the 
two  coils,  upon  the  frequency,  and  upon  the  resistance  in  the  circuit  of 
the  second  coil. 

This  effect  is  likely  to  occur  in  certain  variable  coils  used  in  radio 
circuits;  in  the  type  of  coil  referred  to  the  change  in  the  self-induction 
of  the  coil  is  accomplished  by  using  more  or  less  turns  of  the  coil  by  means 
of  a  sliding  contact  as  indicated  in  Fig.  22.  If  the  sliding  contact  B 
happens  to  make  contact  with  two  adjacent  turns  at  once  (quite  a  nor- 
mal occurrence),  there  is  one  turn  of  the  coil  short-circuited,  and  this  short- 


CHARGING  A   CONDENSER  29 

circuited  turn  is  quite  closely  coupled  with  that  part  of  the  coil  which 
is  being  used.  The  effect  of  this  turn  is  to  decrease  very  much  the  effect- 
ive self-induction  of  the  part  of  the  coil  A-B,  which  is  being  used.  Now 
as  the  slider  is  being  adjusted  it  will,  with  very  little  movement,  make 
contact  with  two  turns  or  with  only  one  turn;  a  signal  may  come  in  very 
strong  at  a  certain  setting  of  the  slider  and  the  slightest  movement  of 
the  slider  one  way  or  the  other  will  make  the  signal  disappear.  This  is 


B- 


Sliding  Contact 


FIG.  22. — Variable  Inductance  with  sliding  contact. 

due  to  the  large  change  in  the  self-induction  of  the  coil  as  the  slider  makes 
the  short-circuited  turn  or  does  not  make  the  double  contact. 

A  short-circuited  turn  in  a  coil  not  only  produces  a  decrease  in  the 
L  of  the  coil,  but  it  also  increases  very  materially  the  resistance  of  the 
coil,  and  this  is  detrimental  to  the  proper  operation  of  the  set;  these  two 
points  will  be  taken  up  more  in  detail  on  pp.  85,  et  seq. 

Capacity — Charging  a  Condenser. — Suppose  a  battery  is  connected 
through  a  switch  to  a  condenser  as  indicated  in  Fig.  23.  The  condenser 


FIG.  23. — Charging  a  condenser. 

C  consists  of  two  metal  plates  a  and  6,  close  together,  but  perfectly  insu- 
lated from  one  another  by  the  layer  of  air  between  them.  When  the 
switch  B  is  closed  the  plate  b  is  made  negative  with  respect  to  a,  by  an 
amount  equal  to  the  e.m.f.  of  the  cell,  perhaps  1.5  volts;  that  this  must 
be  so  follows  from  the  fact  that,  when  the  switch  is  closed,  b  is  connected 
to  the  negative  end  of  the  cell  and  a  is  connected  to  the  positive  end  of 
the  cell. 

As  the  two  plates  a  and  b  were  at  the  same  potential  before  the  switch 
was  closed,  and  after  the  switch  is  closed  b  is  1.5  volts  lower  in  potential 
than  a,  the  closing  of  the  switch  must  have  been  followed  by  a  flow  of 
electrons  in  the  direction  from  a  to  b.  This  redistribution  of  the  electrons 
in  the  circuit,  which  serves  to  bring  the  condenser  plates  to  the  same  dif- 
ference of  potential  as  are  the  terminals  of  the  cell  to  which  they  are  con- 


30  FUNDAMENTAL  IDEAS  AND   LAWS  [CHAP.  I 

nected,  is  called  charging  the  condenser.  A  current  flows  during  the  short 
interval  of  time  required  for  the  redistribution  of  the  electrons;  this  cur- 
rent is  called  the  charging  current  of  the  condenser. 

It  is  more  or  less  evident  that  the  condenser  will  take  sufficient  charge 
to  bring  its  potential  difference  equal  to  that  of  the  battery;  as  long  as 
the  condenser  is  at  a  lower  potential  difference  than  the  terminals  of  the 
battery,  the  e.m.f.  of  the  battery  causes  more  electrons  to  flow;  if,  by 
any  chance,  so  many  electrons  accumulate  on  the  b  plate  of  the  condenser 
that  potential  difference  of  the  condenser  is  greater  than  that  of  the  battery, 
the  excess  of  potential  difference  would  so  act  as  to  make  the  condenser 
discharge  itself  until  it  was  at  the  same  potential  difference  as  the  ter- 
minals of  the  battery. 

Capacity  of  a  Condenser. — Suppose  the  amount  of  electron  flow  neces- 
sary to  charge  two  different  condensers  to  a  certain  potential  difference 
is  measured  by  a  ballistic  galvanometer  or  similar  device.  It  will  be 
found  in  general  that  the  different  condensers  require  a  different  amount 
of  charge  to  bring  them  to  the  same  difference  of  potential.  For  example, 
if  two  condensers  are  made  of  the  same-sized  metal  plates,  but  in  one  the 
plates  are  only  half  as  far  apart  as  in  the  other,  it  will  be  found  that  the 
one  with  closer  plates  requires  twice  as  much  charge  as  the  other;  if  two 
condensers  have  the  same  spacing  for  the  plates,  but  one  has  larger  plates 
than  the  other,  again  it  will  be  found  that  one  requires  more  charge  than 
the  other,  in  this  case  the  one  with  the  larger  plates. 

That  characteristic  of  a  condenser  which  determines  how  many  elec- 
trons it  takes  to  bring  the  condenser  plates  to  a  certain  potential  dif- 
ference is  called  its  capacity.  A  condenser  which  requires  one  coulomb 
of  electricity  to  bring  its  plates  to  a  potential  difference  of  one  volt,  has 
a  capacity  of  one  farad.  Such  a  condenser  would  require  immense  plates 
very  close  together;  the  unit  is  altogether  too  large  to  represent  the  ca- 
pacity of  ordinary  condensers.  In  ordinary  engineering  practice,  such  as 
telephone  circuits,  the  microfarad  is  used  as  the  unit  of  capacity.  A  con- 
denser of  one  microfarad  requires  a  charge  of  one  millionth  of  a  coulomb 
to  charge  it  to  one  volt.  Stated  in  another  way,  a  current  of  one  ampere 
would  have  to  flow  only  one  millionth  of  a  second  to  charge  the  condenser 
to  one  volt  potential  difference,  or  one  microampere,  flowing  for  one  second 
would  charge  it  to  the  same  extent. 

In  radio  circuits  the  microfarad  is  too  large  a  unit  to  be  conveniently 
used;  a  more  suitable  unit  is  the  milli-microfarad,  which  is  the  thousandth 
part  of  a  microfarad.  Another  unit  is  the  micro-microfarad,  which  is  one 
millionth  of  a  microfarad.  Still  another  unit  is  the  centimeter;  which 
is  one  nine  hundred  thousandth  of  a  microfarad.  The  micro-microfarad 
and  the  centimeter  are  nearly  the  same-sized  units,  the  centimeter  being 
about  1.1  of  a  micro-microfarad. 


ENERGY  IN  CHARGED  CONDENSER  31 

The  capacity  of  a  standard  Ley  den  jar  used  in  radio  sets  is  2  milli- 
microfarads.  The  variable  condensers  used  for  tuning  a  receiving  set 
have  a  maximum  capacity  of  one  milli-microfarad  or  less.  Certain  con- 
densers used  with  vacuum-tube  detectors  have  a  capacity  of  100  micro- 
microfarads.  Antennae,  such  as  are  used  on  small  vessels,  have  a  capacity 
of  about  0.5  milli-microfarad,  while  large  land  stations  designed  for  trans- 
oceanic communication  may  have  antennas  of  as  much  as  10  milli-micro- 
farads  capacity. 

Specific  Inductive  Capacity. — Suppose  a  condenser  made  of  two  metal 
plates  separated  by  f-in.  of  air  and  let  the  quantity  required  to  charge 
it  to  one  volt  be  measured.  Then  let  a  f-in.  glass  plate  be  slipped  in 
between  the  two  plates  of  the  condenser  and  let  the  quantity  be  again 
measured;  it  will  be  found  to  be  about  six  times  as  much  as  when  air 
was  used  to  separate  the  plates.  If  various  other  materials  are  used  as 
dielectric  it  will  be  found  that  they  all  take  more  charge  than  the  air  con- 
denser; in  other  words,  when  such  insulators  as  glass,  mica,  rubber,  etc., 
are  used  for  the  dielectric  instead  of  air,  the  condenser  has  more  capacity, 
its  dimensions  being  the  same  in  each  case.  The  ratio  of  the  capacity 
of  a  condenser  in  which  some  dielectric  other  than  air  is  used,  to  that  it 
would  have  if  air  were  used,  is  called  the  specific  inductive  capacity  of  the 
dielectric.  The  values  of  this  constant  for  some  of  the  more  common 
insulators  are  given  in  the  table  on  page  167. 

Energy  Stored  in  a  Charged  Condenser. — It  takes  work,  or  energy, 
to  charge  a  condenser;  the  amount  of  this  work  depends  upon  the  capacity 
of  the  condenser  and  upon  the  voltage  to  which  it  is  charged.  The  problem 
is  analogous  oo  the  "  pumping  up  "  of  a  tire;  the  amount  of  work  done 
in  this  case  is  evidently  proportional  to  the  size  of  the  tire  and  depends 
in  some  way  upon  the  pressure  to  which  the  tire  is  pumped.  Actually 
the  amount  of  work  required  increases  with  the  square  of  the  pressure 
to  which  it  is  pumped ;  pumping  a  given  tire  to  100  Ibs.  pressure  requires 
four  times  as  much  work  as  is  required  to  pump  it  to  50  Ibs.  pressure. 

The  energy  used  in  charging  a  condenser,  and  stored  in  the  electric 
field  between  the  plates  of  the  condenser,  is 

Work  =  %CE2 (8) 

where  C  =  capacity  of  condenser  in  farads ; 

E  =  voltage  to  which  condenser  is  charged,  in  volts,  and  the  work 
is  given  in  joules. 

A  condenser  of  .002  microfarad,  charged  to  15,000  volts  difference 
of  potential,  has  stored  in  its  field  .225  joule  of  energy.  If  the  energy 
stored  in  this  condenser  is  discharged  to  produce  the  oscillatory  currents 
required  in  radio  transmitter,  it  may  be  used  to  supply  about  100  watts 
of  power,  with  a  suitable  charge  and  discharge  frequency. 


32  FUNDAMENTAL  IDEAS  AND  LAWS  [CHAP.  I 

Suppose  sixteen  such  condensers  are  connected  in  parallel,  so  that  each 
is  charged  to  the  same  voltage,  15,000  volts.  There  will  be  stored  in  this 
battery  of  condensers  16  X.  225  joule,  or  3.6  joules.  If  the  condensers 
discharge  through  a  spark  gap  which  operates  1000  times  a  second  (a  com- 
mon spark  frequency)  there  will  be  transformed  into  oscillatory  current 
3600  joules  per  second,  that  is,  3600  watts  of  power.  Hence  sixteen  such 
jars,  good  to  operate  at  15,000  volts,  would  be  sufficient  for  generating 
about  3J  kilowatts  of  high-frequency  power. 

Current  Flow  in  a  Continuous  Current  Circuit  Containing  Resistance 
Only.  —  If  a  continuous  e.m.f.,  such  as  that  from  a  battery,  is  impressed 
upon  a"  circuit  containing  resistance  only,  a  continuous  current  will  flow 
and  its  value  is  given  by  Ohm's  law, 


where   7  =  current  in  amperes; 

E  =  e.m.f.  of  the  battery,  in  volts; 

R  =  resistance,  in  ohms,  of  the  entire  circuit. 

The  current  will  have  this  value  from  the  instant  the  switch  is  closed, 
and  will  be  as  continuous  (constant  in  magnitude)  as  is  the  e.m.f.  of  the 
battery. 

Current  Flow  in  an  Inductive  Circuit.  —  If  the  circuit  to  which  the 
battery  is  connected  contains  inductance  as  well  as  resistance,  the  current 
flowing  will  have  the  value  given  by  Eq.  (9)  only  after  the  switch  has  been 
closed  for  some  instants;  it  does  not  rise  to  the  value  predicted  by  this 
equation  for  quite  some  time  after  the  switch  has  been  closed.  The  fact 
that  there  is  inductance  in  the  circuit  as  well  as  resistance  does  not  affect 
the  final  value  of  current,  but  it  does  affect  the  current  for  a  short  time 
after  closing  the  switch. 

In  an  inductive  circuit  the  current  cannot  at  once  rise  to  its  steady 
value;  it  takes  an  appreciable  time  to  reach  the  final  value  predicted  by 
Ohm's  law.  The  length  of  time  taken  depends  upon  the  ratio  of  the 
inductance  to  the  resistance  of  the  circuit.  The  value  of  current  is 
expressed  at  any  time  after  closing  the  switch  by  the  equation 


in  which  i—  the  current  in  amperes  at  time  t  after  closing  the  switch; 
E  =  the  e.m.f.  of  the  batteiy; 
R  =  the  total  resistance  in  the  circuit,  including  that  of  the 

battery,  in  ohms. 

L  =  the  coefficient  of  self-induction  of  the  circuit,  in  henries; 
i  =  the  number  of  seconds  elapsing  after  the  switch  is  closed; 
e=the  base  of  natural  logarithms  =  2.  7  18. 


THE  OSCILLOGRAPH  33 

This  equation  defines  the  expression  "  logarithmic  rise  of  current." 
If  a  circuit  has  a  very  large  value  of  inductance  compared  to  its  resistance, 
the  rise  of  current  may  be  so  slow  that  it  can  actually  be  observed  by 
means  of  an  ammeter  in  the  circuit.  This  is  very  easy  to  observe,  for 
example,  in  the  field  circuit  of  a  large  generator,  in  which  the  current  may 
take  several  seconds  before  it  approximates  its  final  value. 

Time  Constant  of  an  Inductive  Circuit. — When  the  time  elapsed  after 
the  switch  is  closed  is  equal  to  the  L/R  of  the  circuit  the  current  has  risen 
to  (1  —  1/e)  of  its  final  value,  or  to  about  63  per  cent  of  its  final  value.  The 
time  taken  for  the  current  to  reach  this  "fraction  of  its  final  value  is  called 
the  time  constant  of  the  circuit;  in  most  inductive  circuits  it  has  a  value 
only  a  small  fraction  of  a  second,  but  it  may,  in  special  cases,  be  several 
seconds. 

The  Oscillograph. — In  investigating  problems  to-day  the  electrical 
engineer  uses  very  extensively  an  instrument  called  the  oscillograph.  It 
receives  its  name  from  the  fact  that  its  essential  part  consists  of  a  small 
mirror  mounted  on  some  fine  wires,  through  "which  wires  a  current  may 
be  passed.  The  wires  are  mounted  between  the  poles  of  a  powerful  mag- 
net, and,  due  to  the  force  acting  between  the  magnetic  field  and  the  cur- 
rent in  the  wires,  the  mirror  is  caused  to  oscillate  back  and  forth  as  the 
current  in  the  wires  changes  its  direction.  This  part  of  the  instrument  is 
really  a  small  galvanometer  so  constructed  that  it  can  move  very  quickly  a 
beam  of  light  shining  on  the  mirror  and  which,  reflected  therefrom,  acts  as 
a  pointer  to  indicate  the  motion  of  the  mirror.  By  suitable  devices  the 
motion  of  this  beam  of  light  may  be  either  thrown  on  to  a  translucent 
screen  and  so  serve  for  visual  work,  or  it  may  be  thrown  to  a  rapidly  rotat- 
ing film  and  so  give  a  permanent  record  of  the  excursions  of  the  mirror. 
These  films,  showing  how  current  varies  with  respect  to  time,  are  called 
oscillograms;  such  records  will  be  frequently  used  in  this  text  to  illus- 
trate phenomena  being  analyzed. 

Such  records  are  extremely  valuable,  as  there  are  many  rapid  changes 
of  current  taking  place  in  circuits  which  can  be  examined  only  in  this 
fashion.  Changes  of  current  which  are  so  rapid  that  they  occupy  only 
one-thousandth  of  a  second  are  truthfully  recorded  by  a  properly  used 
oscillograph;  currents  which  alternate  many  hundred  times  a  second  are 
correctly  shown  by  an  oscillogram.  Not  only  will  the  oscillogram  show 
the  number  of  times  a  second  the  current  alternates,  but  it  will  also  show 
how  closely  the  current  approaches  a  sine  wave  in  form  and  similar  effects. 

In  Fig.  24  is  shown  an  oscillogram  of  the  current  rising  in  an  inductive 
circuit;  it  will  be  seen  that  the  current  rises  rapidly  at  first  and  gradually 
approaches  its  steady  value.  If  the  switch  should  be  opened  quickly  in 
such  an  inductive  circuit  a  large  arc  will  form  at  the  point  of  the  switch 
where  the  circuit  is  opened.  The  energy  stored  in  the  magnetic  field 


34 


FUNDAMENTAL  IDEAS  AND   LAWS 


[CHAP.  I 


has  to  disappear  when  the  current  dies  to  zero  because  there  can  be  no 
magnetic  field  without  current.1  The  greater  the  self-induction  of  the 
circuit  the  greater  is  the  amount  of  energy  (for  a  given  current)  and  the 
larger  will  be  the  arc  when  opening  the  circuit.  The  decay  of  current 
in  an  inductive  circuit  cannot  be  well  examined  therefore  by  opening 
the  circuit,  but  it  can  be  shown  by  short-circuiting  the  coil  in  which  the 
current  is  flowing.  In  such  a  case  the  current  dies  away  on  a  logarithmic 


FIG.  24. — Oscillogram  showing  rise  and  fall  of  current  in  an  inductive  circuit. 

curve  quite  similar  to  the  curve  of  current  rise.     The  equation  of  current 
decay  is  quite  similar  to  that  of  the  current  rise  and  is 


Rt 


en) 


where  the  letters  have  the  same  meaning  as  in  Eq.  (10). 

Fig.  24  serves  also  to  show  this  effect,  the  circuit  having  been  arranged 
as  shown  in  Fig.  25.  The  battery  D  was  connected  to  the  inductance 
C  through  a  low  resistance  E  and  switch  A .  The  oscillograph  was  con- 
nected in  the  circuit  at  the  point  0.  A  second  switch  B  served  to  short- 
circuit  the  coil  so  that  the  decay  of  current  in  it  could  be  shown  as  well 
as  the  rise. 

With  B  open,  A  was  closed  and  so  the  oscillograph  recorded  the  rise 
of  current;  when  the  current  had  reached  its  steady  state  switch  B  was 
closed,  and  the  decay  of  current  in  the  coil  was  recorded.  The  resistance 

1  This  statement  of  course  neglects  any  residual  field  left  in  iron  parts  of  the 
magnetic  circuit  when  the  current  has  fallen  to  zero. 


RISE  AND  DECAY  OF  CURRENT  IN  INDUCTIVE  CIRCUITS       35 


E  was  used  in  the  circuit  to  prevent  the  short-circuiting  of  the  battery 
when  B  was  closed. 

The  curves  of  rise  and  decay  are  just  as  is  predicted  by  Eqs.  (10)  and 
(11) ;  the  two  curves  show  a  slight  difference  in  the  rate  of  change  of  current, 
but  this  is  to  be  expected,  because  the  resistance  was  somewhat  greater 
for  the  rise  of  current  than  it  was  for  the  decay,  while  the  inductance 
was  the  same  for  both.  The  time  constant  was  greater  for  the  decaying 

X 

A 


FIG.  25.— Circuit  used  to  obtain  oscillograms  of  growth  and  decay  of  current. 

current  than  for  the  rising  current;  the  rising  current  had  for  its  resistance 
that  of  the  coil,  that  of  the  battery,  and  that  designated  by  E,  while  the 
decaying  current  took  place  through  the  resistance  of  the  coil  only. 

Effect  of  Rising  and  Decaying  Currents  on  Neighboring  Circuits. — As 
the  current  in  the  coil  increases  and  decreases  it  must  induce  electro- 
motive forces  in  any  neighboring  circuits  which  are  so  placed  that  they 
link  with  its  magnetic  field.  If  the  neighboring  circuit  is  closed  current 
will  flow,  in  one  direction  when  the  current  in  the  first  circuit  is  rising 
and  in  the  opposite  direction  when  the  current  in  the  first  circuit  is  falling. 
Hence  when  a  circuit  is  closed  and  current  starts  to  flow  all  neighboring 


FIG.  26. — Circuit  used  to  obtain  oscillogram  of  currents  in  coupled  circuits. 

circuits,  if  closed,  will  have  currents  in  one  direction  and  in  the  opposite 
direction  when  the  circuit  is  opened. 

To  bring  out  this  fact  a  circuit  was  arranged  as  shown  in  Fig.  26;  one 
oscillograph  vibrator  was  introduced  at  C  and  the  other  at  D.  The  cur- 
rents which  flowed  in  each  circuit  during  the  opening  and  closing  of  switch 
E  is  shown  in  the  oscillogram  given  in  Fig.  27.  When  the  switch  was 
closed  current  in  coil  B  flowed*in  the  opposite  direction  to  that  in  coil  A ; 
when  the  switch  was  opened  the  current  in  B  flowed  in  the  reverse  direc- 


36 


FUNDAMENTAL  IDEAS  AND  LAWS 


[CHAP.  I 


CHARGING  AND   DISCHARGING    A   CONDENSER  37 

tion.  The  rather  irregularly-shaped  curve  of  current  at  the  time  of 
opening  the  switch  was  due  to  the  fact  that  an  arc  formed  at  the  point 
of  opening  the  circuit  so  that  although  the  switch  was  open  the  circuit 
was  not  open,  the  arc  serving  to  keep  the  circuit  closed.  As  the  resistance 
of  the  arc  was  indefinite  and  variable  the  current  naturally  followed  no 
regular  curve. 

Current  Flow  on  Connecting  a  Condenser  to  a  Source  of  Continuous 
E.M.F. — When  a  condenser  is  connected  to  a  source  of  continuous  e.m.f. 
the  condenser  takes  sufficient  charge  to  bring  its  plates  to  a  difference  of 
potential  equal  to  the  e.m.f.  of  the  source  to  which  it  is  connected.  This 
charging  would  take  place  instantaneously  if  there  were  no  resistance  in 
the  circuit.  But  the  generator  or 
battery  to  which  the  condenser  is  con- 
nected always  has  resistance  and  the 
condenser  itself  has  a  kind  of  resistance 

due  to  the  losses  occurring  in  its  die-   

lectric,  all  of  tliese  resistance  factors 
act  in  such  a  way  that  the  condenser 
takes  an  appreciable  time  to  charge 
itself. 

A  circuit  was   arranged  as    shown  Fir"  28.— Circuit  used  to  obtain  oscil- 

in  Fig.  28;    A  is   a   100-volt  battery,       lograra  of  charge  and  discharge  of  a 

condenser. 

B  and  D  are  switches,  C  is  the  con- 
denser to  be  charged  or  discharged,  0 

is  the  oscillograph  vibrator,  and  /£  is  a  resistance  which  represents  the 
total  resistance  of  the  circuit,  battery,  connections,  condenser,  etc. 

The  equation  for  the  current  which  flows  in  such  a  circuit  is  given  by 


(12) 


where  E  =  the  battery  voltage  in  volts; 

R  =  the  total  resistance  of  the  circuit  in  ohms ; 
C  =  the  capacity  of  the  condenser  in  farads. 

If  now  switch  B  is  opened  and  switch  D  is  closed  the  condenser  will 
discharge  and  the  current  will  be  given  by 

*--g(e~*c)l (13) 

where  the  letters  have  the  same  meaning  as  they  have  in  Eq.  (12).  This 
current  is  evidently  of  the  same  shape  as  that  taken  by  the  charging 
operation  with  the  exception  that  there  is  a  minus  sign  before  it;  this 


38  FUNDAMENTAL  IDEAS  AND  LAWS  [CHAP.  I 

signifies  that  the  discharge  current  is  of  the  same  form  as  the  charging 
current,  but  it  flows  in  the  opposite  direction. 

Time  Constant  of  a  Condenser  Circuit. — The  quantity  RC  is  called 
the  time  constant  of  the  condenser  circuit;  it  is  evidently  the  time  taken 
for  the  current  to  fall  from  its  maximum  value  to  37  per  cent  of  this  value; 
another  way  of  defining  the  time  constant  of  a  condenser  circuit  is  in 
terms  of  the  charge  on  the  condenser;  the  time  constant  is  the  time  required 
for  the  condenser  to  accquire  63  per  cent  of  its  final  charge  or,  in  the  case 
of  the  discharging  condenser,  it  is  the  time  required  for  the  condenser 
to  lose  63  per  cent  of  its  charge. 

Fig.  29  shows  an  oscillogram  of  charge  and  discharge  which  was 
taken  from  the  circuit  shown  in  Fig.  28.  Some  extra  resistance  must 
be  necessarily  added  to  the  inherent  resistance  of  the  battery  and  con- 
denser because  the  time  constant  of  such  a  circuit  is  excessively  small, 
too  short  for  the  oscillograph  to  function.  Thus  a  one  microfarad 
condenser  in  series  with  two  ohms  (a  probable  value  for  the  battery) 
would  have  a  time  constant  of  .000  002  second,  that  is,  the  current 
would  rise  instantaneously  upon  closing  the  switch,  to  some  value  (de- 
pending upon  the  voltage  used  in  charging)  and  in  .000  002  second 
would  have  fallen  to  37  per  cent  of  this  value,  and  in  a  correspondingly 
short  time  would  have  dropped  to  practically  zero.  Such  an  instanta- 
neous occurrence  is  too  rapid  even  for  the  oscillograph,  hence  to  increase 
the  time  constant  to  a  value  suitable  for  the  use  of  the  oscillograph  an 
extra  resistance  had  to  be  introduced  in  the  circuit. 

The  effect  of  adding  resistance  in  series  with  a  condenser  to  be  charged 
is  shown  by  the  curves  of  Fig.  30;  these  were  calculated  from  Eq.  (12). 
They  show  that  the  initial  current  is  cut  down  as  the  resistance  is  increased, 
in  fact  being  equal  to  E/R,  and  that  the  duration  of  the  current  increases 
with  the  increase  of  resistance.  The  area  between  the  X  axis  and  any  one 
of  the  curves  is  the  same;  this  area  represents  the  quantity  of  electricity 
on  the  condenser  and  so  must  be  the  same  for  all  conditions,  because  the 
quantity  of  electricity  on  the  condenser  after  the  charging  process  is  com- 
plete is  the  same  no  matter  what  the  resistance  of  the  circuit  may  be. 

Power  Expended  in  a  Continuous-current  Circuit. — If  a  current  of  7 
amperes  is  caused  to  flow  through  a  circuit  by  an  e.m.f.  of  E  volts  the 
rate  of  doing  work  in  the  circuit  is 

Watts  =  EI, (14) 

If  the  circuit  has  a  resistance  R  we  know  that  E  =  IR  and  so 

Watts  =  IRXI  =  PR    .......     (15) 

from  which  we  get 

r>    Watts  f 

R=     r>    , (16) 


TIME   CONSTANT  OF   CONDENSER  "CIRCUIT 


39 


40 


FUNDAMENTAL  IDEAS  AND  LAWS 


[CHAP.  I 


Eq.  (16)  is  important;  it  is  the  broadest  possible  definition  for  the 
resistance  of  a  circuit.  This  formula  gives  the  resistance  for  any  kind  of 
current  flow,  whether  continuous,  pulsating,  or  alternating.  In  words  it  is 
stated  thus:  the  effective  resistance  of  a  circuit  is  equal  to  the  amount  of 
power  consumed  by  the  circuit  divided  by  the  square  of  the  current  required 
to  supply  this  power. 

In  simple  continuous  current  circuits  Ohm's  law  is  sufficient  to  obtain 
the  resistance  of  the  circuit,  but  there  are  many  cases  especially  in  alter- 


W 

9 
8 

I7 

I  6 
c 

i  5 

L 


\ 


r  charged 


to  lOO 


olts 


of  condenser 


Dhms 
3hms 


2  x  10  *  fa 


rad 


R  = 


10 


20 


Curve 


40 


Jams 


\\ 


.1,       .2         .3         .4         .5         .6.        .7         .8         .9         1.0       1.1       1.2       1.3       14      J-5 
TimeJixlOOOths  Seconds 

FIG.  30. — Condenser  charging  currents  for  different  values  of  series  resistance. 


nating  current  work,  where  Eq.  (16)  affords  the  only  feasible  means  of 
determining  the  resistance  of  the  circuit. 

Power  Consumed  in  a  Circuit  Excited  by  Pulsating  Current. — In  case 
the  voltage  or  current  of  a  circuit,  or  both  of  them,  are  pulsating  the  power 
consumed  in  the  circuit  cannot  be  obtained  by  using  the  product  of  the 
average  voltage  by  the  average  current,  as  might  at  first  seem  correct; 
an  error  would  be  introduced  making  the  power  consumed  too  low,  the 
amount  of  this  error  depending  upon  the  amount  of  fluctuation.  The 
greater  the  amount  of  fluctuation  or  pulsation  of  the  current  or  voltage, 
the  greater  is  the  error  introduced. 


POWER  USED   BY   PULSATING  CURRENT  41 

The  power  is  accurately  obtained  only  by  taking  the  product  of  the 
effective  resistance  of  the  circuit  and  the  square  of  the  effective  value  of 
the  current.  The  derivation  of  the  effective  value  of  the  current  may 
be  difficult;  it  can  always  be  carried  out  graphically  if  the  form  of  the 
pulsating  current  is  accurately  given,  but  is  not  easily  calculated  by 
ordinary  arithmetic  unless  the  form  of  the  pulsation  is  very  simple.  TThlis 
suppose  that  a  pulsating  current  is  simple  enough  to  be  represented  by 
a  continuous  current,  with  a  sine  wave  alternating  current  superimposed, 
as  shown  in  Fig.  31.  The  actual  pulsating  current  A  is  sufficiently  well 
represented  by  the  continuous  current  B,  of  amplitude  /i,  and  a  sine  wave 
current  C,  of  maximum  value  /2.  The  effective  value  of  such  a  current 
is  given  by  taking  the  square  root  of  the  sums  of  the  squares  of  the  effect- 
ive values  of  the  two  components.  The  effective  value  of  the  continu- 
ous current  is  the  same  as  its  actual  value,  /i;  the  effective  value  of  the 


FIG.  31. — Pulsating  current  equivalent  to  a  continuous  current  with  alternating  current 

superimposed. 

sine  wave  of  current  is  the  square  root  of  one-half  its  (maximum  value).2 
Hence  the  effective  value  of  the  pulsating  current  is  v//12-{-^/22.  The 
power  used  when  such  a  current  flows  through  a  circuit  of  resistance  R  is 

Watts  used  =  /i2#+i/22tf 

If  the  average  value  of  the  current  were  used  in  calculating  the  power 
used,  the  power  represented  by  the  second  term  would  be  completely 
neglected,  and  so  an  error  would  be  incurred  equal  to  J/22/?.  The  amount 
of  this  error  depends  upon  the  amount  of  pulsation  of  the  current.  In 
such  a  circuit  as  the  primary  circuit  of  spark-coil  transmitting  set  excited 
by  storage  battery  the  error  would  be  very  large,  and  the  power  used  in 
the  circuit  cannot  be  obtained  at  all  accurately  without  knowing  the  form 
of  the  current  flowing  in  the  primary  winding  of  the  coil. 

The  above  statement  is  made  with  the  idea  in  mind  that  in  such  a 
circuit  as  this,  excited  by  storage  battery,  a  direct-current  ammeter  would 


42  FUNDAMENTAL   IDEAS   AND   LAWS  [CHAP.  I 

be  used  in  measuring  the  current.  Now  such  an  ammeter  reads  average 
values  and  so  would  read,  when  excited  by  such  a  current  as  sketched 
in  Fig.  31,  only  the  continuous-current  component.  Hence  the  error 
pointed  out  would  occur.  If,  however,  an  alternating  current  ammeter 
were  used  for  reading  the  current,  the  error  would  not  occur,  because  such 
an  ammeter  reads  effective  values,  and  not  average  values.  If  the  power 
used  in  a  pulsa ting-current  circuit  is  to  be  accurately  determined,  there- 
fore, an  alternating-current  ammeter  must  be  used  to  measure  the  current. 

The  above  analysis  of  the  power  used  in  pulsating-current  circuits 
holds  good  only  when  the  resistance  is  constant  throughout  the  cycle 
of  current  variation.  In  many  circuits  this  is  not  so,  the  resistance  being 
a  function  of  the  current  and  so  changing  as  the  current  changes.  The 
calculation  of  the  power  used  in  such  a  circuit  is  not  easily  measured  by 
ammeters  and  voltmeters;  either  a  wattmeter  or  the  oscillograph  must  be 
used.  The  wattmeter  is  an  instrument  having  two  windings  in  the  same 
case,  one  corresponding  to  an  ammeter  and  the  other  to  a  voltmeter. 
An  analysis  of  its  action  and  the  way  in  which  it  is  used  will  be  taken 
up  in  a  subsequent  paragraph  dealing  with  the  power  used  in  an  alter- 
nating-current circuit.  The  oscillograph,  giving  the  form  of  voltage  curve 
and  current  curve,  makes  it  possible  to  calculate  the  power  by  graphical 
methods. 

Current  Flow  in  an  Alternating-current  Circuit  Having  Resistance 
only.  Phase. — If  an  alternating-current  generator  is  connected  to  a  circuit 
having  resistance  only  the  relation  between  current,  resistance,  and  volt- 
age is  given  by  Ohm's  law.  It  is,  of  course,  impossible  to  construct  a 
circuit  "  with  resistance  only  ";  a  circuit  must  have  some  inductance  and 
capacity  no  matter  how  it  is  built,  but  if  the  amount  of  inductance  and 
capacity  are  so  small  that  their  influence  upon  the  current  is  negligible 
compared  to  the  influence  of  the  resistance,  the  circuit  may  be  considered 
to  have  nothing  but  resistance  opposing  the  flow  of  current.  The  filament 
of  an  incandescent  lamp  is  such  a  circuit.  A  rheostat  constructed  of  high- 
resistance  wire  may  be  considered  to  have  no  inductance  when  being  used 
in  ordinary  alternating-current  circuits,  such  as  used  for  power  and  light- 
ing, but  such  a  rheostat  would  probably  have  such  an  amount  of  induc- 
tance that  when  used  in  a  circuit  of  radio  frequency  it  would  be  by  no 
means  negligible.  It  follows  that  a  certain  piece  of  apparatus  might  be 
considered  free  from  inductance  for  some  uses,  but  for  other  circuits  the 
inductance  might  be  of  considerable  importance. 

In  a  circuit  having  resistance  only  the  current  and  voltage  have  the 
same  phase  and  are  similar  in  form.  A  current  and  voltage  are  said  to 
be  in  phase  when  they  pass  through  their  corresponding  values  simulta- 
neously. The  easiest  point  from  which  to  judge  the  equality  of  phase  is 
the  zero  value;  if  the  two  curves  pass  through  their  zero  values  at  the 


PHASE  AND   PHASE   DIFFERENCE 


43 


same  instant  they  are  in  phase.  In  case  the  current  passes  through  its 
zero  value  after  the  voltage  has  passed  through  its  zero  value  it  is  said 
to  be  a  lagging  current;  if  it  goes  through  the  zero  value  before  the  voltage 
it  is  said  to  be  a  leading  current. 

In  Fig.  32  are  shown  curves  of  current  and  voltage  with  (a)  current 
and  voltage  in  phase,  (6)  with  current  lagging  behind  the  voltage  by  the 
angle  <£,  and  (c)  with  the  current  leading  the  voltage  by  the  angle  <£. 

The  magnitude  of  the  angle  of  lag  or  lead  may  be  easily  approximated 
when  it  is  remembered  that  the  time  from  one  zero  point  to  the  next  zero 


Time 


\ 


FIG.  32. — Phase  difference  of  alternating  current  and  voltage. 

point  of  the  same  curve  is  180°;  in  curve  b  the  current  lags  by  about  30° 
and  in  curve  c  the  angle  of  lead  is  about  70°. 

In  case  the  circuit  has  i  esistance  only  the  relation  between  voltage  and 
current  is  expressed  by  Ohm's  law,  whether  instantaneous,  maximum,  or 
effective  values  are  considered.  Thus  the  equation  for  current  flow  in 
this  circuit  is 


R' 


(17) 


Power  Used  in  a  Resistance  Circuit. — The  rate  at  which  electrical 
energy  is  changed  into  heat  by  a  current  i  flowing  through  a  resistance 


44 


FUNDAMENTAL  IDEAS   AND   LAWS 


[CHAP.  I 


R  is  i2R,  as  has  been  shown  for  continuous-current  circuits.     Or,  as  we 
know  that  for  the  circuit  e  =  iR  we  have, 

Rate  of  heat  development  =  power  used  =  e  i 

The  power  curve  has  the  form  shown  in  Fig.  33;  it  is  at  all  times 
positive,  because  although  both  e  and  i  go  through  negative  values  they 
both  reverse  at  the  same  instant;  the  product,  therefore,  is  constantly 
positive.  The  maximum  value  of  this  power  curve  occurs  when  both  e 
and  i  pass  through  their  maximum  values  and  is  therefore  equal  to  Emlm. 


FIG.  33. — Power  curve  for  an  alternating  current  circuit  containing  resistance  only. 

If  the  equation  of  current  is  i  =  Im  sin  cot  and  the  equation  of  voltage 
is  e  —  Em  sin  u>t,  the  equation  of  the  power  curve  must  be 


p  =  EmIm  sin2  ut 


(18) 


The  average  value  of  cos  2ut  is  zero,  hence  the  average  value  of  power 
=  P  =  iEmIm=EI (19) 

It  is  seen  therefore  that  the  power  (in  watts)  used  in  an  alternating- 
current  circuit  containing  resistance  only  is  the  product  of  volts  and 
amperes,  as  read  by  alternating  current  voltmeter  and  ammeter. 

Meters  Used  in  Alternating-Current  Circuits. — It  must  be  remembered 
that  the  ordinary  continuous-current  instrument,  ammeter  or  voltmeter, 
will  not  read  at  all  if  used  in  an  alternating-current  circuit.  Such  instru- 
ments read  the  average  value  of  voltage  or  current  and,  in  an  alternating- 
current  circuit  the  average  values  are  zero.  To  read  correctly  on  an 
alternating-current  circuit  an  instrument  must  give  the  same  reading  on 
a  continuous-current  circuit,  no  matter  which  way  the  continuous  current 
is  flowing  through  it;  everyone  familiar  with  the  ordinary  continuous- 


METERS   USED  IN  ALTERNATING-CURRENT  CIRCUITS          45 

current  instrument  knows  that  if  the  connection  of  the  meter  to  the  cir- 
cuit is  reversed  the  reading  will  reverse.  Such  an  instrument,  if  actuated 
by  an  alternating  current,  would  tend  to  oscillate  between  a  certain  direct 
reading  and  the  equal  reversed  reading,  but,  as  the  alternating  current 
reverses  too  rapidly  for  the  needle  of  a  meter  to  follow,  it  is  evident  that 
the  meter  would  read  zero  no  matter  how  much  current  was  flowing 
through  it. 

Various  types  of  meters  are  suitable  for  use  on  an  alternating-current 
circuit,  the  dynamometer  type,  the  soft-iron  vane  type,  the  induction 
type,  the  thermo-couple  type  and  the  hot  wire  type.  The  last  two  types 
named  are  used  almost  exclusively  for  making  measurements  in  radio 
circuits,  as  it  is  practically  impossible  to  make  the  other  types  function 
properly  at  the  very  high  frequencies  used  in  radio  work. 

Transient  Current  on  Switching  a  Resistance  Circuit  to  an  A.C.  Line. — 
If  a  resistance  circuit  is  switched  to  an  a.c.  line  the  current  rises  instanta- 


Time  of  closing  switch 


Current  rises  at  once 
to  its  proper  value 


FIG.  34. — Current  on  switching  a  resistance  circuit  to  an,a.c.  line. 

neously  to  the  value  it  should  have,  depending  upon  the  value  of  the  volt- 
age at  the  instant  the  switch  is  closed,  as  shown  in  Fig.  34.  This  condition 
of  affairs  is  expressed  by  stating  that  there  is  "no  transient  current "  or 
no  transient  condition,  after  closing  the  switch;  the  current  rises  at  once 
to  the  value  it  would  have  had  (at  the  time  of  closing  the  switch)  in  case 
the  switch  had  been  closed  at  some  previous  time. 

Current  Flow  in  an  A.C.  Circuit  Having  Inductance  and  Resistance. — 
Suppose  that  an  inductance  (without  resistance)  and  a  resistance,  con- 
nected in  series,  are  connected  to  an  a.c.  line  so  that  an  alternating  e.m.f. 
is  impressed,  as  indicated  in  Fig.  35.  Although  the  inductance  must 
really  have  resistance,  it  is  shown  as  resistanceless,  all  the  resistance  of 
the  circuit  being  supposed  concentrated  in  R.  The  current  flowing  in 
such  a  circuit  depends  upon  four  things,  L,  E,  R,  and  the  frequency  of 
the  impressed  e.m.f.  Provided  that  L  and  R  are  constant  throughout 
the  cycle  (do  not  vary  with  the  value  of  the  current)  it  is  a  fundamental 
law  of  electrical  circuits  that  the  current  will  have  the  same  form  as  the 


46 


FUNDAMENTAL  IDEAS   AND   LAWS 


[CllAl-.    1 


impressed  force.     We  may  therefore  assume  that  the  current  is  a  sine 
wave  and  then  find  its  magnitude  and  phase. 

The  impressed  voltage  must  be  equal  to  the  sum  of  the  drops  in  poten- 
tial across  L  and  R. 

T 

Drop=  a)  LI 


To  Supply  of 
alternating  Emf 


Drop  =  I  R 


FIG.  35. — Resistance  and  inductance  in  series  connected  to  an  a.c.  line. 


Suppose  the  current  to  be  i  =  Im  sin  ut. 


The  drop  across  the  resistance 


ImR  sin 


The  drop  across  the  inductance  =  Ldi/dt  =  coL7TO  cos 
The  impressed  voltage  must  be 


=  Im(R  sin 


cos  coO (20) 


In  Fig.  36  these  two  component  voltages  are  snown  as  curves;    the 
impressed  voltage  e  must  be  equal  at  all  times  to  the  sum  of  the  resistance 


Impressed  Voltage 


FIG.  36. — Voltage  components  in  an  a.c.  circuit  containing  inductance  and  resistance. 

drop  and  the  inductance  drop,  and  is  so  shown  by  the  curve  marked  e  in 
Fig.  36. 


CIRCUITS   CONTAINING   RESISTANCE   AND   INDUCTANCE         47 


A  vector  diagram  representing  the  curves  of  Fig.  36  is  given  in  Fig. 
37;  effective  values,  instead  of  maximum  values,  are  shown.  From  this 
diagram  we  have 


or 


-. 
Z 


(21) 


wLI 


O  RI 

FIG.  37. — Vector  diagram  for  an  a.c.   circuit   containing   inductance  and   resistance 

in  series. 

The  quantity  wL  is  called  the  reactance  of  the  circuit  and  the  quantity 
Z  is  called  the  impedance  of  the  circuit.  The  current  lags  behind  the  volt- 
age by  the  angle  0,  which  is  determined  by  the  relation 

R  uL 

cos  0  =  i=   or   tan  0  =  — . 


FIG.  38. — Power  curve  for  an  a.c.  circuit  containing  inductance  and  resistance. 

Power  Used  in  an  Inductive  Circuit. — The  power  used,  at  any  instant, 
in  the  circuit  of  Fig.  35  is  obtained  by  multiplying  the  instantaneous  value 
of  e  by  that  of  i\  it  is  shown  by  the  power  curve  in  Fig.  38.  For  this 
circuit  it  is  evident  that  the  power  is  sometimes  negative,  i.e.,  the  circuit, 


48  FUNDAMENTAL   IDEAS   AND   LAWS  [CHAP.  I 

instead  of  drawing  power  from  the  line,  is  actually  furnishing  power  to 
the  line.     Energy  which  has  been  stored  in  the  magnetic  field  of  the  induc- 
tance, is  flowing  back  into  the  source  of  power  supply. 
The  expression  for  the  power  is, 


p  =  Em  sin 
=  EmIm  sin  totfXsin  (ut  —  <t>) 

The  average  value  of  this  expression  is  given  by  average  value  of  the 
expression 

E  I 

p  =  -~  cos  </>  (1  -cos  2  co/)      ...     (22) 

because  the  average  value  of  Emlm  sin  ut  cos  ut  sin  </>  is  evidently  zero. 
So  average  pcwer 

P  =  EIcos<J) (23) 

The  power  in  the  circuit  is  equal  to  the  product  of  the  volts  and  amperes 
in  the  circuit  and  the  quantity  cos  <£.  For  this  reason  cos  cf>  is  called  the 
power  factor  of  the  circuit:  it  may  have  any  value  between  unity  and 
zero.  In  ordinary  power  circuits  it  has  a  value  between  about  0.7  and 
0.95,  very  seldom  being  unity.  In  some  parts  of  efficient  radio  circuits 
the  power  factor  may  be  as  small  as  .005. 

The  power  may  be  expressed  ir  terms  of  current  and  resistance  by 
changing  the  form  of  Eq.  (23). 

P  =  EI  cos  4> 

V#2+(coL)2 

p 

PR.     .     (24) 

This  equation  for  the  power  used  in  an  a.c.  circuit  is  really  a  definition 
of  the  effective  resistance  of  the  circuit;  the  resistance  of  the  circuit,  for 
alternating  current,  may  be  entirely  different  from  the  continuous-current 
resistance  of  the  circuit.  There  are  many  effects  which  combine  to  make 
the  a.c.  resistance  sometimes  several  times  as  great  as  the  c.c.  resistance 
(or  the  a.c.  resistance  may  be  negative  even,  while  the  c.c.  resistance  is 
positive)  and  the  only  way1  of  measuring  this  resistance  is  by  use  of  Eq. 
(24).  The  power  used  in  the  circuit  is  measured  by  a  wattmeter,  the 
current  by  an  ammeter,  and  the  resistance  found  by  the  relation 

T-cc    j.-                         watts  /OEN 

Effective  resistance  =  —f*- (25) 

1  If  the  circuit  is  such  that  a  measurement  in  an  alternating  current  Wheatstone 
bridge  is  feasible,  of  course  such  method  also  is  available.  Even  in  the  bridge  deter- 
mination the  idea  expressed  in  Eq.  (24)  is,  however,  involved. 


POWER  USED  IN  INDUCTIVE  CIRCUITS  49 

Wattmeter.  —  It  is  generally  not  possible  to  measure  the  power  used 
an  a.c.  circuit  by  use  of  Eq.  (23)  because  the  phase  difference  of  the  volt- 
and  current  is  not  known  and  there  is  no  easy  method  of  measuring 
directly.      To  get  the  power  used  in  an  a.c.  circuit  it  is  nearly  always 
lecessary  to  use  a  wattmeter.     This  is  an  indicating  instrument,  resembling 
ammeter  or  voltmeter  externally,  but  differing  from  these  instruments 
that  it  has  two  independent  electrical  circuits.     Two  coils  inside  the 
tent,  one  in  shunt  with  the  circuit,  and  one  in  series  with  it,  react 
m  one  another  to  produce  the  force  which  moves  the  indicating  pointer. 
le  theory  involved  in  its  operation  is  explained  in  practically  any  text 
m  alternating-current  measurements  and  will  not  be  given  here.     The 
iale  of  the  meter  is  calibrated  directly  in  watts  and,  with  a  properly 
ilibrated  instrument,  the  reading  of  power  is  accurate  no  matter  what 
ic  power  factor  may  be  ;  for  very  small  power  factors,  and  for  circuits  of 
jquency  much  higher  than  that  for  which  the  meter  is  intended,  a  cor- 
rection may  be  necessary.1 

The  power  factor  of  an  a.c.  circuit  is  then  determined  from  the  readings 
of  three  instruments,  ammeter,  voltmeter,  and  wattmeter.  The  power 
factor,  cos  <£,  is  the  quotient  of  the  wattmeter  reading  by  the  product 
of  the  readings  of  the  other  two  instruments.  If  it  is  desired  to  know  the 
angle  <f>  itself,  it  is  only  necessary  to  consult  a  table  of  natural  cosines. 
The  effective  resistance  of  the  circuit  is  obtained  by  finding  the  quotient 
of  the  wattmeter  reading  and  the  square  of  the  ammeter  reading.  As 
stated  before,  this  resistance  will  generally  be  veiy  different  from  the 
resistance  measured  by  a  continuous-current  test. 

Variation  of  Current  with  Frequency  in  an  Inductive  Circuit.  —  The 
magnitude  of  the  current  flowing  in  a  circuit  consisting  of  a  resistance 
and  inductance  in  series  evidently  depends  upon  the  frequency  (see  Eq.  21). 
At  zero  frequency  (continuous  current)  this  equation  reduces  to  7  = 
E/R.  This  relation  holds  good  only  after  the  switch  has  been  closed  long 
enough  for  the  transient  condition  to  disappear  (see  Fig.  24). 

At  very  high  frequencies  the  resistance  becomes  negligible  compared 
to  the  reactance,  and  so  the  value  of  the  current  is  given,  very  nearly, 
by  the  equation  I  =  E/uL.  As  the  frequency  varies  between  high  and 
low  values,  voltage  being  held  constant,  the  current  varies  as  shown  in 
Fig.  39;  for  frequencies  sufficiently  high  that  R  is  small  compared  to  wL, 
the  curve  approximates  a  hyperbola, 

(26) 


Transient  Current  in  a  Circuit  Having  Inductance  and  Resistance.  — 

After  the  switch   has  been  closed  for  some  time  there  is  always  a  definite 
^ee  Morecroft's  Laboratory  Manual  of  Alternating  Currents,  p.  11. 


50 


FUNDAMENTAL  IDEAS  AND  LAWS 


[CHAP.  I 


relation  between  the  instantaneous  values  of  the  current  and  voltage; 
for  every  cycle  the  two  go  through  exactly  corresponding  values.     Thus 


in 

9 

8 

5 

\ 

<s 

I 

V 

L  l  $ 

|fl        E           ? 
1        i           ^ 

V 

\ 

7 

I6 

£ 
*  5 

4 
3 
2 
1 
0 

1 

\ 

\ 

Variation  of  current  with  frequency 

\ 

\ 

\ 

E=100        L=0.1        R=10 

\ 

\ 

\ 

\ 

\ 

^ 

\ 

x 

»s 

•v, 

\ 

>s«^ 

"  —  , 

*--^ 

**"****- 

^*"^* 

-—  . 

-  — 

—  -^ 

10         20         30         40          50         60         70         80         90         100 
-l£requency 

FIG.  39. — Current  variation  with  frequency  in  an  a.c.  circuit  containing  inductance  and 

resistance  in  series. 


FIG.  40.— Curves  of  e  and  i  in  a  circuit  containing  inductance  and  resistance,  for  steady 

state. 

in  Fig.  40,  when  e  has  a  maximum  value  AC,  the  current  has  the  value 
AB,  and  whenever  the  voltage  has  the  value  AC  the  current  will  have 


TRANSIENT  CURRENT  IN   INDUCTIVE  CIRCUIT 


51 


the  value  AB.  Now  suppose  the  switch  to  be  closed  when  the  voltage 
has  the  value  AC',  the  current  should  have  the  value  AB,  but  in  an  induc- 
tive circuit  the  current  cannot  rise  instantaneously;  this  was  shown  by 
the  oscillograms  in  Figs.  24  and  25.  The  complete  equation  for  the  cur- 
rent in  an  inductive  circuit  must  therefore  include  a  transient  term  as 
well  as  the  term  for  the  steady  state;  it  is  properly  written 


Rt 


sn   co£- 


Rt 


.     .     (27) 


The  second  part  of  the  current,  Ke    L ,  is  determined  in  magnitude 
by  the  value  of  the  current,  in  the  steady  state,  at  the  time  in  the  cycle 


Switch 


closed 


\ 


Steady  c 


rrent 


FIG.  41. — Curves  of  e  and  i  in  a  circuit  containing  inductance  and  resistance  for  transient 

state. 


corresponding  to  the  time  in  the  cycle  that  the  switch  is  closed.  Thus 
in  Fig.  41,  at  the  time  of  closing  the  switch  the  current  should  have  the 

value  AB;    this  fixes  the  value  of  K  in  Eq.  (27).     In  Fig.  41  are  plotted 

_m 

the  steady  value  of  the  current  i,  the  transient  current  Ke  ~ L ,  and  the 
actual  current  for  the  first  cycle  after  closing  the  switch;  this  actual  cur- 
rent is  the  sum  of  the  other  two. 

In  Figs.  42  and  43  are  shown  oscillograms  of  the  current  flowing  in 
an  inductive  circuit  for  the  first  few  cycles  after  the  switch  had  been  closed; 
in  one  the  switch  was  closed  at  the  peak  of  the  voltage  and  in  the  other 
it  was  closed  when  the  voltage  was  very  nearly  zero.  In  Fig.  42  the  effect 
of  the  transient  term  is  plain;  the  current  (steady  value)  has  been  plotted 
in  dotted  lines,  as  has  also  the  transient  term,  the  latter  having  been 


52 


FUNDAMENTAL  IDEAS  AND  LAWS 


[CHAP.  I 


1 

I 
•8 

tn 

1 


« 


n3    o 


II 

M      02 

.a 


|S 


CIRCUITS   HAVING   IRON   CORE  INDUCTANCE 


53 


Iculated  from  the  value  of  the  steady  current  at  the  time  the  switch 
was  closed  and  the  L  and  R  of  the  circuit.  It  may  be  seen  that  the  actual 
current  is  correctly  given  by  Eq.  (27).  In  Fig.  43  the  switch  was  closed 
at  that  part  of  the  e.m.f.  cycle  which,  in  the  steady  state,  is  the  proper 
time  for  the  current  to  be  zero;  it  is  seen  that  for  this  case  the  transient 
term  reduces  to  zero,  and  the  actual  current  is  represented  completely 
by  only  the  first  term  of  Eq.  (27). 

Circuits  Having  Resistance  and  Iron-core  Inductance.— In  case  the 
L  of  the  circuit,  Fig.  35,  consists  of  an  inductance  having  a  closed  iron 
path  for  its  magnetic  circuit,  the  conclusions  deduced  will  not  be  correct. 
The  value  of  L  in  this  case  is  not  constant,  but  varies  throughout  the 


FIG.  43. — Oscillogram  illustrating  absence  of  transient  current  in  an  inductive  circuit. 


cycle,  and  for  this  reason  the  relation  between  the  current  and  voltage 
is  a  complex  one;  the  current  in  this  case  requires  an  equation  with  an 
infinite  number  of  terms  to  express  it  accurately.  The  current,  instead 
of  being  sinusoidal,  has  a  decided  hump,  as  shown  by  Fig.  44,  which  shows 
the  magnetizing  current  of  a  closed-core  transformer. 

Not  only  is  vthe  steady  value  of  current  in  such  a  circuit  irregular, 
but  the  transient  current  may  show  even  greater  irregularities.  This 
irregularity  may  last  for  many  cycles,  depending  upon  the  kind  of  iron 
used  in  the  core  and  upon  its  condition  of  magnetization  at  the  time  the 
switch  is  closed,  as  well  as  upon  the  part  of  the  cycle  selected  for  the  clos- 
ing of  the  switch.  Thus  in  Fig.  45  is  shown  the  current  in  the  primary 
circuit  of  a  transformer  for  a  few  cycles  after  closing  the  switch;  the  tran- 
sient current  may  be  so  large  in  this  case  that  during  the  first  cycle  the 
current  never  reverses  its  direction. 


54 


FUNDAMENTAL  IDEAS   AND   LAWS 


[CHAP.  I 


I 


TRANSIENT  CURRENT  WITH  IRON  CORE  INDUCTANCE    55 

The  rise  of  current  in  such  an  inductive  circuit  as  this  is  not  as  simple 
as  that  illustrated  in  Fig.  24;  the  analysis  given  in  explaining  this  figure 
assumed  constant  L  so  will  not  hold  good  if  L  varies  during  the  rise  of 


FIG.  45. — Oscillogram  showing  the  transient  current  when  switching  an  iron  core 
inductance  to  an  a.c.  line. 

current.  The  actual  form  of  rising  current  in  such  a  circuit,  when  con- 
nected to  a  c.c.  line,  is  shown  in  Fig.  46;  it  is  quite  evidently  different 
from  that  shown  in  Fig.  24,  which  was  for  an  air-core  inductance. 


FIG.  46. — Peculiar  growth  of  current  when  an  iron  core  inductance  is  switched  to  a 
source  of  continuous  e.m.f. 

Current  Flow  in  a  Condenser. — By  the  definition  of  a  condenser  no 
electrons  can  actually  pass  from  one  plate  to  the  other;  they  are  insulated 
from  one  another.  If,  however,  a  condenser  is  connected  to  a  source  of 


56 


FUNDAMENTAL  IDEAS  AND   LAWS 


[CHAP.  I 


alternating  e.m.f.,  current  will  flow  in  this  circuit,  as  may  be  seen  by  the 
reading  of  an  a.c.  ammeter  placed  in  series  with  the  condenser. 

Suppose  a  condenser  of  capacity  C  farads  is  connected  to  a  line  the 
e.m.f.  of  which  is  given  by  the  equation  e  =  E  sin  ut.  The  condenser  will, 
of  course,  take  enough  charge  to  bring  the  potential  difference  of  its  plates 
continually  equal  to  that  of  the  line  to  which  it  is  connected.  As  this 
impressed  e.m.f.  continually  varies  in  magnitude  and  direction,  electrons 
must  be  continually  running  in  and  out  of  the  condenser  to  maintain  its 
plates  at  the  proper  potential  difference.  This  continual  charging  and 
discharging  of  the  condenser  constitutes  the  current  read  by  the  ammeter. 
The  electrons,  the  motion  of  which  constitutes  the  current,  do  not  actually 
pass  from  one  plate  of  the  condenser  to  the  other  through  the  dielectric; 


FIG.  47.  —  Current  and  voltage  for  a  perfect  condenser  connected  to  an  a.c.  line. 

they  merely  flow  in  and  out  of  the  condenser.  With  this  idea  in  mind 
it  is  easy  to  see  why  the  changing  current  of  a  condenser  increases  with 
the  capacity  of  the  condenser,  also  with  the  frequency  of  the  impressed 
e.m.f. 

The  magnitude  of  the  charging  current  is  obtained  as  follows: 

The  charge  q  =  Ce  and  the  current  i  =  dq/dt. 


Now  q  =  CEm  sin  ut, 


so 


(28) 


This  current  is  then  of  the  same  form  as  the  impressed  e.m.f.  (a  cosine 
curve  is  similar  to  a  sine  curve  in  form)  but  leads  it  by  90°  as  shown  in 
Fig.  47;  its  maximum  value,  in  amperes,  is  equal  to  uCEm. 

In  effective  values  the  relation  between  the  impressed  voltage  and 
the  charging  current  is, 

...       (29) 


I  CIRCUITS  CONTAINING  RESISTANCE  AND  CAPACITY  57 

is  evident  that,  other  things  being  equal,  the  charging  current  of  a  con- 
nser  is  directly  porportional  to  the  frequency  of  the  impressed  e.m.f. 
mis  should  be  contrasted  to  the  inductive  circuit  in  which  the  current 
varies  inversely  as  the  frequency,  if  the  resistance  is  small  compared  to 
the  reactance. 

The  relation  between  the  current  and  voltage  may  be  written 

(30) 


The  quantity        n  is  called  the  reactance  of  the  condenser,  generally 

27T/C 

specified  as  capacity  reactance  to  distinguish  it  from  inductance  reactance 

27T/L. 

Condenser  and  Resistance  in  Series.  —  If  a  condenser  and  resistance 
are  connected  in-  series  and  a  sine  wave  of  voltage  is  impressed,  a  sinu- 
soidal current  will  flow;  its  magnitude  and  phase  depend  upon  the  R, 
C,  E,  and  /  of  the  circuit.  Suppose  this  current  to  be  given  by  i  =  Im  sin  ut. 

The  resistance  drop  =  ImR  sin  coZ. 

The  capacity  reactance  drop,  in  magnitude,  is  —  ^  cos  coZ.  But  as  shown 

wC 

before,  the  current  leads  the  voltage  impressed  on  a  condenser;  the  capacity 
drop  is  therefore  properly  written, 

Capacity  drop  =  —  —  £  cos  ut 
coC 

The  impressed  voltage  must  be  the  sum  of  the  drop  over  the  resistance 
and  that  over  the  condenser  and  is  so  shown  in  Fig.  48.  The  current  leads 
the  impressed  voltage  by  the  angle  </>,  the  magnitude  of  which  is  fixed  by 
the  relative  magnitudes  of  the  reactance  and  resistance  drops. 

The  three  curves  of  Fig.  48  are  shown  vectorially  in  Fig.  49,  effective 
values  being  used  instead  of  maximum  values.  From  this  vector  diagram 
we  have 


or 

(31) 


and 

J_ 

P"y  1 

(32) 


58 


FUNDAMENTAL  IDEAS  AND  LAWS 


[CHAP.  I 


The  current  in  the  circuit,  as  shown  in  Eq.  31,  evidently  depends  upon 
the  frequency;  its  variation  as  the  frequency  is  changed,  is  shown  in  Fig. 
50.  At  very  high  frequency  the  current  approaches  the  value  E/R,  the 


Impressed  emf 


R  i  drop 


RI 


FIG.  48.  —  Voltage  and  current  curves  for  circuit  containing  R  and  C,  in  series. 

capacity  reactance  being  negligible,  while  at  zero  frequency,  the  current 

is  zero,  the  condenser  being  equivalent  to  an  open  circuit. 

Transient  Current  in  a  Circuit  Consisting  of  Resistance  and  Condenser 

in  Series.  —  In  general  there  will  be  a  transient  current  when  switching 

such  a  circuit  to  an  a.c.  line; 
the  duration  of  the  transient 
term  is  so  short,  however,  on 
all  commercial  circuits  that  an 
oscillogram  shows  the  current 
rising  immediately  to  its  proper 
value,  this  being  fixed  by  the 
time  on  the  e.m.f.  cycle  that  the 
switch  is  closed. 

Current  Flow  in  a  Circuit 
Having  Resistance,  Inductance, 
and  Capacity  in  Series.  —  The 
current  flowing  in  the  circuit 
shown  in  Fig.  51  will  require 

three    components    of   e.m.f.,  the    resistance    drop  IR,  the    inductance 

drop   27T/L7,  and   the    capacity  drop  _-—  —  .     The   resistance    drop   is  in 


FIG.  49. — Vector   diagram   of   voltages  and 
current  for  circuit  containing  R  and  C 


phase  with  the  current,  the  inductance  drop  is  90°  ahead  of  the    current 


EFFECT  OF  FREQUENCY   IN   CONDENSIVE   CIRCUIT 


59 


10 


£6 


R 


E=200 


10         20         30         40         50         60         70         80         90        100 
Frequency 

FIG.  50. — Variation  of  current  with  frequency  in  circuit  containing  R  and  C  in  series. 


Drop  =o>  L  I 


To  Supply  of 
alternating  Euf. 


Drop=R 


FIG.  51.  FIG.  52. 

FIG.  51. — Circuit  containing  R,  L,  and  C  in  series. 
FIG.  52.— Vector  diagram  of  voltages  and  current  for  circuit  containing  R,  L  and  C  in 


series. 


60  FUNDAMENTAL  IDEAS  AND  LAWS  [CHAP.  I 

and   the    capacity  drop  is  90°  behind  the  current.     These  three  compo- 
nents of  the  impressed  e.m.f.  are  shown  vectorially  in  Fig.  52.     The  two 
reactance  drops  evidently  tend  to  neutralize  one  another. 
The  total  reactance  drop 


The  resultant  required  impressed  voltage  is  seen  to  be 

——i  f^r> 

rt-fn  I    > V°*/ 


and  the  magnitude  of  the  current  may  be  written 

E  E 


(35) 


The  phase  difference  between  impressed  voltage  and  current  is  fixed  by 
the  equation 

1 

cos  <t>  =  -&   or   tan  </>  = — (36) 

LJ  .ft 

The  reactance  of  the  circuit  may  either  be  positive  or  negative,  according 
to  which  component  of  the  reactance  predominates.     If  2irfL  is  greater 

than  n—ffj  the  reactance  is  positive  and  the  current  lags,  whereas  if  the 


capacity  reactance  is  the  greater,  that  current  leads  the  impressed  e.m.f. 

The  magnitude  of  the  current  will  evidently  depend  upon  the  frequency 
and  will  have  about  the  form  shown  in  Fig.  53.  At  zero  frequency  the 
condenser  offers  infinite  reactance  so  the  current  is  zero;  at  infinitely 
high  frequency  the  inductance  reactance  becomes  so  great  that  again  the 
current  approaches  zero;  at  some  intermediate  frequency  the  inductance 
reactance  just  balances  the  capacity  reactance  so  that  the  total  reactance 
is  zero.  For  this  frequency  the  current  has  a  maximum  value,  as  shown 
for  frequency  fr  in  Fig.  53.  The  form  of  this  curve  could  have  been  pre- 
dicted by  considering  the  two  curves  given  in  Figs.  39  and  50. 

Resonance. — For  such  a  circuit  as  shown  in  Fig.  51  there  will  always 
be  one  frequency  which  will  give  a  total  reactance  zero;  this  will  be  true 
no  matter  what  values  of  L  and  C  may  be  chosen.  At  this  frequency 
the  current  will  be  in  phase  with  the  e.m.f.  and  its  magnitude  will  be  a 
maximum,  being  limited  only  by  the  resistance  of  the  circuit,  I  =  E/R. 

The  frequency  at  which  this  occurs  is  called  the  resonant  frequency 
of  the  circuit;  it  is  at  this  frequency  that  most  radio  circuits  are  operated. 


RESONANCE  WITH  INDUCTANCE  AND  CAPACITY  IN  SERIES    61 

Unless  care  is  exercised  when  performing  experiments  on  resonance 
the  condensers  used  in  the  circuit  will  be  spoiled  by  the  puncturing  of 
the  dielectric  at  the  resonant  frequency.  For  any  frequency  whatever 
the  drop  across  the  condenser  is  fixed  by  the  relation, 

Ec  = 


0    20    40    60    80    100   120   140   160   180   200   220 

Frequency 

FIG.  53. — Variation  of  current  with  frequency  in  circuit  containing  R,  L,  and  C  in  series. 

If  we  substitute  in  this  equation  the  value  of  the  current,  in  terms  of 
impressed  voltage  and  resistance  we  get,  at  resonance, 


ZirfCR' 


(37) 


As  the  value  of        „     may  be  much  greater  than  unity  so  the  voltage 

across  the  condenser  may  be  many  times  as  great  as  the  impressed  voltage; 
in  a  certain  laboratory  circuit  used  in  preforming  low-frequency  resonance 
tests  the  drop  across  the  condenser  at  resonant  frequency  is  eighteen  times 
as  great  as  the  impressed  voltage.  At  this  frequency  the  drop  across  the  in- 
ductance is  equal  to  that  across  the  condenser,  but  this  excessive  voltage 


62  FUNDAMENTAL  IDEAS  AND  LAWS  [CHAP.  I 

across  the  inductance  coil  will  generally  do  no  harm.  In  radio  circuits 
it  is  possible  to  have  the  drop  across  the  inductance  and  condenser  as 
much  as  400  times  greater  than  the  impressed  voltage. 

Resonant  Frequency. — A  circuit  is  said  to  be  resonant  when  the  react- 
ance is  zero.     Therefore  we  have  for  the  resonant  frequency, 

2;r/L=    l 


27T/G" 

from  which  we  get  the  value  of  the  resonant  frequency 

•     .......     (38) 


I  n  this  equation  L  must  be  in  henries,  C  in  farads,  and  /  will  be  in  cycles 
per  second.  As  the  microfarad  is  the  usual  unit  of  capacity  a  more  con- 
venient form  is 

f-   100° 
'          ' 


C  being  in  microfarads.  In  determining  this  frequency  the  separate  values 
of  L  and  C  do  not  matter;  the  product  LC  is  the  quantity  which  fixes 
the  critical  frequency.  That  is,  a  circuit  having  L  =  .24  henry  and  C=10 
microfarads  will  be  resonant  at  the  same  frequency  as  one  which  has 
L  =  .06  henry  and  C  =  40  microfarads. 

The  sharpness  of  the  resonance  curve  is  determined  by  the  resistance 
of  the  circuit,  the  inductance  being  fixed,  the  less  the  resistance  the  more 
sharply  defined  is  the  resonant  frequency  and  the  larger  is  the  current 
at  the  resonant  frequency.  In  Fig.  54  are  shown  the  resonance  curves 
obtained  for  a  circuit  having  L  =  .15  henry  and  C  =  28.5  microfarads. 
The  one  curve  shows  the  variation  of  current  with  a  circuit  resistance  of 
5.8  ohms  and  the  other  shows  the  same  thing  after  the  resistance  had 
been  increased  to  17.2  ohms. 

In  a  low  resistance  circuit  the  resonance  is  said  to  be  sharp  and  in 
a  high  resistance  circuit  it  is  said  to  be  flat  or  dull. 

Series  Resonance  with  Varying  Capacity  —  Decrement.  —  If  the  fre- 
quency impressed  on  the  circuit  of  Fig.  51  is  held  constant  and  the  capac- 
ity or  inductance  varied,  resonance  curves  similar  to  those  in  Fig.  53 
will  be  obtained  except  the  variables  will  be  different.  Suppose  such  a 
curve  has  been  obtained,  as  shown  in  Fig.  55.  We  shall  now  show  how 
the  shape  of  the  curve  depends  upon  the  resistance  and  how  to  actually 
calculate  the  value  of  this  resistance  from  the  shape  of  the  curve,  provided 
that  the  value  of  L  is  known. 

The  quantity  which  is  actually  determined  from  the  resonance  curve 
is  the  ratio  R/2/L,  f  being  the  resonance  frequency  of  the  circuit.  This 


FORM  OF  RESONANCE  CURVE 


63 


ratio  is  called  the  decrement  of   the   circuit,  for   reasons  which  will   be 
apparent  when  the  subject  of  oscillations  is  discussed. 

Referring  to  Fig.  55,  let  CT  be  the  capacity  which  gives  resonance,  the 
current  for  this  value  of  capacity  being  IT.  Let  Ci  and  €2  be  the  two 
values  of  capacity,  one  greater  than  Cr  and  the  other  less  than  Cr,  which 
serve  to  reduce  the  current  to  7r-f-  V2  or  .707  Ir.  When  the  capacity  has 
the  value  Cr  there  is  no  effective  reactance  in  the  circuit,  so  we  have,  for 


andforC  = 


1  = 


E 


.707  IT 


100 


FIG.  54. — Effect  of  resistance  on  resonance  curve, 
which  can  be  true  only  on  condition  that  X2  =  R,  or 


27T/C2 


(40) 


which  can  be  true  only  if 


(41) 


64 


FUNDAMENTAL  IDEAS  AND  LAWS 


[CHAP.  I 


The  capacity  reactance  is  greater  than  the  inductance  reactance  for  Ci 
and  less  than  the  inductance  reactance  for  €2,  hence  the  reversal  of  the 
signs  in  front  of  the  reactance  terms  in  Eqs.  (40)  and  (41). 

Adding  (40)  and  (41)  we  get 

™-  ••••••  (42) 


or 


Multiplying  through  by  «— TJ-~  we  £e^> 

1_  _J 2# 

(27T/)2LCl        (27T/)2LC2  ~  27T/L 

'C2-Ci\       272 

(W 


C  i     C  j*      C  2 
Capacity 

FIG.  55. — Variation  of  current  with  capacity  in  a  resonant  circuit. 

Now  if  C2  and  Ci  do  not  differ  from  Cr  very  much  (say  10  per  cent)  we 
may  put  without  appreciable  error 

CiCi-a" (44) 

This  is,  of  course,  an  approximation,  and  is  more  nearly  true  the  sharper 
the  resonance  curve.     We  may  now  put, 

1_     /C2-Ci\  _  2R 

(27T/)2LCA     Cr    )~2riL'      •••••• 

But   (27r/)2  =  -^-  as  may  be  seen  by  writing  the  equation  for  resonance, 

f=———— 

2wVLCr 

Cr  being  the  «value  of  the  capacity  which  gives  resonance. 


DECREMENT  FROM   FORM   OF  RESONANCE   CURVE 


65 


So  (45)  becomes, 


C2-Ci      2R 


or 


Cr          2-rrjL 

R          IT  G2  —  Cl 


2/L     2      Cr 


(46) 


As  an  illustration  of  the  application  of  this  formula  suppose  that  the 
resonant  capacity  for  a  certain  circuit  is  32  microfarads  and  that  the  values 
of  C2  and  C\  are  34  microfarads  and  30.2  microfarads  respectively.  Then 
for  this  circuit  the  decrement,  generally  designated  by  the  Greek  letter 
d,  is 

R  ^TT  34-30.2 
2/L    2       32 


=  0.187 


The  decrement  may  also  be  calculated  from  a  resonance  curve  plotted 
with  frequencies  as  abcissse  as  given  in  Fig.  56;  we  have  derived  the 
formula  when  capaci- 
ty is  used  for  abscissae 
because  such  is  gen- 
erally the  case  in  ra- 
dio measurements.  If 
however,  frequency, 
is  used  as  abscissae, 
the  frequency  having 
been  varied  in  getting 
the  resonance  curve, 
L  and  C  having  been 
maintained  constant, 
the  derivation  of  5 
from  the  half  energy 
points  of  the  resonance 


ip 
W 


/l       fr      X> 

Frequency 


curve  is  as  follows: 


FIG.  56. — Variation  of  current  with  frequency  in  a  resonant 
circuit. 


27T/2L- 


27T/1C 

1 

27T/2C 


To  eliminate  C  from  these  two  equations,  multiply  them  by  2wfiC  and 
27r/2C  respectively  and  get  the  two  equations 


C((2T/2)2L-27T/2#}=1. 


66  FUNDAMENTAL  IDEAS  AND  LAWS 

Put  these  in  the  forms 


Combining 


So 


Dividing  by  /r,  the  resonant  frequency, 


[CHAP.  1 


fl(27T/l+27r/2)  =  L  {  (27T/2)2-  (27Tfl)2}  . 

fi_27r(/22-/12)_ 
2L~ 


- 

2/rL 


/r 


(47) 


/•    r  i    si    /~i 

For  a  given  circuit     f      is  approximately  equal  to  ~  — ^ — -.     This 

Jr  *         l/i 

follows  from  the  relation  between  frequency  and  capacity;  to  pro- 
duce a  certain  small  percentage  change  in  the  natural  frequency  of  a  cir- 
cuit it  is  necessary  to  change  the  capacity  of  the  circuit  by  twice  this 
amount,  the  frequency  varying  not  with  the  capacity,  but  with  the  square 
root  of  the  capacity. 

Flow  of  Current  in  Parallel  Circuits  and  Relation  of  Line  Current  to 
Branch  Currents. — When  a  circuit  consists  of  two  or  more  branches  in 
parallel  the  line  current  cannot  be  obtained  by  calculating  the  branch 
currents  and  adding  them  arithmetically  as  is  done  in  continuous  current 
circuits,  because  of  the  difference  in  phase  of  the  various  branch  currents. 
The  line  current,  instead  of  being  equal  to  the  arithmetical  sum  of  the 
branch  currents,  may  be  even  smaller  than  either  of  the  branch  currents 

and,  in  fact,  is  so  in 
many  radio  circuits.    It 
is  necessary  to  calculate 
3.67  ohms  not  only  the  magnitude 

of  the  different  branch 

.llohms         |  currents,  but  also  their 

phase ;  these  branch 
currents  are  then  added 
vectorially  to  give  the 
line  current. 

Suppose  a  circuit 
made  up  as  shown  in 
Fig.  57,  the  current  /i 

being  10  amperes,  in  phase  with  the  line  voltage  and  the  current  /2  being  15 
amperes,  leading  the  line  voltage  by  60°;    the  line  current  will  be  the 


^=E,,,sin  wt 


o 


420  microfarads 


FIG.  57. — Parallel  circuits. 


CURRENT  WITH   PARALLEL  CIRCUITS 


67 


vector  sum  of  10  and  15  as  shown  in  Fig.  58.  It  proves  to  be  21.8  amperes. 
The  angle  of  the  lead  is  found  by  the  relation  of  the  reactive  and  active 
components  of  the  line  current  (the  active  component  of  a  current  is  that 
component  which  is  in  phase  with  the  voltage  and  the  reactive  component 
is  that  which  is  90°  out  of  phase  with  the  voltage).  I\  has  no  reactive 
component  and  so  contributes  10  amperes  to  the  active  component  of  the 
line  current  only;  /2  has  a  reactive  component  equal  to  15  sin  60°  or 
13  amperes,  and  an  active  component  of  15  cos  60°  or  7.5  amperes.  The 
total  active  line  current  is  therefore  17.5  amperes  and  the  reactive  com- 
ponent is  13  amperes.  The  angle  of  lead  of  the  line  current  is  then 
tan-1  13/17.5  or  36.6°. 


1 2  cos  60  =7.5  amp. 
FIG.  58. — Vector  diagram  of  currents  in  the  parallel  circuit  shown  in  Fig.  57. 

If  the  impressed  voltage  is  110  volts  the  impedance  of  the 
branched  circuit  is  equal  to  110/21.8  or  5.05  ohms. 

The  equivalent  resistance  is  Z  cos  <f>  =5.05  cos  36. 6°  =  4.06  ohms. 
The  equivalent  reactance  is  Z  sin  0  =  5.05  sin  36. 6°  =  3. 02  ohms. 
The  equivalent  scrios  condenser  of  the  combined  circuit  is  found  by 

putting  the  reactance  equal  to  ^--77.     If  the  frequency  of  the  supply  is 

ZTTjL 

60  cycles  this  gives 

2—^77=3.02  ohms,  or  C'  =  654  microfarads. 

Hence  the  branched  circuit  shown  in  Fig.  57  is  exactly  equivalent  to 
the  single  circuit  shown  in  Fig.  59,  for  the  frequency  assumed;  for  a  dif- 
ferent frequency  other  values  of  equivalent  resistance  and  equivalent 
capacity  would  bo  obtained.  A  more  detailed  analysis  of  a  branched 
circuit,  using  complex  quantities,  is  given  elsewhere. 


68 


FUNDAMENTAL  IDEAS  AND  LAWS 


[CHAP.  I 


FIG.  59. — Simple  series  circuit  equivalent 
to  parallel  circuit  of  Fig.  57. 


In  case  the  branched  circuit  is  more  complex  than  that  given  in  Fig. 
57,  such  as  that  given  in  Fig.  60,  the  branched  part  must  first  be  replaced 
by  its  equivalent  single  circuit,  calculated  as  shown  for  Fig.  57;  the  resist- 
ance and  reactance  of  this  equivalent 
H  circuit  must   then   be   added   to  the 

§  resistance    and    reactance    of  Ri  and 

<>R=  3.02  ohms  .    . 

">  LI.     By    vectonally    combining   this 

total  resistance  and  reactance  the  im- 

__^__  pedance  of  the  simple  equivalent  cir- 

' -Lkrofarads        cuit  is  obtained. 

Impedance  of  a  Circuit  Made  Up 
of  L,  R,  and  C,  in  Series. — The 
reactance  of  this  circuit  is  calculated 
by  finding  the  sum  of  the  inductance 

and  capacity  reactances  at  all  the  frequencies  necessary;  the  equivalent 
resistance  of  this  circuit  is  independent  of  frequency  and  equal  at  all 
frequencies  to  the  actual  resistance,  R.  The  several  quantities  are  shown 

in  the  form  of  curves  in  Fig.  61.     The  reactance,  TTT;  ,  is  shown  negative; 

Z7T/C 

the  total  reactance,  X,  is  negative  at  frequencies  lower  than  the  resonant 
value  and  positive  above  this  value.  The  impedance  is  positive  for  all 
values  of  frequency,  having  its 
minimum  value  when  the  total 
reactance  X,  is  zero,  then  being 
equal  to  R. 

The  current  leads  the  volt- 
age for  frequencies  lower  than 
the  resonant  value  and  lags 
behind  the  voltage  for  higher 
frequencies. 

Impedance  of  a  Branched 
Circuit,  Having  L  and  R  in 
One  Branch  and  C  and  R  in 
the  Other. — The  simplest  way 

of  comprehending  the  impedance  of  this  complex  path,  Fig.  62,  is  to  calcu- 
late for  each  value  of  frequency,  the  magnitude  and  phase  of  the  current 
in  each  branch.  The  active  and  reactive  components  of  the  two  branch 
currents  are  then  calculated.  The  active  component  of  line  current  is 
found  by  adding  the  two  active  branch  currents  and  the  reactive  com- 
ponent of  the  line  current  is  found  by  adding  the  reactive  branch 
currents.  These  additions  are  to  be  algebraic;  in  the  case  of  the  active 
current  the  algebraic  sum  is  the  arithmetic  sum  but  the  reactive  current 
in  the  line  is  the  difference  of  the  reactive  currents  of  the  branches. 


p 


FIG.  60. — Series-Multiple  circuit. 


REACTANCE  AND   IMPEDANCE   FOR  SERIES   CIRCUIT 


69 


In  Fig.  63  is  shown  the  vector  diagram  for  frequency  above  the  reso- 
nant frequency  of  the  circuit;  the  line  current  in  this  case  leads  the  voltage 


(I. 


FIG.  61. — Variation  of  reactance,  resistance  and  impedance  with  frequency  in  a  circuit 
containing  L,  R,  and  C  in  series. 

so  the  equivalent  simple  circuit  would  consist  of  a  condenser  in  series  with 
a  resistance,  the  two  having  such  values  that  when  the  simple  circuit  was 

connected    to    a   line  voltage   E,  the         __^________ 

current  flowing    would    be    equal,  in 
magnitude  and  phase,  to  /  of  Fig.  63. 

In  Fig.  64  is  shown  the  condition 
when  impressed  frequency  is  so  ad- 
justed  that  the  reactive  currents  in 
each  branch  neutralize  each  other;  in 
this  case  the  simple  circuit  would  con- 
sist of  a  resistance  only.  The  resistance 
of  the  simple  circuit  would,  in  general, 
be  many  times  as  great  as  the  resist- 
ance in  the  actual  branched  circuit. 

In  Fig.  65  the  frequency  is  supposed  lower  than  the  resonant  frequency, 
the  current  taken  by  the  inductive  branch  being  greater  than  that  taken 


FIG.  62. — Branched  circuit,  having  L 
and  R  in  one  branch  and  C  and  R  in 
the  other. 


70 


FUNDAMENTAL  IDEAS  AND   LAWS 


[C 


r 


by  the  capacity  branch;  the  equivalent  simple  circuit  for  this  case  would 
consist  of  a  resistance  in  series  with  an  inductance. 

The  above  simple  analysis  shows  that  the  branched  circuit  of  Fig.  62 
may  be  represented  by  a  single  circuit,  but  the  constants  of  this  single 
circuit  must  be  made  to  vary  as  the  frequency  is  varied. 

The  equivalent  R  may  be  obtained  by  calculating  the  I2R  loss  in  each 
branch  and  adding  to  give  the  total  loss  in  the  circuit;  this  total  loss, 


FIG.  63. 


FIG.  64. 


FIG.  65. 


FIG.  63. — Vector  diagram  for  circuit  of  Fig.  62,  line  current  leading. 
FIG.  64. — Vector  diagram  for  circuit  of  Fig.  62,  line  current  in  phase  with  impressed 

e.m.f. 
FIG.  65. — Vector  diagram  for  circuit  of  Fig.  62,  line  current  lagging. 


divided  by  the  square  of  the  line  current  (obtained  vectorially  as 
shown  in  Figs.  63-65),  gives  the  equivalent  resistance  of  the  com- 
bination. 

The  equivalent  inductance  or  capacity  is  obtained  by  calculating  the 
reactive  component  of  the  impressed  e.m.f. ;  this  equals  E  sin  <£  where  E  is 
the  value  of  the  impressed  voltage  and  <f>  is  the  angle  between  the  impressed 
voltage  and  the  line  current.  This  value  of  e.m.f.,  E  sin  0,  is  put  equal  to 
27T/Z/7,  where  L'  is  the  equivalent  inductance  and  /  is  the  line 
current. 


ANALYSIS  OF   PARALLEL  CIRCUITS  71 

In  case  the  line  current  is  leading  sin  </>  is  negative  and  the  equivalent 
inductance  would  be  negative.  In  this  case  the  reactive  component  of 

the  impressed  voltage,  E  sin  0,  is  put  equal  to        .„, ,  where  C"  is  the 

equivalent  series  capacity  of  the  circuit. 

The  circuit  is  analyzed  exactly  most  easily  by  the  use  of  complex  alge- 
bra, a  method  of  treatment  explained  in  all  standard  texts  on  alternating 
currents. 

Let  Zi  =  impedance  of  branch  1  =  RL-\-juL', 
2*2  =  impedance  of  branch  2  =  Rc  —j  —^ ', 
Z  =  impedance  of  the  joint  path. 

1,1+1.    _L          1 

17         rt       \     rj  i  j        i     _•       7      I 

/J         Zl         Z2          L 


Hence  Z  = 


Rationalize  by  multiplying  numerator  and  denominator  by 


Collecting  terms  we  have 

H\R^L-RL^,-^L-^)] 


Of  this  complex  impedance  the  real  part  is  the  effective  resistance  of 
the  branched  circuit  and  the  imaginary  part  is  the  reactance,  or  o>Z/, 
where  Z/  is  the  effective  inductance. 


72  FUNDAMENTAL  IDEAS  AND  LAWS  [CHAP.  I 

So 


*--  ,  x.v"~'     •     •     •     •     (48) 


(49) 


In  case  the  resistance  of  the  inductance  is  large  compared  to  that  of 
the  condenser,  Eqs.  (48)  and  (49)  may  be  simplified  to  the  approximately 
correct  forms 


m2R2~-\-(m2-!)2 
Li 


(50) 


(51) 


where  R'  =  equivalent  series  resistance; 

L'  =  equivalent  series  inductance  ; 
R  =  total  actual  resistance  in  the  circuit,  that  is,  resistance 

of  the  inductive  branch  plus  that  of  the  capacity 

branch  ; 

C  =  actual  capacity  of  the  capacity  branch  ; 
L  =  actual  inductance  of  the  inductive  branch  ; 
m  =  ratio  of  the  impressed  frequency  to  the  resonant  fre- 

quency of  the  circuit  =  27T/VLC. 

In  case  L'  comes  out  a  negative  quantity  it  is  converted  to  its  equiv- 
alent series  capacity  by  the  relation 


(52) 


An  interesting  condition  obtains  in  a  circuit  having  parallel  resonance. 
Thus  suppose  that  the  values  of  L  and  C  and  the  frequency  of  supply  for 
the  circuit  of  Fig.  66  have  been  so  adjusted  that  for  a  voltage  impressed 
across  A-B  the  circuit  shows  no  reactance;  the  power  factor  is  unity  and 
the  circuit  shows  resistance  only. 

If  the  supply  voltage  is  impressed  across  any  other  two  points  in  the 
circuit,  the  circuit  will  be  approximately  in  resonance  for  these  points 
also;  if,  for  example,  the  voltage  is  impressed  across  points  C—D,  the  cir- 
cuit will  show  resistance  only. 


REACTANCE  AND  RESISTANCE  OF  PARALLEL  CIRCUITS         73 


The  resistance  will  not  be  the  same  when  measured  between  points 
C-D  as  it  is  for  the  points  A-B.  It  may  be  proved  that  the  resistance 
between  any  two  points  in  the  circuit  is  nearly  proportional  to  the  square 
of  the  reactance  included  between  the  two  points,  in  either  branch^  JThe 
reactance  in  each  branch  of  the  parallel  circuit  will  be  the  same,  no  matter 
where  the  two  points  are  taken,  but  the  reactance  will  be  inductive  in  one 
branch  and  capacitive  in  the  other. 

Fig.  67  illustrates  another  combination  of  inductance  and  condensers; 
such  a  circuit  is  used  in  one  of  the  common  forms  of  radio  telephone  appa- 
ratus. The  frequency  of  current  in  the  closed  circuit  is  fixed  by  the  reso- 


nant period  of  this  circuit,  that  is  '/= 


—  where  C  = 


The 


alternating  current  supply  for  the  circuit  is  furnished  across  the  condenser 


B 
FIG.  66. 


FIG.  67. 


FIG.  66. — Resonant  multiple  circuit. 
FIG.  67. — Resonant  multiple  circuit  used  in  a  radio-telephone  set. 

Cij  and  the  power  factor  of  this  circuit  (i.e.,  between  points  A  and  B) 
is  unity;  the  impedance  offered  to  the  supply  circuit  is  resistance  only.  If 
the  point  B  is  moved  around  the  circuit  so  as  to  include  part  of  the  induct- 
ance L  in  either  path,  as  shown  at  B',  the  impedance  between  the  two 
points  A  and  B'  would  still  be  resistance  only. 

It  is  often  desired  in  radio  circuits  to  alter  the  impedance  of  the  circuit 
to  which  the  power  is  supplied.  Thus  in  certain  vacuum-tube  circuits 
a  resonant  circuit  (as  shown  in  Fig.  67)  is  used  as  load  for  the  tube  output 
and,  to  get  the  maximum  output  from  the  tube,  the  circuit  must  offer  re- 
sistance only  (no  reactance),  and  this  resistance  must  have  a  proper  value. 
Evidently  such  a  circuit  as  that  shown  in  Fig.  67  offers  such  possibility ;  by 
properly  adjusting  the  position  of  B'  the  desired  resistance  will  be  obtained. 

We  might  keep  B'  fixed  and  vary  the  value  of  Ci ;   varying  the  value  of 


74 


FUNDAMENTAL  IDEAS  AND   LAWS 


[CHAP.  1 


d,  however,  has  the  disadvantage  of  changing  also  the  frequency  of  the 
circuit.  If  Ci  is  held  constant  and  the  point  B  is  moved  along  the  induct- 
ance, the  effective  resistance  between  points  A  and  B  will  vary  while  the 
frequency  is  maintained  practically  constant.  Such  a  connection  scheme 
is  generally  used  in  practice. 

To  illustrate  this  idea  with  experimental  data  a  simple  test  was  per- 
formed.    An  inductance  coil,  having  a  tap  near  its  center,  was  connected 
A  to  a  condenser  as  shown  in  Fig. 

68  and  resonant  frequency  was 
impressed  across  A-C.  The 
values  of  inductance  and  capac- 
ity were  about  as  shown  in  the 
diagram,  the  resistance  of  the 
coil  being  about  10.8  ohms.  A 
watt-meter,  voltmeter,  and  am- 
meter were  used  to  measure  the 
input;  the  frequency  was  held 
constant  at  45  cycles,  which  is 
the  frequency  to  give  resonance 
FIG.  68.— Experimental  resonant  multiple  f°r  ^  =  -628  henry  and  C  =  20 
circuit  similar  to  that  of  Fig.  67.  microfarads.  The  effective  re- 

sistance was  calculated  by  divid- 
ing the  wattmeter  reading  by  the  square  of  the  ammeter  reading.  The 
results  obtained  are  tabulated  below: 


20  microfarads 


Volts. 

Amperes. 

Watts. 

Effective 
Resistance,  Ohms. 

Terminals  C-A  
Terminals  C-B  

105 
105 

.050 
.145 

5 
14.8 

2000 
705 

Terminals  B-A  

100 

.170 

16.6 

575 

These  values  of  resistance  are  nearly  proportional  to  the  square  of  the 
value  of  reactance  between  the  respective  terminals;  better  results  can- 
not be  obtained  by  this  method,  because  the  current  taken  by  a  condenser 
exaggerates  the  non-sinusoidal  form  of  the  impressed  voltage  and  so  may 
differ  quite  appreciably  from  the  true  sine  form.  In  parallel  resonance 
the  very  small  minimum  line  current  obtained  is  a  result  of  the  inductive 
and  capacitive  currents  of  the  two  branches  neutralizing  each  other;  if, 
however,  the  two  currents  are  not  of  the  same  form,  it  is  evident  that  the 
neutralization  cannot  be  very  complete  and  the  line  current  at  resonance 
will  not  be  as  small  as  it  should  normally  be. 

A  case  of  this  kind  is  shown  clearly  in  the  oscilligram  of  Fig.  69;  the 
generator  supplying  the  power  was  of  an  ordinary  commercial  type,  having 
however,  a  rather  smaller  air  gap  than  is  usual.  The  inductance  and  ca- 


COMPLEX  CURRENTS  IN  PARALLEL  CIRCUITS 


75 


p      Q) 

£M       W 

8  '&, 


I! 


11 


76 


FUNDAMENTAL  IDEAS  AND  LAWS 


[CHAP.  I 


pacity  were  connected  in  parallel  and  the  impressed  frequency  was  varied 
until  the  line  current  showed  a  minimum  value.  The  form  and  phase  of 
the  currents  ki  the  two  branches  of  the  circuit  are  shown  well  on  the  film, 
and  it  is  at  once  evident  that  the  great  difference  in  form  of  the  two  cur- 
rents would  prevent  the  resonance  phenomena  being  very  marked.  Prob- 
ably 50  per  cent  of  the  current  flowing  in  the  condenser  circuit  is  of  some 
frequency  much  higher  than  that  for  which  the  circuit  was  resonant  and 
at  least  this  much  current  would  persist  in  the  supply  line  no  matter  how 
carefully  the  circuit  was  adjusted  for  resonance. 


45 


oaw 

300 
280 
260 

240 
220 

i>° 

.22140 

\ 

I 

1 

I 

i 

\\ 

J 

l3 

Volts  —  L.     ^ 

< 

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1 

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li=j.2dc 

efy 

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/ 

i 

R  =16.01 

hilis 

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C='30 

m 

crofa 

ra 

/ 

i 

/ 

/ 

1  1  Re 

SIS 

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nc 

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J 

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100 
80 
60 
40 
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—  _ 

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—  -  >«< 

50 


55 


60 


65  70 

Frequency 


75 


80 


90 


95 


FIG.  70. — Reactance  and  resistance  curves  for  a  parallel  resonant  circuit  having  low 

resistance. 


This  question  of  upper  harmonics  is  often  of  much  importance  in  the 
operation  of  radio  apparatus;  more  specific  mention  of  the  occurrences 
will  be  made  when  discussing  certain  types  of  radio  generators. 

It  is  possible  to  move  points  A  and  B'  (Fig.  67)  to  such  a  position  that 
there  is  no  reactance  in  either  path.  In  this  case  we  have  a  maximum 
possible  line  current  (for  a  given  impressed  voltage)  and  the  resistance  of 
the  combination  is  a  minimum.  It  is  equal  to  the  resistance  of  one  path 
divided  by  two,  if  the  two  paths  have  equal  resistances ;  if  not  it  is  equal 
to  the  reciprocal  of  the  sum  of  the  reciprocals  of  the  resistances  in  the 
separate  paths.  In  Figs.  70  and  71  are  some  experimental  curves  showing 


REACTANCE  AND  RESISTANCE  OF  PARALLEL  CIRCUITS        77 

the  characteristics  of  parallel  resonance;  they  were  obtained  by  ammeter, 
voltmeter,  and  wattmeter  readings,  frequency  being  varied  and  impressed 
voltage  being  held  constant.  The  equivalent  resistance  was  obtained 
directly  by  dividing  the  wattmeter  reading  by  the  squared  value  of  the 
line  ammeter  reading;  the  equivalent  inductance  or  capacity  was  found 
after  calculating  the  reactive  component  of  the  inpressed  voltage  and 
knowing  the  line  current  from  the  ammeter  reading.  The  alternator 
used  had  a  very  pure  sine  wave  of  e.m.f.  compared  to  that  given  by  the 
average  machine. 


260 

2 

o 

i 

24 
22 
20     M 

18    I 
16    .8 

14    .7 
12    .6 
10   .5 
8   .4 
6  .3 
.2 
.1 

r 

)J50 

^.           1 

Volts    T          5 

- 

240 

\ 

/ 

\ 

\ 

220 
200 
v    180 
c|16o 

£3  OT 

J 

\l 

\\ 

f 

\ 

L  = 

.^^ry|     I 

I 

\\ 

G  = 

30  1  m 

crofarads 

1 

Ri  = 

10,.2 

oh'm^ 

A 

R2= 

6. 

)  ( 

hr 

ns 

I 

1\N 

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r" 

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5             50              55              60             65              70              75             80              85             90             95 
Frequency 

FIG.  71. — Effect  of  increasing  the  resistance  in  a  parallel  resonant  circuit;   compare 

with  curves  of  Fig.  70. 

A  rather  extraordinary  effect  is  seen  in  these  curves;  the  equivalent 
series  resistance  at  resonance  is  higher  the  lower  the  actual  resistance  of 
the  circuit.  Thus  in  the  first  case  where  the  actual  resistance  was  6  ohms 
the  equivalent  resistance  has  a  maximum  value  of  320  ohms ;  in  the  second 
case  where  the  actual  resistance  has  been  increased  to  16  ohms  the  maxi- 
mum value  of  R  is  only  240  ohms.  In  neither  case  is  the  equivalent 
resistance  nearly  as  great  as  calculation  by  Eqs.  (48)  and  (49)  would  indi- 
cate; the  reason  for  this  discrepancy  lies  in  the  method  of  measurement 
which  involves  an  error  depending  upon  the  non-sinusoidal  form  of  the 
voltage  impressed  on  the  circuit  as  outlined  above. 


78  FUNDAMENTAL  IDEAS  AND  LAWS  [CHAP.  I 

It  will  be  noticed  from  the  curves  given  in  Figs.  70  and  71  that  the 
effective  inductance  of  a  coil  may  be  increased  by  putting  a  condenser 
in  parallel  with  the  coil ;  the  equivalent  resistance  of  the  coil  also  increases 
and  this  increase  rapidly  grows  larger  as  the  amount  of  capacity  shunting 
the  coil  is  increased. 

For  the  frequencies  far  removed  from  the  resonant  frequency  of  the 

circuit  (so  that  (w2— 1)  is  large  compared  to  m2R2j\WQ  get  rather  simple 

formulae  for  the  equivalent  inductance  and  resistance  of  the  coil.     Formulae 
(50)  and  (51)  in  this  case  reduce  to  the  forms 


(52) 


L'  --    -j  ..........     (53) 

ra2—  1 

Inspection  of  these  equations  shows  that  the  effective  resistance  of 
the  circuit  rises  more  rapidly  than  does  the  effective  inductance,  especially 
as  the  resonant  frequency  is  approached. 

A  Peculiar  Case  of  Parallel  Resonance.  —  A  very  interesting  case  of 
resonance  occurs  if,  with  an  inductance  and  condenser  in  parallel,  the 
resistances  in  each  path  are  properly  adjusted.  Thus  suppose  that  the 
resistance  in  the  two  paths  are  equal  and  also  equal  to 


that  is, 


By  inserting  this  condition  in  Eqs.  (48)  and  (49)  it  will  be  found  that  the 
reactance  of  the  circuit  is  zero  for  all  frequencies  and  that  the  resistance  is 
constant  for  all  frequencies  and  equal  to  the  resistance  of  each  path. 

Resonant  Frequency  of  Parallel  Circuits.  —  If  we  define  the  resonant 
frequency  of  a  parallel  circuit  as  that  frequency  which  makes  the  reactance 
of  the  circuit  zero,  thus  making  the  power  factor  of  the  circuit  unity,  we 
find  the  resonant  frequency  by  using  Eq.  (49),  putting  the  numerator 
equal  to  zero.  This  gives  the  equation 


or 

!/A_ 

co2lc2     CC 
from  which  we  get, 

-~  (    . 

'    (54) 


COUPLING   OF  VARIOUS  KINDS 


79 


In  case  the  resistance  of  the  condenser  arm  is  negligible  a  simpler  form 

is  obtained,  

/  1       P2 

(55) 


/_!_#! 

~\LC     L2' 


It  is  to  be  noted  that  in  parallel  circuits  the  resistances  in  the  circuit 
affect  to  some  extent  the  resonant  frequency  of  the  circuit,  whereas  in 
the  series  circuit  the  resonant  frequency  is  independent  of  the  resistance. 

The  condition  for  resonance  in  parallel  circuits  (unity  power  factor) 
will  in  general  not  be  the  frequency  which  gives  minimum  line  current. 
In  case  we  had  defined  resonance  as  that  condition  which  gave  minimum 
line  current,  formulae  somewhat  different  from  Eqs.  (54)  and  (55)  would 
have  been  obtained. 

Coupling  of  Various  Kinds — Coefficient  of  Coupling. — When  two  cir- 
cuits are  so  placed  or  interconnected  that  energy  may  be  transferred  from 
one  to  the  other  they  are  said  to  be  coupled.  There  are  three  types  of 


TJocx; 


OOO 


:c« 


FIG.  72. — Direct  coupling. 


FIG.  73. — Inductive  coupling. 


coupling,  resistance,  inductance,  or  condenser  coupling.  In  the  first  (prac- 
tically never  used)  that  part  of  the  network  which  is  common  to  the  two 
circuits  is  a  resistance;  in  the  second,  part  of  the  magnetic  field  generated 
by  currents  in  the  network  is  common  to  both  circuits;  in  the  third,  a 
part  of  the  electro-static  field  set  up  in  the  network  is  common  to  both 
circuits.  The  coupling  which  uses  the  magnetic  field  is  called  inductive 
or  magnetic  coupling,  and  that  which  uses  the  electric  field  is  called  capac- 
itive  or  static  coupling.  The  magnetic  coupling  may  be  through  an 
inductance  common  to  both  circuits  called  direct,  or  it  may  be  through 
a  mutual  inductance  in  which  case  it  is  generally  called  inductive  coupling. 

The  three  principal  types  of  coupling  are  shown  in  Figs.  72,  73,  and 
74,  that  of  Fig.  72  being  direct,  that  of  Fig.  73  being  inductive,  and  that 
of  Fig.  74  being  capacitive. 

The  extent  to  which  circuits  are  coupled  is  given  quantitatively  by 
the  coupling  coefficient  or  coefficient  of  coupling.  This  is  defined  as  the 
ratio  of  the  common  reactance  of  the  two  circuits  to  the  square  root  of  the  react- 
ances (of  similar  kind  to  that  giving  the  coupling)  of  the  two  circuits. 


80 


FUNDAMENTAL  IDEAS  AND  LAWS 


[CHAP.  I 


Thus  if  Xm  =  reactance  common  to  both  circuits; 
Xi  =  reactance  of  circuit  1 ; 
X2  =  reactance  of  circuit  2; 
k  =  coupling  coefficient. 


(56) 


In  Fig.  72  the  total  reactance  of  circuit  1  is  w(Li+M),  that  of  cir- 
cuit 2  is  u(Lt2+M),  and  the  common  reactance  is  coM.     Therefore 


k  =  - 


M 


cm 


C:  C, 

FIG.  74. — Capacitive  coupling. 


(57) 


In  Fig.  73  the  total  inductance  of 
circuit  1  is  indicated  by  La+L&;  part 
of  this  is  in  inductive  relation  to 
circuit  2  and  part  is  not.  Similarly 
the  inductance  of  the  second  circuit 
consists  of  two  parts  Lc  and  Ld,  one 
part  magnetically  coupled  to  circuit  1 
and  the  other  part  not  so  coupled. 
The  common  reactance  is  wM.  Hence 
for  this  case  we  have, 


M_ 

V(La+Lb)(Lc+Ld) 


(58) 


The  inductively  coupled  circuit  of  Fig.  73  can  always  be  considered 
as  a  direct-coupled  circuit  after  the  proper  transformations  have  been 
made.  The  inductance  of  circuit  2  must  be  decreased  in  the  ratio  Lb/Lc 
and  the  capacity  of  circuit  2  must  be  increased  in  the  ratio  LC/L&.  This 
transformation  of  the  in- 

0.1  henry  5  hcnrys 

j — Wmr- 


OOOCT 


0.1  henry 


1  henry 


0.8  nf 


ductance  and   capacity  of 
circuit  2  leaves  the  oscilla- 
tion constant  (LC)  the  same     c 
as  it  was  with  the  original 
values  of  L  and  C.  ^ 

The  M  of  the  equivalent 
circuit  is  obtained  by  multi- 
plying the  actual  value  of  M 
by  the  ratio  VLb/Lc.  Let 
us  call  these  new  values  M',  „ 

L'c,  L'd,  and  C'2.  The  inductively  coupled  circuit  is  now  replaced  by  the 
direct-coupled  circuit  similar  to  that  of  Fig.  72.  For  the  LI  of  Fig.  72 
we  use  (La+L6)-AT  and  for  the  L2  of  Fig.  72  we  use  (L'c+L'd)  -M'. 


FIG.  75. — Inductively  coupled  circuits. 


CALCULATION  OF  COEFFICIENT  OF  COUPLING 


81 


An  actual  inductively  coupled  circuit  is  shown  in  Fig.  75;  the  coefficient 
of  coupling  of  the  two  coils  of  the  transformer  is  80  per  cent,  or 

M  =  0.8 VTXO1  =  0.253  henry. 

In  Fig.  76  the  inductances  of  the  second  circuit  have  been  decreased 
in  the  ratio  0.1/1  and  the 
capacity  has  been  increased 
in  the  ratio  1/0.1.  The 
coefficient  of  coupling  must 
remain  as  it  was  for  Fig.  75, 
so  we  decreaseMin  the  ratio 

,  giving  it  a  value  of 


1 

-^ooooo 

0.1  h 

o 

9  pW3^ 

o 

£    fc> 

0.1  hg 

1  |o.ih       =; 

8 

^.    o 

O 

8    P 

8/c/ 


0.08  henry. 

The  direct-coupled  cir-  FlQ   76._circuit  of  Fig  75  reduced  to  an  equivalent 
cmt,    which    is     the   exact  1:1  ratio  circuit, 

equivalent   of    the    induc- 
tively coupled  circuit  of  Fig.  76,  is  now  given  in  Fig.  77.     The  total  L  of 
circuit  1  is  the  same  as  that  of  Fig.  76,  0.08  henry  being  coupled  100  per 
cent  to  circuit  2;  similarly  the  total  inductance  of  circuit  2  is  the  same  as 
it  is  in  Fig.  76. 

The  coefficient  of  coupling  of  the  circuit  of  Fig.  77  is 


0.08 


V0.2X0.6 


=  0.232, 


and  for  the  actual  inductively  coupled  circuit  of  Fig.  75  it  is 

0.253 


V0.2X6.6 


=  0.232, 


o  o  os  h 


8/T/ 


which  is  just  the  same  as  for  the  substituted  direct  coupled  circuit. 

----.,,,.,-  ^-^r^r^-v  It  is  possible  to  replace 

™*^  (j()()[)()f)()  I     i  •••^  r\r\f\r\r\7\7\  ^ 

tug  h  <X52  h  an  inductively  coupled  cir- 

|  cuit  by  one  directly  coupled 

without  making  the  trans- 
formations explained  above. 
Calling  the  total  inductance 
in  primary  and  secondary 
1 1  of  the  inductively  coupled 

circuit  Lz  and  L±  respect- 

FIG.  77.— Direct-coupled    circuit   equivalent   to    in-   ively,    and  the  mutual   in- 
ductively coupled  circuit  of  Fig.  76.  ductance  M ,then  the  direct- 
coupled   circuit   is   written 
down  at  once  as  shown  in  Fig.  72  by  making  Li  =  L3  —  M  and  L2  =  L4  —  M. 


82  FUNDAMENTAL  IDEAS  AND   LAWS  [CHAP.  I 

The  same  values  of  M,  C\  and  €2  are  used  in  the  direct-coupled  circuit 
as  in  the  inductively  coupled  circuit.1  The  justification  for  making  the 
change  from  one  type  of  circuit  to  the  other  may  be  seen  upon  writing 
the  equations  for  the  reactive  voltages  of  the  two  circuits  of  Figs.  72  and 
73.  For  Fig.  72  we  have, 


/2)=0,       .....     (59 
co 

and 

/1)=0  ......     (60) 


2 


For  the  circuit  shown  in  Fig.  73  we  may  put  La+L6  =  L3  and  Lc-\-Ld  = 
the  reactive  voltages  for  these  circuits  then  become, 


0,  .     .     .     (61) 

coi 

and 

=  0.  (62) 


Put  Ls  =  Li-}-M  and  7/4  =  7/2+717  and  these  equations  become 

0,  (63) 


and 

0  .....          (64) 


By  collecting  terms  these  may  be  changed  into  the  forms, 

coLi7i-J^+coM(7i-72)  =  0, (65) 

and 

-70=0.  (66) 


But  these  equations,  which  are  for  an  inductively  coupled  circuit,  are 
identical  with  Eqs.  (59)  and  (60),  which  are  for  the  directly  ocupled 
circuit. 

The  author  does  not  believe  that  this  method  is  as  satisfactory  a  one 
as  that  using  transformed  L  and  C  in  the  secondary  because  of  certain 
ambiguities  which  may  arise.  As  an  illustration  of  the  cases  in  which 
the  method  works  out  all  right  we  take  Fig.  78.  For  the  LI  of  Fig.  72 
we  must  put  0.2  —  0.1  =  0.1  henry  and  for  L2  of  Fig.  72  we  put  0.4  —  0.1  = 
0.3  henry.  M,  C\  and  C2  remain  as  in  Fig.  78.  The  equivalent  directly 
coupled  circuit  is  given  in  Fig.  79;  it  is  electrically  equivalent  to  Fig.  78. 

1  See  Bulletin  74  of  the  Bureau  of  Standards,  p.  50. 


CAPACITIVE   COUPLING 


83 


Now  suppose  the  circuit  of  Fig.  75  to  be  treated  in  this  manner;  for 
Li  we  obtained  0.2  — 0.253= —0.053  henry.  This  means  that  instead  of 
putting  in  an  inductance  for  the  LI  of  Fig.  72  we  must  put  a  condenser, 
the  capacity  of  which  is  such  that  its  reactance  is  equal,  in  magnitude, 
to  that  given  by  0.053  henry  of  inductance. 


0.3  h 


0.1  h 


FIG.  78.  FIG.  79. 

FIG.  78. — Inductively  coupled  circuit. 
FIG.  79. — Direct-coupled  circuit  equivalent  to  circuit  of  Fig.  78. 

For  the  circuit  shown  in  Fig.  74,  we  get  the  coupling  coefficient  from 
Eq.  (56)  in  the  following  manner.1 

1 


Mutual  capacity  reactance  = 

Capacity  reactance  of  circuit  1  =  — ^-  +  — ^ 


in  which 


Capacity  reactance  of  circuit  2  =  —^-+—  —  =  —  —  -, 


in  which 


Hence  Eq.  (56)  becomes  for  this  case, 

1 


(\ 


(67) 


1  For  more  complete  analysis  of  capacitively  coupled  circuits  and  comparison  of 
capacitive  and  inductive  coupling  see  Cohen,  "Electrostatically  coupled  circuits," 
Proc.  I.  R.  E.,  Vol.  8,  No.  5,  Oct.,  1920. 


84 


FUNDAMENTAL  IDEAS  AND  LAWS 


[CHAP.  I 


A  rather  more  complicated  case  of  static  coupling  is  given  in  Fig.  80; 

in  this  case  the  application  of  Eq. 
(56)  results  in  the  formula  1 


to' 


k  = 


(68) 


in  which 


C'C' 


C'+C"' 


FIG.  80. — Complex  capacitive  coupling. 


In  certain   radio  receiving  sets 
combined  capacitive  and  inductive 

couplings  are  used,  as  indicated  in  Fig.  81,  in  this  case  the  coefficient  of 
magnetic  coupling  and  that  of  static  coupling  are  calculated  separately, 
and  the  actual  coeffi- 
cient of  coupling  is 
the  sum  or  difference 
of  these  two,  accord- 
ing as  the  e.m.f.'s 
induced  in  circuit  2 
through  the  two  types 
of  coupling  are  in  phase 
or  180°  out  of  phase 
with  each  other. 

In  another  coupling 
scheme  (shown  in  Fig. 
82)  a  so-called  link  cir- 
cuit, untuned,  is  used  to  connect  the  other  two  circuits.     In  this  case  the 
coupling  between  circuits  1  and  2  is  obtained  by  calculating  the  coupling 
of  circuits  1  and  3  and  then  that  of  3  and  2. 


J 

? 

M 
1  IC/ 

cx 

0 

S) 

11 

[ 

C2 
II 

Ci         c3 

He" 

FIG.  81. — Combined  capacitive  and  inductive  coupling. 


&1-3 


-2 


1-2  = 


Then 


-2  =  ki  -3X^3-2  = 


(L2+L3)VLiL4 


(69) 


1  In  case  it  is  not  evident  just  what  the  mutual  reactance  of  the  two  circuits  is  it 
may  be  obtained  by  calculating  the  voltage  generated  in  circuit  2  when  a  current  of 
one  ampere  is  flowing  in  circuit  1,  or  vice  versa.  This  voltage  is  equal  to  the  mutual 
reactance,  in  ohms. 


EFFECT  OF  NEIGHBORING   CIRCUIT  ON   RESONANCE  CURVE    85 

Resonance  in  a  Circuit  to  which  Another  Circuit  is  Magnetically 
Coupled. — In  discussing  this  question  we  shall  calculate  the  effect  of  cir- 
cuit 2  on  the  resistance  and  reactance  of  circuit  1.  The  method  of  analysis 
is  somewhat  more  elementary  than  that  ordinarily  given  (which  depends 


i 

I 

|           L, 

0 

o 

0 

o 

§ 

",-,, 

0 

0 

o            — 

I1'  ] 

Link  Circuit            §i 

L8                                            tj 

Circuit  1  Circuit  3 

FIG.  82. — "  Link-circuit  "  coupling. 


Circuit  2 


upon  the  solution  of  simultaneous  differential  equations),  and  perhaps 
leads  to  a  clearer  insight  into  the  mutual  reactions  of  the  two  circuits. 
We  shall  assume  unit  current  flowing  in  the  primary  (circuit  1),  and  get 
the  voltage  Ez  induced  in  the  second  circuit  by  this  current.  This  volt- 
age will  produce  current  in  the  second  circuit,  which  current  will  be  divided 
into  its  active  and  reactive  components  (in  phase  with  #2  and  90°  out 
of  phase  with  E%).  The  active  component  will  be  90°  behind  the  pri- 
mary current  and  will  produce  a  voltage  back  in  the  primary  circuit 
which  will  be  180°  out  of  phase  with 
the  primary  current;  from  this 
voltage  we  calculate  the  effect  of 
the  second  circuit  on  the  resistance 
of  the  first. 

The  resistance  of  a  circuit  may 
be  defined  as  the  counter  voltage  set 
up  in  the  circuit  by  a  current  of  one       FlG   83._inductiveiy  coupled  circuits, 
ampere  flowing,  this   counter  voltage  neither  circuit  having  a  condenser. 

to  be  180°  out  of  phase  with  the  cur- 
rent; in  the  same  way  the  reactance  of  a  circuit  may  be  considered  as  the 
counter  voltage  set  up  in  the  circuit  by  a  current  of  one  ampere,  the  counter 
voltage  to  be  90°  out  of  phase  with  the  current. 

In  Fig.  83  suppose  the  current  7i,  is  one  ampere  at  frequency  o>/27r. 

Voltage  induced  in  the  secondary 


Current  in  circuit  2, 


__ 


(70) 


(71) 


86  FUNDAMENTAL  IDEAS  AND  LAWS  [CHAP.  I 

and  this  current  lags  behind  E2  by  an  angle  6,  defined  by  the  equation 
tan  6  =  coZ/2/#2.     The  active  component  of  /2  is  in  phase  with  £2  so  we  put 


72  cos  0  =  -=-  -XTT. 

j  /2         62 

The  voltage  induced  in  circuit  1  by  this  current  is 

I,  cos  ex»M  =        &M-  2R*-      •  •  (72) 


As  this  voltage  lags  90°  behind  the  inducing  current  /2  cos  6  and  as  I  2  cos  6 
lags  90°  behind  /i  this  voltage  (7)  &  is  180°  behind  h  and  so  is  an  IR 

\  ^2  / 

reaction.     As  we  assumed  unit  current  in  circuit  1  this  voltage  (  "  -  )   #2 

\62  / 

is  really  the  increase  in  resistance  of  circuit  1,  in  ohms,  due  to  the  current 
in  circuit  2.     Hence  the  apparent  resistance  of  circuit  1  is  evidently 


(73) 


Now  the  reactive  current  in  circuit  2  is  72  sin  0,  and  this  current  lags 
90°  behind  #2,  which  itself  lags  90°  behind  I\.  The  voltage  induced  in 
circuit  1  by  this  current  /2  sin  0  will  be  equal  to  wM/2  sin  0,  and  this 
will  lag  90°  behind  the  inducing  current  /2  sin  0,  and  hence  will  lag  270° 
behind  /i,  that  is  it  leads  /i  by  90°. 

Now  the  reactive  voltage  in  circuit  1  due  to  L\  is  90°  behind  the  cur- 
rent /i.  This  may  seem  incorrect  at  first  glance,  because  it  makes  the 
current  I\  lead  the  reactive  voltage  by  90°,  whereas  we  know  that  an 
inductive  circuit  draws  a  lagging  current.  It  must  be  remembered  that 
the  component  of  the  impressed  voltage  which  overcomes  the  reacting 
voltage  of  the  circuit  must  be  180°  ahead  of  the  reacting  voltage  itself; 
this  makes  the  current  in  an  inductive  circuit  lag  behind  the  impressed 
voltage,  as  it  should. 

It  appears  then  that  the  voltage  induced  in  circuit  1  by  the  current 
/2  sin  0  is  180°  out  of  phase  with  the  reactive  voltage  in  circuit  1  due  to 
LI  of  circuit  1,  hence  the  total  reactive  voltage  of  circuit  1  will  be  less 
when  circuit  2  is  present  than  when  it  is  not  present. 

The  amount  of  voltage  induced  in  circuit  1  by  /2  sin  0  is  coM/2  sin  0 
2 

^2  / 

So  the  total  reactive  voltage  in  circuit  1  when  a  current  of  one  ampere 
is  flowing  is 


and  this  is  equal  to  ( —  -  i 


\ 

' 


RESISTANCE   AND   REACTANCE   OF   COUPLED   CIRCUITS          87 

and  from  this  we  get  the  equivalent  self  induction  of  circuit  1, 

,  /<joM\2T  ,„.. 

L'i  =  Li-    -^-  )  L2  ........     (74) 

\  *2  / 

It  is  therefore  seen  that  the  effect  of  the  current  in  circuit  2  is  to-merease 

(  -= 

\  "2 


the  resistance  of  circuit  1  by  the  amount  (  -=—  )  R2  and  to  decrease  its  self- 


induction  by  an  amount  (  ~~—  )  L2. 

\"2   I 

In   such  a  circuit  as  that  shown  in  Fig.  84  we  can  at  once  write  the 

characteristics  of  circuit  1  by  using  Eqs. 


[—     — VWV" 


(73)   and  (74). 


^-    R* 


I 

FIG.  84. — Inductively  coupled  cir- 
cuits with  a  condenser  in  the 
primary. 


7? 


'  '  (75) 


r~T2  * 


These  two  equations  may  be  written  in  a  somewhat  more  convenient  form 
by  combining  terms, 


EZ2 


(77) 


Ji- 


~} 


— 


.  (78) 


In  case  the  impressed  frequency  is  adjusted  to  give  resonance  in  the 
primary  circuit  (without  the  presence  of  the  secondary)  these  equations 
reduce  to  the  forms 


(79) 


(80) 


88  FUNDAMENTAL  IDEAS  AND  LAWS  [CHAP.  I 

If  M  is  varied  a  maximum  current  will  occur  in  the  secondary  when 


(coL2)2  =  RiZ2 

For  this  value  of  M  the  values  of  the  two  currents  become 

EZ2 


/!  = 


RiV2(Z22+R2Z2) 


RiV2(Z22+R2Z2) 


(81) 

(82) 
(83) 


.01 


.03  .04  .05 

Value  of  M,  in  henrys 


.07 


.08 


FIG.  85. — Variation  of  current  with  M  in  circuit  of  Fig.  84,  for  two  values  of  secondary 

resistance. 

Fig.  85  shows  a  set  of  experimental  curves  to  illustrate  the  relations  given 
above;  the  circuits  were  arranged  as  shown  in  Fig.  84  and  the  frequency 
adjusted  for  the  value  which  gave  resonance  in  the  primary  alone;  the 
coupling  was  then  varied  and  the  two  currents  went  through  variations 
as  appear  from  the  curves. 

With  the  same  value  of  frequency  as  used  for  the  curves  of  Fig.  85 
and  that  coupling  which  gave  maximum  secondary  current  (which  value 
of  coupling  does  not  vary  greatly  as  the  secondary  resistance  is  varied, 
so  long  as  the  secondary  resistance  is  small  compared  to  the  secondary 
reactance)  a  series  of  readings  was  taken  to  show  the  effect  of  the  secondary 
resistance  on  secondary  current  and  so  on  the  amount  of  power  trans- 
mitted to  the  secondary  circuit.  The  results  are  shown  in  Fig.  86;  it 


CURRENT  AND  POWER  IN  COUPLED  CIRCUITS 


89 


0         10        20        30       40        50        60        70        80        90       100      110      120      130      140      150 
Secondary  Resistance,  in  ohms 

FIG.  86. — Variation  of  power  and  current  (in  Circuit  2)  with  secondary  resistance  in 
circuit  of  Fig.  84,  coupling  constant. 


Ri 


4.0 


3.0 


2.0 


1.0 


Circuit 


=  Circuit 


closed 


.036 


68        70        72 


92        94 


76        78       80        82        84        86       88 
JFrequency 

FIG.  87. — Current  vs.  frequency  ha  primary  circuit  of  Fig.  84  with  secondary  open 

and  closed. 


90 


FUNDAMENTAL  IDEAS  AND   LAWS 


[CHAP.  1 


is  seen  that  the  adjustments  for  maximum  power  of  this  circuit  are  not 
very  critical. 

The  resonance  curve  for  such  a  circuit  as  that  shown  in  Fig.  84  differs 
from  the  curve  of  the  primary  alone  in  that  the  critical  frequency  is  higher 
and  the  resonance  curve  is  not  so  sharp.  The  resistance  of  circuit  1  is  in- 
creased by  the  amount  given  in  Eq.  (73)  and  the  inductance  is  decreased  by 
the  amount  shown  in  Eq.  (74).  Fig.  87  shows  the  resonance  curve  of  a  cir- 
cuit arranged  like  that  of  Fig.  84;  in  dotted  lines  is  shown  the  resonance 
curve  of  the  primary  without  the  presence  of  the  secondary.  The  same 


open 


4.0 


3.0 


2.0 


\A 


closed 


Ro-8.0 


=.14 


L    = 


10  b 


=45 


M    =056 


1.0 


70       72       74       76       78       80       82       84 
Frequency 


88        90       92       94        96 

FIG.  88. — Current  vs.  frequency  in  circuit  of  Fig.  84  with  added  secondary  resistance. 


voltage  was  applied  to  the  primary  circuit  in  getting  the  two  sets  of  curves, 
hence  the  magnitudes  of  current  for  the  two  curves  give  an  exact  measure 
of  the  effect  of  the  secondary  circuit  upon  the  first.  The  calculated  Rf 
and  L'  of  the  primary,  using  first  the  experimental  data  on  the  curve  sheet 
of  Fig.  87  and  then  Eqs.  (73)  and  (74)  agree  within  the  precision  of  the 
experimental  work. 

The  resistance  Of  the  secondary  circuit  was  then  increased  by  12  ohms 
and  another  resonance  curve  taken;  the  results  are  shown  in  Fig.  88; 
the  curves  of  Fig.  87  are  shown  in  dotted  lines  for  comparison.  It  is  seen 
that  the  addition  of  resistance  to  the  secondary  circuit  makes  the  sharp- 


REACTANCE  AND  RESISTANCE  OF  COUPLED  CIRCUITS 


91 


ness  of  resonance  less  and  the  effect  of  the  secondary  in  determining  the 
resonant  frequency  of  the  primary  is  somewhat  less  than  for  the  lower 
resistance  secondary  circuit. 

We  will  next  consider  the  circuit  shown  in  Fig.  89  ;  the  condenser  is  now 
in  the  secondary  circuit  instead  of  the  primary. 

In  this  circuit  the  resistance  of  the  primary  is  always  increased  by 
the  presence  of  the  secondary,  but  the  effect  upon  the  inductance  depends 
upon  the  frequency  impressed  on  the  primary  circuit.  If  the  fre- 
quency is  such  as  to  satisfy  the  condition  for  resonance  in  the  secondary 

(f=^~~7r==^=  )>  the  apparent  inductance  of  circuit  1  will  be  the 
ZirV  L-zLz/ 


same  as 


the  actual  inductance,  that  is,  the  presence  of  circuit  2  does  not  affect  the 
inductance  of  circuit  1.     With  higher 


than   resonant   frequency  the  appar-          vWvv        ^ 
ent  inductance  of  circuit  1  is  decreased 


t    ^ 

J 


? 
' 


\ vww~~ 


c2 


by  circuit  2  and  with  lower  fre- 
quency the  inductance  of  circuit  1  is 
increased .  In  other  words,  if  h  lags 
behind  #2,  the  effect  on  circuit  1  is 
to  reduce  the  apparent  inductance, 
whereas  if  the  current  in  circuit  2 

leads  the  generated  voltage  in  this  circuit,  the  effect  on   circuit   1  is  to 
cause  an  increase  in  the  apparent  inductance. 

Applying  Eqs.  (73)  and  (74)  to  the  circuit  of  Fig.  89  we  get, 


FIG.  89.— Inductively  coupled  circuit 
with  condenser  in  secondary. 


L'i  =  Li- 


in  which 


2 


(84) 
(85) 


It  is  seen  that  if    9,,  is  greater  than  LI,  L\    is  greater  than  L\ ;  if 

CO    C2 

=  -o7r>  Z/i  =  I/i;  if  Z/2  is  greater  than  —^r  then  L'\  is  less  than  L\. 
orC2  orC2 

Using  the  constants  given  in  Eqs.  (84)  and  (85)  we  can  write  at  once 


/2  = 


1,     •     (87) 


92  FUNDAMENTAL  IDEAS  AND  LAWS 

which  may  be  somewhat  simplified  to  the  forms 
r  EZ% 


[CHAP.  I 


(88) 


(89) 


y, 

p 

J, 

R 

1 

S 

a 

0 

R 

2 

1 

(( 

3) 

L 

,? 

§L 

-2 

0 

o 

Rs 

=  7 

I 

Rj 

=  6 

B 

L 

r-L 

c 

jor. 

C 

2=2 

8.6 

xlC 

r\ 

On 

•ve 

1 

C 

om 

lin 

(r  = 

• 

/ 

\ 

» 

2 

" 

= 

» 

2  0 

/ 

V 

1 

» 

= 

.0 

,3 

/ 

\ 

1 

N 

= 

.0 

00 

1  8 

\ 

^y 

\ 

1  fi 

^ 

s 

^x 

s^l 

^ 

* 

\" 

N 

Sy 

1  4 

^ 

s 

§ 

sX 

j 

s^ 

\ 

S 

\ 

X. 

/ 

1 

"N 

s, 

1  9 

S 

\ 

X 

V 

^v 

/ 

/ 

> 

s 

"V, 

s 

\ 

^"•^ 

/ 

s 

X 

V 

r^ 

K, 

"S 

0 

"X^ 

s 

s 

s 

1 

± 

^ 

^--« 

-^, 

^. 

9 

^« 

-^ 

•«, 

\ 

S^ 

s 

-- 

•^ 

-  — 

^*** 

*—**• 

—  , 

—  | 

\ 

/ 

""— 

*-- 

t^ 

iS 

?-«  . 

~-.^_ 

0.8 

V 

/ 

•-.. 

^rr: 

0  fi 

s 

S 

s  / 

0  4 

0  *> 

t 

1 

.    e 

8 

& 

0    ; 

A 

( 

i 

& 

3   5 

i 

6 

i 
F 

7 
rec 

0    J 
iue 

i 

nc 

6 

y 

8 

8 

)    £ 

4 

e 

1 

9( 

)    2 

I 

6 

S 

1C 

0  2 

1 

FIG.  90 — Current  versus  frequency  in  primary  circuit  of  Fig.  89. 

In  Fig.  90  are  shown  curves  of  primary  current  in  such  a  circuit  as 
given  in  Fig.  89;  the  voltage  impressed  on  the  primary  circuit  was  held 
constant  at  100  volts,  and  the  frequency  varied  through  a  suitable  range 
and  current  readings  taken  for  three  values  of  coupling  between  the  two 
circuits.  The  value  of  primary  current  was  also  taken  with  secondary 
circuit  open,  and  is  shown  in  dotted  line.  From  these  curves  it  is  seen 
that  the  effect  of  the  secondary  circuit  may  be  either  an  increase  or  decrease 
in  the  primary  current,  depending  upon  the  frequency  used.  In  Fig.  91 
are  shown  the  values  of  change  in  primary  resistance  and  reactance  brought 


REACTANCE  AND  RESISTANCE  OF  COUPLED  CIRCUITS 


93 


about  by  the  action  of  the  current  in  circuit  2;  they  were  determined  b> 
subtracting  from  the  apparent  resistance  and  reactance  of  circuit  1  the 
values  of  these  quantities  when  the  secondary  circuit  was  open. 


R2-7.2    Rj-6.5 


C2-  28.6x10 


60 

Kf> 

130 
120 
110 
100 

90 

1 

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40 
30 
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Frequency 

FIG.  91. — Change  in  primary  resistance  and  reactance  due  to  presence  of  secondary 
circuit,  for  various  frequencies. 

A  closer  study  of  these  curves  will  be  worth  while  when  analyzing  the 
action  of  certain  oscillating  tube  circuits.  An  oscillating  tube  may  refuse 
to  function  if  the  resistance  of  the  circuit  to  which  it  is  connected  is  too 
high  and  it  will  be  found  that  a  tube  may  be  made  to  stop  oscillating  by 
tuning  to  its  circuit  another  circuit  coupled  to  it.  The  reason  is  to  be 


'94 


FUNDAMENTAL  IDEAS   AND   LAWS 


[CHAP.  I 


found  in  the  extra  value  of  the  resistance  added  to  the  oscillating  circuit 

by  the  second  circuit  when 
this  second  circuit  is  brought 
into  resonance  with  the  tube 
circuit. 

9  G!          oj     K  We  next  consider  the  more 

II  II  general   case   of   two   coupled 

circuits,    each    of   which    has 


i.  92. — General  case  of  inductively  coupled 


inductance,      capacity,      and 

.  ,  .     •,.          i      • 

resistance,    as     indicated     in 


circuits. 

Fig.  92.     The  resistance  and 

inductance  of  circuit  1  are  obtained   from  Eqs.  (73)    and  (74),  as  before. 


(90) 


•  •  •  •  <»» 


Then  we  have, 


E 


4p   ,  /«M\2       2 
*+\f)  «-J 


in  which 


(92) 


=,  (93) 


We  assume  that  the  resistance  term  of  the  impedance  in  Eq.  (92)  is  nearly 
constant  as  the  frequency  is  varied.  The  fraction  coM/Z2  is  evidently 
nearly  constant  as  co  is  varied  until  co  approaches  such  a  value  that 
(  coL2  —  l/wC2)  is  nearly  equal  to  zero.  In  this  region  of  frequency  vari- 
ation the  resistance  R'\  varies  greatly  as  frequency  is  varied  and  any 
solution  which  we  may  reach  on  the  basis  of  R'i  remaining  constant, 
therefore,  will  not  be  accurate  for  frequencies  in  the  vicinity  of  the  natural 
frequency  of  the  secondary  circuit. 

Resonant  Frequencies  in  Coupled  Circuits.  —  On  the  assumption  that 
R'\  is  constant  it  is  evident  that  I\  will  be  a  maximum  for  any  frequency 
that  makes  the  reactance  term  of  the  impedance  equal  to  zero.  Hence  we 
write  as  the  condition  for  resonance 


\ 


(94) 


RESONANT  FREQUENCIES  OF  COUPLED   CIRCUITS  95 

If  now  we  again  neglect  Rz  in  comparison  with  ( coZ/2 77-)  thus  making 

it  possible  to  replace  Zi  by  f  ooZ/2 ~-  j ,  we  have 


Now  Eq.  (95)  can  be  written, 


which  can  be  changed,  by  multiplying  through  by  -j—j-,  to  the  form 

co4 
If  we  now  put 


"2  +_  J ^=0. 

LiC \L2C2     LiL2 


1  ,    7 

and   /c  = 


L2C2 
we  get 

+^^^O.      ....     (96) 


The  solution  of  this  equation  is  obtained  by  dividing  through  by  (1  —  k2), 
properly  completing  the  square  of  the  left-hand  member  and  extracting 
the  square  root,  which  gives 


2(l-*») 

By  combining  terms  under  the  radical  this  becomes 


The  two  real  solutions  for  co,  which  we  call  co'  and  co",  are 

co  ==  \  / f  Q7^ 

\  2(1 /c2)  '  \V'J 

and 

^"V"  ~2TY^l^~  '     ^ 

When  ^  is  large  (approximately  unity)  the  values  of  co'  and  co"  are  nearly 

co'     \c^TS' .     (99) 

and 


96 


FUNDAMENTAL  IDEAS  AND   LAWS 


[CHAP.  I 


When  k  is  small  the  values  of  co'  and  co"  approach  the  limits 


CO    = 


and 


Vi-k2' 


(101) 


(102) 


In  Fig.  93  are  shown  the  relations  between  co'  and  co"  and  fc;  for  small 
values  of  k  Eqs.  (101)  and  (102)  determine  the  values  and  for  the  large 
values  of  k  Eqs.  (99)  and  (100)  are  used. 

In  radio  operation  it  is  the  practice  to  tune  the  primary  and  secondary 
circuits,  that  is,  adjustments  are  made  to  make  on  equal  to  o>2.  In  this 
case  Eqs.  (97)  and  (98)  reduce  to  the  very  simple  forms 


(103) 
(104) 


CO 


Value  of  fc 
FIG.  93. 


Value  of  k 
FIG.  94. 


FIG.  93. — Variation  of  «'  and  u"  with  k  in  coupled  circuits^  primary  and  secondary  not 

tuned. 
FIG.  94. — Variation  of  a/  and  o>"  with  k  in  tuned  coupled  circuits. 

The  curves  of  variation  in  co'  and  co"  as  the  coupling  is  varied  for  this 
case  of  tuned  circuits  are  shown  in  Fig.  94.  It  is  seen  that  for  weak  cou- 
pling both  co'  and  co"  approach  co,  the  natural  frequency  of  each  circuit;  how- 
ever, it  has  been  pointed  out  that  the  neglect  of  /fe  in  obtaining  the  solu- 
tions of  the  resonant  frequencies  that  the  values  of  co'  and  co"  do  not  hold 
good  when  they  have  values  in  the  vicinity  of  the  natural  frequency  of 


RESONANCE  IN  COUPLED  CIRCUITS 


07 


the  secondary  circuit.     Hence  we  can  now  see  that  for  weak  couplings  the 
solutions  for  co'  and  co"  do  not  hold  good. 

Referring  to  Eq.  (93)  it  is  seen  that  /2  =  /i  -^— ,  and  hence  in  so  far  as 

^2  __ 

the  factor  -=-  is  independent  of  the  frequency  changes,  h  will  have  maxi- 

Z2 

mum  values  at  the  same  frequencies  as  give  maxima  for  I\.     However,  the 
factor  -=-  is  not  independent  of  the  frequency,  and  this   is  especially  so 

Z2 

in  the  region  of  frequency  fixed  by  the  relation  ( col/2 ^-1  =0;    for  fre- 


0)  O)  (i) 

Frequency 
FIG.  95. — Resonance  curves  for  circuit  of  Fig.  92. 

quencies  less  than  this  the  value  of  -~—  increases  with  the  frequency  and 
for  values  of  frequency  higher,  the  value  of  -=--  decreases  with  an  increase 

Z2 

of  frequency. 

We  can  then  conclude  that,  for  frequencies  in  the  region  of 


0)2 


1 


VL2C2' 


Eqs.  (103)  and  (104),  while  incorrect  for  primary  current  maxima,  are 
still  more  incorrect  for  the  maxima  of  secondary  current.  In  consequence 

of  the  changes  in  the  value  of  -=—  noted  above,  we  may  predict  that  when 

Z/2 

«'  and  co"  are  not  in  the  region  of  a>2  the  calculated  values  of  co'  and  co" 
will  be  more  accurate  for  the  primary  than  for  the  secondary  circuit,  and 
that  the  actual  value  of  co'  of  the  secondary  circuit  will  be  somewhat 


98 


FUNDAMENTAL  IDEAS  AND  LAWS 


[CHAP.  I 


higher  than  that  for  the  primary  and  that  the  actual  value  of  co"  for  the 
secondary  will  be  somewhat  lower  than  co"  for  the  primary  current. 

The  general  form  of  the  resonance  curve  of  the  circuit  shown  in  Fig. 
92  is  indicated  in  Fig.  95;  the  dotted  curve  shows  the  resonance  for  one 
circuit  by  itself. 

The  value  of  the  coefficient  of  coupling  can  be  calculated  from  the 
spacing  of  the  resonance  peaks  of  the  current  curves;  thus  from  Eqs. 
(103)  and  (104)  we  get  the  relation 


CO 


1-k. 

1+k' 


from  which  there  is  obtained 


*            "2    I        /•>  V.AU*JJ 

CO     ^  —  1  —  CO  ^ 

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Frequency 

FIG.  96.  —  Experimental  resonance  curve  for  single  circuit. 

In  case  the  resonance  frequency  of  one  circuit  by  itself  is  known,  and 
assuming  tuned  circuits,  the  equation  for  coupling  value  becomes  more 
simple  in  form,  giving  the  closely  approximate  value 


k  = 


(106) 


co  being  the  frequency  of  one  circuit  by  itself. 

In  the  foregoing  discussion  of  resonant  frequencies  formulae  have  been 
derived  using  co  for  frequency;   it  is  of  course  to  be  remembered  that  co  is 


RESONANCE   CURVES  OF   COUPLED   CIRCUITS 


99 


not  frequency,  but  2w  times  the  frequency.  The  value  of  co  has  been  used 
rather  than  frequency  itself  to  save  the  repeated  writing  of  the  quantity 
2r  throughout  all  the  derivations. 

In  Figs.  96  to  103  are  shown  some  experimental  curves  of  resonance 
in  coupled  circuits  for  different  conditions  as  regards  coupling,  resistances, 
tuning,  etc. ;  Fig.  96  shows  the  resonance  curve  for  a  single  circuit  having 
L  =  0.140  henry,  C  =  28.9  microfarads,  and  72=4.50  ohms. 

Fig.  97  shows  the  resonance  curves  for  two  coupled  circuits,  each  cir- 
cuit had  the  same  constants  as  those  given  for  Fig.  96;  the  coefficient  of 
coupling  was  0.36.  The  curve  of  primary  current  is  shown  by  the  full 
line  and  that  for  the  secondary  circuit  by  the  dotted  line.  The  two  reso- 


L 

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= 

Ro 

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"50  24     68  60  24     08  70  24     68    80  24     68  90   24     68  100  2468  HQ  2468  120  246 

Frequency 

FIG.  97. — Resonance  curve  for  coupled  circuits;  each  circuit  having  constants  as  in 
Fig.  96.  The  values  of  current  at  the  two  resonant  frequencies  in  this  and  the  three 
succeeding  figures  indicate,  by  their  dissimilarity,  that  the  circuits  were  not  tuned 
as  accurately  as  the  data  would  indicate. 

nant  frequencies  check  with  those  calculated  from  Eqs.  (103)  and  (104) 
within  the  precision  of  the  test. 

In  Figs.  98  and  99  are  shown  curves  of  current  for  the  same  two  cir- 
cuits as  those  used  in  Fig.  97  but  with  different  values  of  coupling,  this 
being  0.18  for  Fig.  98  and  0.07  for  Fig.  99.  It  may  be  seen  that  with 
small  values  of  coupling  the  two  frequencies  merge  into  one  another  and 
Eqs.  (103)  and  (104)  do  not  predict  accurately  the  resonant  frequencies 
of  the  primary  circuit  and  for  reasons  noted  in  the  derivation  of  the  formulae ; 
the  predicted  values  of  co'  and  a/'  for  the  secondary  circuit  differ  from  the 
actual  values  more  than  do  those  of  the  primary  circuit. 

A  peculiarity  of  all  these  resonance  curves  is  seen  in  the  relative  values 
of  the  primary  and  secondary  currents;  between  the  two  resonant  fre- 


100 


FUNDAMENTAL  IDEAS  AND  LAWS 


[CHAP.  I 


quencies  the  secondary  circuit  carries  a  greater  current  than  the  primary 
but  for  all  other  frequencies  the  primary  carries  a  greater  current.  If 
a  weaker  coupling  than  that  used  in  the  adjustments  for  Fig.  99  had  been 


8.0 
2.0 
1.0 

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_L 

1     1 

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1 

1 

1 

1 

L,=  L0=.140       C,=  C 

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FIG.  98. — Resonance  curves  for  circuit  as  shown  in  Fig.  97,  /c  =  0.18. 


4-.U 
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Frequency 
FIG.  99. — Resonance  curves  for  circuit  as  shown  in  Fig.  97,  &=0.07. 


used  it  would  have  been  found  that  the  primary  current  was  greater  than 
the  secondary  current  for  all  values  of  frequency. 

In  Fig.   100  is  shown  the  result  of  increasing  the  resistance  of  the 
secondary  circuit  from  4.5  to  9.7  ohms;   with  this  exception  the  circuits 


RESONANCE   CURVES  OF  COUPLED  CIRCUITS 


101 


were  exactly  the  same  as  those  used  for  Fig.  97.  By  comparison  of  the 
two  sets  of  curves  it  will  be  seen  that  the  two  resonant  frequencies  are, 
within  the  precision  of  measurements,  the  same  for  the  two  conditions; 
the  value  of  the  current  at  resonance  is,  however,  decreased  in  nearly  the 
proportion  predicted  from  the  value  of  resistance,  calculated  from  Eq. 
(90).  The  decrease  in  current,  it  will  be  noted,  takes  place  in  both  cir- 
cuits although  the  resistance  of  the  secondary  circuit  only  was  increased. 
The  resonance  is  much  less  marked  than  for  the  lower  resistance  used 
in  Fig.  97. 

Form  of  Resonance  Curve. — The  form  of  the  resonance  peaks  is  deter- 
mined by  the  combined  decrements  of  both  circuits.     For  the  simplest 


2.0 

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.6 
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1 

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Frequency 
FIG.  100. — Resonance  curves  for  circuit  shown  in  Fig. 97  with  added  secondary  resistance. 

case,  that  of  tuned  circuits,  it  will  be  found  that  the  decrements  will  be 
nearly  given  by  the  approximate  formulae: 
For  the  frequency  a/ 

d'=   MJ2- (107) 


and  for  the  frequency  «' 


(108) 


in  which  5i  and  52  are  the  decrements  of  circuits  1  and  2  when  not  affected 
by  other  circuits. 

The  decrements  6'  and  5",  calculated  from  the  shape  of  the  curves  of 
Figs.  97  and  98  by  use  of  Eq.  (47)  check  with  the  values  given  by  Eqs. 


102 


FUNDAMENTAL  IDEAS  AND  LAWS 


(107)  and  (108)  fairly  well;   it  is  noticeable  that  in  all^the  curves  given 
the  width  of  the  resonance  curve  is  greater  for  the  higher  frequency  than 


4.0 

\ 

\ 

1 

1 

1 

1 

\ 

1 

1  1 

1 

L,=  U=.140      R,=  R.=  4.50      C,  =  28.9xl<T°      C.=38.5  x  10~"     E  =  20  volts       K  =  .36 

\ 

to 

ill  ^ 

r^r 

|L«     c 

1 

/ 

1 

\ 

\ 

3.0 

I 

£ 
•32.0 

/ 

\ 

LI 

I 

It 

\ 
\ 

V 

/  ' 

I 

\ 

1  f 

f 

» 

\ 

\ 

// 

ry 

' 

\ 

^ 

f\ 

/^ 

/ 

\ 

\ 

J 

\ 

/ 

s 

^ 

\ 

0 

/ 

\ 

/A 

s 

> 

•s 

-s 

, 

/ 

\ 

N 

„ 

-?> 

^ 

x 

"> 

1  — 

^ 

* 

1 

p3 

x» 

•^ 

-^ 

»» 

^~~ 

**** 

g 

X 

L— 

- 

•  — 

._ 

l**f 

** 

| 

50  2     i     6     8   60   *     *     6     8   70   2     4     6     8  80    2     *     <"'     8  QQ   2     4     6     8  1QQ  2     4     6     •  110  *    *    '     8 120  2 

Frequency 
FIG.  101. — Resonance  curves  for  coupled  untuned  circuits. 


4.0 


e.o 


;2.0 


1.0 


L,=  U=.14Q      R1=  R?  =  4.50      Ct=  28.9  x  10        Cg=  48  2  1 10        E  =  20  volts        K  =  .36 


50    24     6     8  60    24     6     87Q24     6     8g024     0     8992     4     6     81QQ2     4     6     8HQ2     4     6     8I2Q2     4, 

Frequency 
FIG.  102. — Resonance  curves  for  coupled  untuned  circuits. 

for  the  lower,  indicating  thereby  a  greater  decrement.  With  weak  cou- 
pling the  form  of  the  curves  does  not  permit  the  calculation  of  5'  and  5", 
because  the  two  peaks  merge  into  one. 


RESONANCE  CURVES  OF  COUPLED   CIRCUITS 


103 


Circuits  not  Tuned. — In  Figs.  101  and  102  are  shown  the  resonance 
curves  for  two  circuits  which  are  not  tuned,  that  is,  coi  is  not  equal 
to  052.  For  this  condition  the  curves  are  not  as  symmetrical  as  for 
the  tuned  condition,  and  the  currents  in  the  two  circuits  are  no  longer 
nearly  equal  to  each  other  at  the  two  resonant  frequencies.  "At  one 
resonant  frequency  the  primary  circuit  carries  more  current  than  the 
secondary  and  at  the  other  frequency  the  reverse  is  true.  The  dif- 
ference in  the  two  currents  is  greater  the  greater  the  difference  in  the 


I  I  I  I  I  II  I  I  I  I  I 


2.2 

2.0 

1.8 

1.6 

1.4 

1.2 

1.0 

.8 

.6 

.4 

.2 


K    °|_2 


q~ 


Li=Ls=.140 


uency  at 


resonant  value 


for  eac 


h  cirlzu 


?ivingcJ=430 


condary  current 


0      .02     .04     .06 
FIG.  103. — Secondary  current  vs.  coefficient  of  coupling  in  tuned  coupled  circuits. 


.10     .12     .14    .16     .18    .20      22     .24    .26    .28     .30     .32     .34     .36 
Coefficient  of  Coupling 


natural  peroids  of  the  two  circuits.  For  Fig.  101  the  natural  fre- 
quency of  circuit  2  is  15  per  cent  lower  than  that  of  circuit  1,  and  for 
Fig.  102  circuit  2  has  a  natural  frequency  29  per  cent  lower  than  that 
of  circuit  1. 

Variation  of  Coupling  with  Tuned  Circuits. — In  Fig.  103  is  shown 
the  effect  of  varying  the  coupling  between  circuits  1  and  2,  they  being 
tuned  alike.  A  constant  e.m.f.  was  impressed  on  circuit  1  and  the 
coupling  of  the  two  circuits  was  gradually  increased  from  zero  to  the 
maximum  obtainable.  It  might  seem  at  first  sight  that  the  secondary 
current  would  be  greater  the  greater  the  coupling,  as  would  occur  in 
ordinary  transformer  tests,  but  with  tuned  circuits  as  used  in  radio 
this  is  not  the  case.  For  a  given  resistance  of  circuits  there  will  be 


104 


FUNDAMENTAL  IDEAS  AND  LAWS 


[CHAP..  I 


a  certain  coupling  which  gives  the  greatest  secondary  current  and  the 
lower  the  resistance  of  the  circuits  the  less  this  critical  value  of  coupling 
will  be. 

This  might  be  predicted  from  Eq.  (93)  by  differentiating  I2  with 
respect  to  M ;  it  will  be  found  that  with  tuned  circuits  having  impressed 
on  the  primary  a  voltage  of  the  same  frequency  as  that  for  which  the  cir- 
cuits are  tuned,  a  certain  value  of  M  will  produce  a  maximum  secondary 
current  and  this  value  of  M  will  depend  upon  the  resistances  in  the  two 
circuits.  This  condition  for  maximum  secondary  current  proves  to  be 
fixed  by  the  relation, 

.     .     .     (109) 


.02 


.03  .04  .05 

Value  of  M  in  henrys 


.06 


.07 


FIG.  104. — Current  vs.  mutual  inductance  in  tuned  coupled  circuits,  with  different 
values  of  secondary  resistance. 

The  curves  of  Fig.  104  were  taken  with  the  idea  of  proving  this  relation 
and  also  to  show  the  effect  of  the  secondary  resistance  on  the  sensitive- 
ness of  the  adjustment  for  maximum  secondary  current.  If  the  two  cir- 
cuits are  tuned  alike  and  the  frequency  of  the  e.m.f .  impressed  on  the  pri- 
mary is  the  same  as  the  natural  frequency  of  either  circuit  the  values  of 
the  primary  and  secondary  current  may  be  obtained  by  simplifying  Ec(s. 
(92)  and  (93)  and  are  found  to  be 


(110) 


CIRCUITS  WITH  CAPACITIVE   COUPLING 


105 


and 


(111) 


The  experimental  curves  given  in  Fig.  104  follow  the  values  predicted 
from  Eqs.  (110)  and  (111)  within  the  precision  of  measurement,  that  is, 
within  less  than  1  per  cent. 

Resonance  in  Circuits  with  Capacitive  Coupling. — The  equations  for 
7i  and  /2  are  obtained  for  this  case  in  a  fashion  exactly  the  same  as  that 
used  for  the  magnetic  coupling,  and  the  conclusions  reached  are  nearly 
the  same.  Using  coi,  o>2  and  k  in  the  same  sense  as  for  the  magnetically 
coupled  circuits  we  get  for  the  two  resonant  frequencies  of  the  combi- 
nation 


(112) 


(113) 


In  applying  these  formulae  the  values  of  coi  and  co2  must  be  calculated  in 
a  somewhat  different  manner  than  was  used  for  the  magnetically  coupled 
circuits.  It  will  be  remembered  that  for  magnetic  coupling  these  two 
frequencies  were  fixed  by  the  L  and  C  of  the  circuit  in  question  and  were 
independent  of  the  constants  of  the  other  circuit  and  of  the  coupling  used. 
Such  is  not  the  case  for  M 

capacitive  coupling,  how- 
ever. The  frequencies 
coi  and  co2  depend  upon 
the  capacity  used  in  the 
other  circuit  and  upon 
the  coupling  in  the  fol- 
lowing manner. 

In  Fig.  105  the   fre- 
quency coi  is  fixed  by  Li  FIG.  105.— Capacitively  coupled  circuits, 
and  by  the  capacity  Ci 

in  parallel  with  Cs  and  €2  in  series.  Thus  coi  may  be  varied  by  changing 
either  the  coupling  condenser  £3,  or  the  capacity  of  the  second  circuit  €2. 
Hence  we  have  the  formulae 


.     -     (114) 


106 
and 


FUNDAMENTAL  IDEAS  AND  LAWS 


[CHAP.  I 


002  = 


(115) 


For  the  value  A:,  we  have 


(116) 


In  Fig.  106  are  shown  the  resonance  curves  for  a  combination  of  cir- 
cuits nearly  like  that  shown  in  Fig.  105,  the  coupling  condenser  was  in 
two  parts  as  shown  in  the  sketch  on  the  curve  sheet. 


46    8  50   2    1    6    8  60   2    i    6    8    70  2    46 


FIG.  106. — Resonance  curves  for  capacitively  coupled  circuits. 

Using  the  values  of  L  and  C  indicated  on  the  curve  sheet  we  have 

103 


coi 


4.55X18.3 


=470 


or  /i  =  74.8  cycles  and  the  same  value  for  /2. 


DISTRIBUTED   INDUCTANCE  AND   CAPACITY  107 

From  the  curve  sheet/'  =  82.5  and/7  =  67.0,  so  we  find  k  from  the  curve 
sheet  to  be  0.208,  by  Eq.  (106).  By  using  the  known  values  of  L  and  Ci, 
C2,  and  C3,  and  Eq.  (116),  we  find  k  to  be  0.207. 

The  value  of  k  could  have  been  calculated  without  knowing  the  con- 
stants of  the  circuits,  by  using  Eq.  (105). 

We  have 

/C  =  82.52+67.02  =  '2°7' 
When  LiCi  =  L2C2,  Eqs.  (112)  and  (113)  reduce  to  the  simple  forms 

(117) 


and  if  further  Ci  =  C2  then  when  €3  is  varied,  thus  varying  the  coupling,  a/ 
stays  constant  and  equal  to 


Characteristics  of  Circuits  having  Distributed  Inductance  and  Capac- 
ity. —  The  analyses  of  circuits  given  so  far  apply  to  those  in  which  the 
inductance  and  capacity  are  concentrated;  another  way  of  specifying  the 
circuits  with  which  we  have  been  dealing  is  to  state  that  the  current,  at 
any  given  instant,  is  exactly  the  same  at  every  point  in  the  circuit.  This 
condition  holds  for  the  majority  of  radio  circuits,  but  there  are  cases  where 
it  evidently  does  not  obtain,  thus  every  antenna  has  zero  current  at  its 
farther  end,  whereas  the  current  entering  it  at  the  base  may  be  many 
amperes.  This  is  the  most  striking  case  of  a  circuit  which  has  a  current 
varying  along  its  length,  but  there  are  others  in  which  the  same  effect 
exists  to  a  lesser  degree.  A  coil,  for  example,  may  have  an  internal  dis- 
tributed capacity  which  appreciably  affects  its  behavior. 

The  change  in  current  at  successive  points  along  an  antenna  is  due 
entirely  to  the  distributed  capacity  ;  each  unit  length  contributes  its  share 
to  the  total  capacity  and  of  course  requires  its  proportion  of  the  total 
charging  current.  The  current  flowing  in  at  the  base  of  the  antenna 
must  be  sufficient  to  charge  the  whole  length,  while  that  flowing  past  the 
middle  point  of  the  antenna  must  be  sufficient  to  charge  merely  the  upper 
half  of  the  antenna,  and  so  will  be  considerably  less  than  the  current  at 
the  base  of  the  antenna. 

Every  coil  has  more  or  less  distributed  capacity,  every  piece  of  the 
winding  acting  as  one  plate  of  a  condenser  for  every  other  part  because 
the  various  parts  are  at  different  potentials  and  so  will  have  electric  fields 
set  up  between  them  when  the  coil  is  excited.  But,  if  when  a  coil  is  used, 
it  sets  up  an  electric  field  as  well  as  a  magnetic  field,  it  must  be  considered 


108 


FUNDAMENTAL  IDEAS  AND  LAWS 


[CHAP.  I 


as  a  combination  of  coil  and  condenser.  This  internal  capacity  varies 
in  magnitude  appreciably  as  the  frequency,  at  which  the  coil  is  used,  is 
varied  and  so  cannot  be  treated  correctly  as  a  concentrated  capacity.  As 
ordinarily  used  a  coil  does  not  show  much  effect  from  this  internal  capacity 
because  the  condenser  to  which  the  coil  is  attached  has  so  much  more 
capacity  that  the  internal  capacity  is  completely  masked;  if,  however, 
the  coil  is  used  for  tuning  a  circuit  and  the  tuning  condenser  used  has  a 
small  capacity  then  the  internal  capacity  may  produce  an  appreciable 
effect  on  the  tuning  qualities  of  the  circuit.  The  calculation  of  this 
internal  capacity  and  its  effect  on  the  apparent  inductance  of  a  coil  will 
be  taken  up  in  the  next  chapter. 

Now  the  resistance  and  reactance  of  such  a  circuit  (having  distributed 
capacity  and  inductance)  vary  with  the  frequency  through  a  very  large 
range  of  values;  the  resistance  (as  measured  at  the  base  of  the  antenna) 


L  R 


L  R 


L  R 


L  R         L  R 


L  R 


L  R 


L  R        LR 


cr 

00  w~ 

~   cr 

-ww- 

~        C3~ 

-Ww 
~      cf 

-"00  ^AT 

00  W" 

~          Co" 

-^oo^v— 
~      cf 

-'OO  V\T 

^00  W 

-00  W~ 

°~ 
i« 

L=.0415  henry       R<=-.702  ohms 
Ci=C10=18.3  microfarad 


C=36.6  microfarad 


FIG.  107. — A  circuit  having  distributed  inductance  and  capacity,  similar  to  an  antenna. 

goes  from  very  small  to  very  large  values,  while  the  reactance  changes 
from  a  large  inductive  reactance  to  an  equally  large  capacitive  reactance. 
Moreover,  these  changes  occur  periodically  as  the  impressed  frequency  is 
continually  changed. 

To  demonstrate  experimentally  the  peculiar  characteristics  of  a  cir- 
cuit having  distributed  constants,  the  author  built  an  artificial  line  having 
inductance,  capacity,  and  resistance,  as  shown  in  Fig.  107;  this  line 
resembles  somewhat  a  long  antenna,  having  inductances  and  capacities, 
however,  several  hundred  times  as  large  as  those  of  an  actual  antenna.1 

A  variable  frequency  was  impressed  on  this  artificial  line  and,  by  means 
of  a  wattmeter,  ammeter,  and  voltmeter  its  resonance  characteristics  were 
determined.  The  impressed  voltage  was  kept  constant  at  20  volts  and 
the  frequency  varied  in  small  steps,  from  12  to  152  cycles  per  second. 
Fig.  108  shows  the  current  which  flowed  from  the  generator  into  the  line 
at  the  various  frequencies,  the  line  being  open  at  its  distant  end.  The 
line  showed  six  frequencies  in  the  range  used,  at  which  we  can  say  the  line 

1  See  "Some  Experiments  with  Long  Electrical  Conductors,"  by  John  H.  Morecroft, 
Proc.  I.R.E.,  Vol.  5,  No.  6,  Dec.,  1917. 


DISTRIBUTED   INDUCTANCE  AND   CAPACITY 


109 


10       20       30       40       50      60       70       80       90      100     110     120     130     140     150     160     17.0     180 
Impressed  Frequency 

FIG.  108. — Current  vs.  frequency  for  circuit  shown  in  Fig.  107. 


280 
260 
240 
220 
200 
180 
160 
140 
120 
100 


8 


ri 

8  « 
*§ 

y  .2 

S    3 
tf  £ 


-Res  stance 


Rea:tanc 


Character  st  cs  of  a 


orig  ele 


ctr 


cal  condu 


10      20       30      40       50       60       70       80       90      100     110     120     130     140     150     160 
Impressed  Frequency 

FIG.  109. — Resistance  and  reactance  vs.  frequency  for  circuit  shown  in  Fig.  107 


110  FUNDAMENTAL  IDEAS  AND  LAWS  [CHAP.  I 

was  in  resonance,  meaning  by  the  term  resonance  a  frequency  at  which 
the  power  factor  was  unity,  the  line  offering  resistance  reaction  only. 
Three  of  the  frequencies  correspond  to  what  we  have  called  parallel  reso- 
nance, the  current  being  a  minimum  and  the  other  three  to  series  reso- 
nance giving  large  values  of  current. 

The  resistance  and  reactance  of  the  line  were  calculated  from  the  meter 
readings  and  are  shown  in  Fig.  109.  The  resistance  varies  periodically 
from  a  low  value,  corresponding  to  series  resonance,  to  a  high  value,  cor- 
responding to  parallel  resonance. 

The  reactance  of  the  line  varies  periodically  from  inductive  to  capaci- 
tive  reactance  and  takes  all  values  between  165  ohms  positive  and  165 
ohms  negative.  From  the  results  shown  in  Fig.  109  it  may  be  judged 
how  indefinite  are  the  so-called  constants  of  such  a  circuit. 


CHAPTER    II 
RESISTANCE— INDUCTANCE— CAPACITY 

General  Concept  of  Resistance. — The  elementary  idea  of  resistance, 
obtained  by  a  student  analyzing  continuous  current  circuits,  must  be 
very  greatly  enlarged  and  generalized  when  studying  high  frequency  cir- 
cuits. In  the  continuous-current  circuit,  Ohm's  law  is  in  general  a  sufficient 
definition  for  the  term  resistance,  that  is,  R  =  E/I.  This  definition  pre- 
supposes that  all  of  the  voltage  E  is  used  up  in  overcoming  the  resistance 
reaction  of  the  circuit;  there  must  be  no  reaction  such  as  the  c.e.m.f.  of 
a  motor,  or  c.e.m.f.  such  as  exists  in  a  circuit  in  which  storage  batteries 
are  being  charged,  or  else  the  definition  is  ordinarily  changed  to  the  form 

j.,       Eimp  —  EC 
K  —       —j , 

where 

E imp  =  the  impressed  voltage; 

Ec  =  ihe  counter  voltage  of  motor,  batteries,  etc. 

This  restated  definition  must  be  still  more  generalized  when  the  ordi- 
nary alternating  current  circuit  is  considered,  in  fact,  a  new  concept  of 
resistance  must  be  obtained.  It  might  seem  that  Joule's  law  would  serve 
sufficiently  to  define  resistance;  this  law  states  that  the  electrical  power 
liberated  as  heat  in  a  circuit  is  given  by  the  equation 

Heat  generated  =  I2Rt. 

Certainly  this  law  is  a  more  general  definition  of  resistance  than  Ohm's 
law  because  it  automatically  excludes  the  effects  of  counter  e.m.f.'s.,  etc.; 
thus  a  storage  battery,  being  charged,  might  (if  suitable  precautions  were 
taken)  be  immersed  in  a  calorimeter  while  being  charged  and  the  heat 
produced  be  measured  by  the  rise  in  temperature  of  the  calorimeter 
water.  This  amount  of  heat,  properly  substituted  in  Joule's  law,  will 
determine  the  resistance  of  the  circuit  in  so  far  as  this  resistance  manifests 
itself  in  producing  heat. 

However,  electric  energy  may  be  dissipated  in  forms  other  than  heat; 
thus  radiation  of  electro-magnetic  waves  from  an  antenna  dissipates  energy 
from  the  circuit  as  truly  as  does  the  ordinary  heating  of  the  circuit. 

111 


112 


RESISTANCE— INDUCTANCE— CAPACITY 


[CHAP.  II 


These  elementary  considerations  force  us  to  adopt  a  new  concept  of 
resistance,  it  being  based  on  the  idea  that  any  transfer  of  energy  from 
(or  to)  that  part  of  the  circuit,  the  resistance  of  which  is  desired,  must 
be  considered  in  determining  the  resistance.  Thus  the  resistance  between 
two  points  in  a  circuit  a-b,  Fig.  1,  is  defined  by  the  equation, 


R 


power  transferred  between  points  a  and  b 


(1) 


This  "  power  transferred  "  between  a  and  b  may  be  leaving  the  electrical 
circuit  between  these  two  points  or  it  may  be  entering  the  circuit 
between  these  points.  If  power  is  leaving  the  circuit  between  these  points, 
as  heat  or  otherwise,  the  resistance  is  positive;  if  power  is  entering  the  cir- 
cuit between  these  two  points  the  resistance  is  negative,  and  if  power  is  en- 
tering the  circuit  at  the  same  rate  as  it  is  leaving  then  the  resistance  is  zero. 

From  this  standpoint  any  electrical 
circuit  carrying  current,  after  reach- 
ing the  steady  state  (no  change  in 
the  amplitude  of  the  current)  has 
on  the  whole,  zero  resistance.  Of 
course  we  know  that  the  circuit 
does  actually  have  resistance,  but 
we  may  consider  the  source  of  power 
supply  as  having  as  much  negative 
resistance  as  the  rest  of  the  circuit 
has  positive  resistance.  At  the 
generator  (or  other  source  of  power 


Direction  of 
energy  flow 


FIG.  1. — If  power  is  leaving  the  circuit  the 
resistance  is  positive  so  that  if  power  is 
entering  the  circuit  its  resistance  must 
be  considered  negative. 


supply)  energy  is  entering  the 
circuit  as  fast  as  it  is  dissipated 
in  other  parts  of  the  circuit.  If 
the  circuit,  as  a  whole,  has  positive 

resistance  the  current  must  be  decreasing  in  amplitude;  this  state  of 
affairs  occurs  in  the  ordinary  damped  oscillatory  discharge  of  a  con- 
denser, whereas  a  circuit  which  takes  an  appreciable  time  to  build  up 
to  its  steady  state  has,  during  the  time  required  to  reach  the  steady  state, 
on  the  whole  a  negative  resistance  because,  considering  the  circuit  as  a 
whole,  energy  is  entering  at  a  rate  faster  than  that  at  which  energy  is 
leaving. 

Various  Factors  Affecting  the  Resistance  of  a  Circuit. — Among  the 
factors  contributing  to  the  resistance  of  a  radio  circuit  are  to  be  con- 
sidered (1)  resistance  of  the  conductor  itself;  (2)  resistance  of  neighbor- 
ing closed  ciruits  and  their  proximity;  (3)  magnetic  material  close  enough 
to  the  circuit  to  be  magnetized  by  it;  (4)  losses  in  the  dielectric  of  any 
condenser  in  the  circuit;  (5)  corona  losses  from  parts  of  the  circuit;  (6) 


VARIOUS   FACTORS  AFFECTING  RESISTANCE  113 

radiation  of  electro-magnetic  energy.  All  of  these  factors  vary  with  the 
frequency  of  the  current  in  the  circuit,  some  of  them  with  the  magnetic 
gradient  set  up  by  the  circuit  and  some  with  the  electric  gradient  set  up 
by  the  circuit.  Each  will  be  taken  up  in  turn  and  analyzed  as  much  as 
seems  suitable  for  a  text  of  this  kind. 

Conductor  Resistance.  —  The  resistance  of  a  conductor,  in  the  form  of 
a  wire,  to  the  flow  of  continuous  current  is  given  by  the  formula 


(2) 


in  which  p  is  the  specific  resistance  of  the  material  composing  the  con- 

ductor; 

I  is  the  length  of  the  conductor; 
a  is  the  cross-sectional  area  of  the  conductor. 

This  formula  assumes  that  all  parts  of  the  cross-section  of  the  con- 
ductor carry  the  same  proportion  of  the  total  current;  in  other  words 
that  the  current  density  is  uniform  throughout  the  section  of  the  con- 
ductor. This  assumption  is  true  for  continuous  current  or  for  alternating 
current  of  very  low  frequency.  If  the  conductor  is  large  in  cross-section 
or  the  frequency  is  high,  the  inner  sections  of  the  conductor  carry  a  rela- 
tively small  part  of  the  total  current,  the  density  of  current  being  greatest 
at  the  surface  of  the  conductor;  in  fact  for  very  high  frequencies  a  com- 
paratively thin  skin  on  the  surface  of  the  conductor  carries  practically 
all  the  current,  so  much  so  that  if  the  center  part  of  the  conductor  were 
removed,  leaving  nothing  but  a  thin  walled  tube  of  the  same  diameter 
as  the  original  wire,  the  resistance  would  be  practically  the  same.  This 
tendency  of  the  current  to  concentrate  on  the  outer  surface  of  the  wire  at 
high  frequencies  is  called  the  skin  effect,  the  reason  for  the  name  being 
obvious.  If  there  are  no  other  conductors  carrying  current  in  the  vicinity 
of  the  one  in  question  this  distribution  of  current  will  be  symmetrical 
about  the  axis  of  the  wire,  but  if  there  are  other  current-carrying  con- 
ductors in  the  neighborhood  the  distribution  of  current  through  the  cross- 
section  of  the  wire  may  be  irregular,  perhaps  only  the  surface  part  of 
the  conductor  on  one  side  carrying  an  appreciable  current. 

Any  distribution  of  current  other  than  the  regular  distribution  of 
equal  current  density  throughout  the  section  of  the  conductor  will  result 
in  an  increase  in  the  resistance  of  the  conductor;  this  increase  may  be 
so  great  that  the  resistance  for  a  high  frequency  alternating  current  may 
be  many  times  as  much  as  the  resistance  of  the  same  wire  for  continuous 
current. 

A  simple  illustration  of  this  effect  is  given  in  Fig.  2,  showing  three 
10-ohm  resistances  in  parallel.  Suppose  the  resistance  of  this  combi- 
nation is  determined  by  the  power  loss  instead  of  by  the  ordinary  law  for 


9  amperes 


10  ohms 


10  ohms 


114  RESISTANCE— INDUCTANCE— CAPACITY  [CHAP.  It 

resistances  in  parallel.  Let  3  amperes  flow  through  each  resistance,  giving 
a  line  current  of  9  amperes  and  a  power  loss  of  3X(32X10)  =270  watts. 
Then  the  total  resistance  will  be  obtained  by  the  equation  R  =  P/I2  or 
270/9  =3.33  ohms,  the  same  as  we  should  get  by  the  law  for  resistances 
in  parallel. 

Now  suppose  that  for  some  reason  or  other  the  current  redistributes 
itself  so  that  the  two  outside  paths  carry  4  amperes  each  and  the  center 

! wvwvwww\^-|  one  carries  1  ampere.     (Such 

a    redistribution    might    well 
>  occur  if  the  combination  were 

used    in    a    high     frequency 
circuit.)       The    line    current 

10  ohms  .n  ,         _ 

will  again  be  9  amperes  and 

FIG.  2.-A  solid  conductor  of  3.33  ohms  resistance  fhe  logs  will  be  (2X(42X10)) 
may  be  considered  as  three  separate  filaments         /         ,   2          ,, 
each  of  10  ohms  resistance.  +  (l  X  (I2  X 10))  =  330      watts, 

which,  divided  by  the  square 

of  the  line  current,  gives  a  resistance  of  4.08  ohms,  a  considerable  increase 
over  the  value  for  a  uniform  distribution  of  current  between  the  different 
paths. 

The  paths  shown  in  Fig.  2  might  represent  three  of  the  imaginary 
filaments  into  which  a  wire  may  be  supposed  divided,  and  the  calculation 
shows  that  any  distribution  of  current  between  the  filaments  other  than 
uniform  distribution  results  in  an  increase  in  the  resistance  of  the  con- 
ductor; moreover,  the  greater  the  non-uniformity  of  current  density  the 
greater  will  be  the  corresponding  increase  in  resistance. 

Skin  Effect  in  Straight  Wires. — The  non-uniformity  of  current  dis- 
tribution referred  to  above  occurs  in  every  conductor  carrying  alternating 
current,  the  current  density  being  greater  at  the  surface  than  at  the  center 
of  the  wire,  but  this  non-uniformity  is  not  appreciable  unless  the  wire  is 
large  in  diameter,  or  the  frequency  is  high;  the  increase  in  resistance  due 
to  skin  effect  depends  upon  the  product  of  the  cross-section  and  the  fre- 
quency and  for  copper  wires  the  general  idea  given  by  the  following  table 
is  useful. 

Frequency  multiplied  by  the  Ratio  of  a.c.  to  c.c. 

Cross-section  in  circular  mils.  resistance. 

10,000,000  1.003 

20,000,000  1.012 

100,000,000  1.30 

As  an  example  No.  10  wire  has  a  cross-section  of  10,000  circular  mils; 
at  a  frequency  of  2000  cycles  its  a.c.  resistance  is  1.2  per  cent  greater  than 
its  c.c  resistance,  while  at  10,000  cycles  its  resistance  would  have  increased 
over  its  c.c.  value  by  30  per  cent. 


SKIN  EFFECT  IN  STRAIGHT  WIRES 


115 


An  exact  analysis  shows  that  the  ratio  of  a.c.  resistance  to  c.c.  resist- 
ance may  be  expressed  in  terms  of  diameter,  permeability,  frequency,  and 
resistivity;  a  correct  expression  involves  an  infinite  series  of  terms,  but 
these  series  have  been  summed  so  that  accurate  data  are  available  for 
calculating  the  resistance  of  any  round  wire,  the  permeability  and  resis- 
tivity of  which  are  known.  For  copper  wire,  in  which  the  permeability 
is  unity,  tables  have  been  compiled  which  present  the  data  in  convenient 
form.  In  the  curves  of  Figs.  3  and  4  is  shown  the  factor,  ra,  by  which 
the  c.c.  resistance  must  be  multiplied  to  give  the  resistance  for  alternating 
current.  Plotted  as  abcissse  are  values  of  rVf,  where  r  is  the  radius  of 
the  wire  in  cm.  and  /  is  the  frequency  of  the  current  being  used. 

It  is  sometimes  useful  to  know  how  a  large  wire  can  be  used  without 
having  its  a.c.  resistance  exceed  its  c.c.  resistance  by  more  than  a  specified 
amount.  The  data  given  in  the  accompanying  table,  compiled  by  L.  W. 
Austin,  may  be  useful  for  this  purpose: 

TABLE  I 

WIRE  DIAMETERS 

Largest  wire  (straight)  which  can  be  used  without  the  high  frequency  resistance  exceeding  the  c.c. 
resistance  by  more  than  1  per  cent 


DIAMETERS  GIVEN  IN  MILLIMETERS. 

Wave  length 

in  meters. 

Advance. 

Manganin. 

Platinum. 

Copper. 

100 

0.30 

0.29 

0.13 

0.006 

200 

0.46 

0.40 

0.20 

0.045 

300 

0.57 

0.50 

0.27 

0.09 

400 

0.66 

0.60 

0.30 

0.10 

600 

0.83 

0.75 

0.37 

0.15 

800 

0.98 

0.88 

0.42 

0.20 

1000 

1.10 

0.99 

0.50 

0.21 

1200 

1.20 

1.10 

0.57 

0.22 

1500 

1.30 

1.21 

0.63 

0.26 

2000 

1.52 

1.38 

0.73 

0.30 

3000 

1.82 

1.62 

0.80 

0.33 

Frequency  =  3  X 108  -5-  wave  length 

In  the  case  of  a  wide  flat,  conductor,  such  as  the  earth's  surface,  the 
currents  which  are  set  up  in  the  surface  penetrate  into  the  substance  of 
the  conductor  according  to  the  specific  resistance  of  the  material,  perme- 
ability, and  frequency.  The  relation  between  the  density  of  current  at 
the  surface  and  the  density  at  a  point  distant  x  below  the  surface  is  given 


(3) 


. 

Xsm      ><- 


116 


RESISTANCE— INDUCTANCE— CAPACITY 


[CHAP.  II 


4.5 

4.0 

g3.5 

,2  3.0 

1 

S2.5 


High 


of 


'reojuenby  resistam 


round 


Ra 


opper  w 


R< 


10 


15 


20 


25 


35 


40 


45 


50 


Radius  V  frequency 

FIG.  3. — Variation  of  resistance  of  round,  straight,  copper  wire  with  frequency  and 

radius. 


80 
70 

60 
* 

H 

igh 

fre 

juei 

icy 

resi 

stan 

ce 

^ 

/ 

0 

'  roi 

ind 

cop 

>er 

vin 

s 

X 

f 

Ra 

,=7? 

»R< 

^ 

x 

/ 

X 

ys 

r° 

X 

> 

x 

5 

& 

r 

20 

10 
0 

/ 

jT 

/ 

> 

x 

^ 

jT 

x 

X 

/ 

^ 

X 

100          200         300         400         5C 
Radius  V 

0          600 

700          800          900         1000 

frequency 

FIG.  4. — Variation  of  resistance  of  round,  straight,  copper  wire  with  frequency  and 

radius. 


SIMPLE  ANALYSIS  OF  SKIN  EFFECT  117 

in  which 

7o  =  current  density  at  surface; 

i  =  current  density  a  distance  x  cm.  below  the  surface; 
co  =  27r/,  where  /  is  the  frequency  of  current; 
n  =  permeability  of  the  substance; 
p  =  specific  resistance  of  the  substance,  abohms  per  cm3. 

Not  only  does  the  density  of  current  decrease  as  the  distance  below 
the  surface  is  increased  but,  as  indicated  by  Eq.  (3),  it  reaches  its  corre- 
sponding values  at  later  time  than  at  the  surface,  this  amount  of  time  lag 
increasing  as  the  depth  below  the  surface  is  increased.  This  really  means 
that  the  current  penetrates  into  the  substance  with  a  wave  motion;  the 
attenuation  is,  however,  very  high,  so  that  probably  only  a  fraction  of 
a  wave  length  is  actually  set  up  in  the  conductor  with  an  appreciable 
amplitude. 

A  Simple  Analysis  of  Skin  Effect.  —  Although  an  exact  analysis  of  skin 
effect  in  a  conductor  requires  the  theory  of  wave  propagation,  and  special 
mathematical  series  for  a  solution,  a  very  good  idea  of  its  cause  (and, 
what  is  much  more  important,  its  remedy)  may  be  had  from  the  ordinary 
laws  of  current  flow  in  inductive  circuits.  The  first  thing  to  notice  about 
the  problem  is  the  effect  of  frequency  upon  the  division  of  current  between 
two  paths  in  parallel,  as  shown  in  Fig.  5,  the  two  paths  having  equal 


>T  wwv  —  lyronffT  —  i 


At  low  frequency     -±  --=-^ 
I2      Rx 

At  high  frequency  -Ii  =-Hl 
la      l-it( 

FIG.  5.  —  For  branched  circuits  the  resistance  controls  the  division  of  current  at  low  fre- 
quency whereas  the  reactance  controls  the  division  at  high  frequency. 

resistance  but  unequal  inductance.     The  formula  for  the  current  flow  in 
each  path  is 

E 


1  = 


At  very  low  frequency  the  coL  term  is  negligible,  and  so  we  have  the 
currents  dividing  between  the  two  paths  inversely  as  the  two  resistances, 
that  is,  the  two  currents  will  be  alike.  At  very  high  frequency,  however, 
the  resistance  term  becomes  relatively  negligible  and  the  current  divides 
inversely  proportional  to  the  inductance  in  the  two  branches.  The  same 


118  RESISTANCE—  INDUCTANCE—  CAPACITY  [CHAP.  II 

voltage  is  applied  to  both  paths,  so  the  sum  of  the  resistance  reaction 
and  the  inductance  reaction  (added  vectorially)  in  each  path  must  be  the 
same.  It  is  from  this  standpoint  that  we  will  investigate  the  skin  effect 
in  wires. 

Imagine  a  round  copper  wire  carrying  current  uniformly  throughout 
its  cross-section,  Fig.  6.  The  density  of  magnetic  flux  at  a  point  A  on 
the  surface  of  the  wire  is  given  by  the  formula 


(4) 


where  7  =  total  current  in  amperes; 

a  =  radius  of  the  conductor  in  cm. 


At  a  point  B  inside  the  conductor, 
the  amount  of  current  producing  flux 
(for  of  course  there  is  magnetic  flux  inside 
the  conductor)  is  only  that  part  of  the 
total  current  which  flows  inside  the  circle 
inscribed  through  the  point  B.  This 
amount  of  current  is,  for  uniform  cur- 
rent density,  equal  to  IXri'2/a2.  The 
magnetic  flux  density  at  B  is,  therefore, 
FIG.  6.  —  Cross-section  of  wire  of  by  Eq.  (4) 

radius  a;    magnetic  field  density 

to  be  calculated  at  points  A,  B,  p>   _.27ri2      1  _  .27ri  f  . 

andC.  ^B~~    a2     Xn~    a2   ' 

For  a  point  C  outside  the  wire,  distant  r2  from  the  axis  of  the  wire,  the 
flux  density  is  given  by  the  equation 


From  Eqs.  (4)  and  (6),  the  flux  density  throughout  th  ecross-section  of 
the  wire  and  in  the  region  surrounding  the  wire  may  be  calculated  ;  Fig. 
7  shows  the  result  of  such  a  calculation.  In  the  upper  part  of  the  figure 
the  flux  is  shown  in  the  form  of  circles  concentric  with  the  axis  of  the  wire, 
the  closeness  of  the  circles  representing  the  flux  density,  and  in  the  lower 
part  of  the  figure  is  shown  a  plot  of  the  flux  densities,  ordinates  being 
values  of  flux  density  and  abscissae  being  distance  from  center  of  wire. 

The  total  flux  surrounding  any  point  is  obtained  by  adding  the  flux 
from  a  point  infinitely  distant  from  the  wire,  up  to  the  point  in  question; 
a  curve  showing  the  value  of  this  flux  for  different  points  inside  and  out- 
side the  wire  is  shown  in  Fig.  8.  The  ordinates  of  the  curve  are  obtained 
by  integrating  the  density  curves  of  Fig.  7.  The  flux  <£i,  is  the  total  flux 
produced  by  the  current  in  the  wire,  outside  of  the  wire  itself,  whereas 


SIMPLE  ANALYSIS  OF  SKIN  EFFECT 


119 


surrounding  any  point  outside  the  wire  as,  e.g.,  C  of  Fig.  6,  there  is  a 
flux  equal  to  <fa.  There  is  a  certain  amount  of  flux  inside  the  wire 
itself  and  the  flux  surrounding  the  innermost  filament  is  obtained  by 
adding  to  4>i  this  internal  flux;  it  is  shown  by  02  in  Fig.  8. 

Now  let  us  consider  the  wire  made  up  of  a  bundle  of  separate  parallel 
filaments,  such  a  wire  as  would  be  obtained  by  using  a  cylindrical 
bundle  of  very  fine  wires,  each  insulated  from  its  neighbor,  except  at  the 


FIG.  7. — Closeness  of  circular  lines  show  the  density  of  magnetic  field  around  a  non- 
magnetic wire;  in  lower  part  of  figure  magnetic  field  density  is  shown  by  distance 
from  reference  line  to  curve  marked  B. 


ends  of  the  wire  in  question,  where  they  are  all  electrically  connected 
together.  Let  the  resistance  of  each  of  these  filaments  be  R.  If  an 
e.m.f.,  E  sin  co£,  is  impressed  across  the  ends  of  this  composite  wire, 
all  filaments  will  have  the  same  impressed  e.m.f.,  and  it  is  therefore 
evident  that  the  sum  of  the  reactions  in  each  filament  must  add  up 
(vectorially)  to  equal  this  impressed  force. 

The  resistance  drop  in  each  filament  is  IR  and  the  inductance  drop 
is  —  =  oo0  where  <£  is  the  maximum  amount  of  flux  surrounding  the 


120 


RESISTANCE— INDUCTANCE— CAPACITY 


[CHAP.  II 


filament  in  question.    Hence  for  two  filaments,  one  at  0  and  the  other  at 
A  (Fig.  6)  we  must  have 

E2  =  (7i#)2+O/>i)2 
and 


where  I\  and  /2  are  the  currents  in  the  two  filaments  considered. 

In  these  equations  E,  I,  and  </>,  must  have  corresponding  values, 
i.e.,  either  effective  values  or  maximum  values. 

At  very  high  frequencies  the  resistance  drop  is  negligible  compared 
to  the  flux  reaction  drop,  and  so  we  must  conclude  that,  for  frequencies 
which  make  IR  negligible  compared  to  co<£,  the  flux  surrounding  all  fila- 
ments of  the  wire  must  be  the  same.  Referring  to  Fig.  8  this  statement 
means  that  fa—  </>i  =  0,  that  is,  there  is  no  flux  inside  the  wire  itself.  If 


(of  Fig.  6) 


FIG.  8. — Curve  showing  total  flux  outside  any  point  considered  in  Fig.  7. 

there  is  no  internal  flux  the  flux  density  everywhere  inside  the  wire  must 
be  zero,  and  as  the  flux  density  at  any  point  in  the  wire  distant  r  from  the 
axis  is  equal  to  .21 /r,  where  /  now  signifies  the  current  flowing  in  the  wire 
inside  of  a  circle  through  the  point  in  question,  we  must  conclude  that  there 
is  no  current  anywhere  inside  the  wire. 

At  ordinary  frequencies  the  resistance  drop  is  not  negligible  in  com- 
parison with  the  reactance  drop,  so  that  the  sweeping  conclusion  of  the 
previous  paragraph  (no  current  anywhere  inside  the  conductor)  is  not  true, 
but  it  is  evident  that,  as  the  frequency  increases  more  and  more  the  dif- 
ference between  02  and  <f>i  of  Fig.  8  must  continually  decrease. 

If  instead  of  a  copper  wire  an  iron  wire  had  been  assumed,  the  internal 
flux  density  would  have  been  very  much  increased  so  that  Figs.  7  and  8 
would  have  more  nearly  the  appearance  of  Figs.  9  and  10.  The  value 
of  the  internal  flux  ($2  — <£i)  would  be  very  much  increased,  so  that  the 


EFFECT  OF  PERMEABILITY  ON  SKIN  EFFECT 


121 


frequency  at  which  the  IR  drop  becomes  negligible  compared  to  the  oxj> 
drop  is  much  less  than  for  copper  wire. 

Offsetting  this  effect  to  some  extent,  however,  is  the  fact  that  the 
specific  resistance  of  the  iron  is  greater  than  that  of  copper;  the- result 
is  that  iron,  while  it  has  a  greater  skin  effect  than  copper,  does  not  have 
as  much  greater  effect  as  the  increased  value  of  /*  would  indicate. 

The  change  in  current  density  throughout  the  cross-section  of  wire 
due  to  the  effect  of  the  internal  flux,  is  indicated  (for  a  certain  wire)  in 


FIG.  9. — Strength  of  magnetic  field  in  and  around  a  wire  of  magnetic  material. 

Fig.  11,  the  three  curves  showing  how,  as  the  frequency  is  increased, 
the  current  shifts  more  and  more  to  the  outer  skin  of  the  conductor.  The 
current  density  at  the  surface  of  the  conductors  has  been  assumed  the 
same  for  the  three  frequencies. 

It  is  evident  from  the  foregoing  discussion  that  a  substance  having 
high  specific  resistance  and  low  permeability  will  have  the  least  skin  effect; 
this  is  shown  in  Table  I  on  p.  1 15.  The  wires  used  for  resistance  in  making 
tests  and  measurements  in  high-frequency  circuits  should  be  made  of 
small  wires  of  the  high-resistance  alloys,  practically  all  of  which  have  unity 
permeability. 


122 


RESISTANCE— INDUCTANCE— CAPACITY 


[CHAP.  II 


Elimination  of  Skin  Effect. — One  obvious  remedy  for  skin  effect  is 
to  so  construct  the  conductor  that  there  is  no  internal  flux,  or  rather  that 
the  internal  flux  is  negligible  compared  to  the  external  flux,  which  of  course 
produces  no  skin  effect,  as  it  affects  all  filaments  of  the  wire  equally.  A 


FIG.  10. — Total  flux  outside  any  point  considered  in  Fig.  9. 

conductor  with  no  internal  flux  is  impossible,  but  such  a  condition  may 
be  approximated  by  using  a  tubular  conductor;  such  a  construction  is 
used  for  high-frequency  ammeters  designed  to  carry  comparatively  large 
currents  (say  25  amperes  or  more).  The  current  to  be  measured  is  carried 


FIG.  11. — Current  density  in  a  solid,  round,  conductor  at  three  different  frequencies. 

from  the  connectors  of  the  ammeter  to  two  circular  disks,  and  these  disks 
are  connected  by  a  set  of  very  thin  high-resistance  strips,  the  whole  arrange- 
ment having  the  appearance  of  a  barrel,  the  thin  strips  taking  the  place 
of  the  barrel  staves.  Such  a  construction  is  shown  in  Fig.  12,  this  showing 
the  construction  of  a  40-ampere,  so-called  "  hot-wire  "  meter.  As  the 


METHODS  OF  ELIMINATING  SKIN   EFFECT 


123 


radial  thickness  of  these  strips  is  only  about  .004  cm.,  there  is  practically 
no  internal  cross-section  to  the  conductor;  it  is  all  "  skin." 

In  the  scheme  ordinarily  employed  for  reducing  skin  effect  the  required 
cross-section  of  conductor  (which  depends  upon  the  amount  of  current  to 
be  carried),  is  made  up  of  a  great  many  small  wires,  each  completely 
insulated  from  all  the  rest;  a  common  form  of  this  cable  used  for  winding 
radio  coils  consists  of  48  No.  38  enameled  wires  properly  woven  together. 
In  eliminating;  skin  effect  by  this  construction  it  is  not  sufficient  to  merely 


FIG.  12. — A  hot  wire  ammeter  showing  how  the  skin  effect  is  minimized  by  special 
arrangement  of  very  thin  strips  of  high-resistance  metal. 

subdivide  the  conductor  into  small  well-insulated  strands;  these  strands 
must  be  so  woven  or  twisted  together  that  each  strand  is  as  much  on  the 
outer  surface  of  the  cable  as  every  other  one. 

If  48  No.  38  insulated  wires  are  laid  loosely  together,  parallel  to  one 
another,  it  will  be  found  that  the  increase  in  resistance  due  to  skin  effect 
is  nearly  as  much  as  though  a  solid  wire  (of  the  same  cross-section  as  that 
of  the  cable)  were  used.  (The  stranded  cable  would  be  somewhat  better 
than  the  solid  wire,  because  of  its  somewhat  greater  useful  outer  surface.) 
It  is  therefore  important  in  getting  the  stranded  wire  (sometimes  called 


124  RESISTANCE— INDUCTANCE— CAPACITY  [CHAP.  II 

litzendraht)  to  see  that  not  only  is  it  made  up  of  a  great  number  of  well- 
insulated  strands,  but  also  that  these  strands  are  properly  interwoven. 
A  real  braiding  process  will  accomplish  the  result  but  a  suitably  twisted 
cable  is  nearly  as  good.  A  properly  twisted  cable  must  be  made  up  of 
several  component  twisted  cables  to  be  free  from  marked  skin  effect.  For 
48  No.  38  cable,  e.g.,  three  separately  twisted  cables,  each  of  16  wires,  may 
be  twisted  together  and  the  resulting  cable  will  be  nearly  as  good  as  braided 
cable. 

It  is  important  to  note  just  what  effect  is  to  be  obtained  in  making 
these  high-frequency  radio  cables ;  the  cable  must  be  so  constructed  that 
each  strand  has,  per  unit  length  (say  per  meter)  the  same  flux  surrounding 
it,  when  each  strand  is  carrying  the  same  current.  When  the  strand  is  in 
the  center  of  the  cable  it  has  more  flux  surrounding  it  than  when  it  is  on 
the  periphery,  hence  each  strand  must  occupy  corresponding  positions  in 
the  cross-section  of  the  cable  for  equal  distances,  in  order  that  it  may  have 
the  same  surrounding  flux  per  unit  length  as  all  the  other  strands. 

Even  in  suitably  woven  cable  there  is  still  some  skin  effect  due  to  the 
finite  size  of  the  strands  themselves,  each  strand  in  itself  having  an  appreci- 
able skin  effect  at  very  high  frequencies. 

It  is  important  in  purchasing  radio  cable  of  the  kind  just  described  to 
make  tests  for  the  continuous-current  resistance.  In  making  this  test  the 
enamel  must  be  removed  carefully  from  each  strand,  at  both  ends  of  the 
piece  to  be  tested,  and  the  strands  be  well  soldered  together.  The  c.c. 
resistance  should  be  calculated  from  the  total  cross-section  of  copper  in 
the  cable  and  the  measured  value  should  approach  this  very  closely.  In 
making  cable  a  strand  may  break  and  the  operator  insert  another  and  con- 
tinue the  process  of  weaving  the  cable.  But  such  a  broken  strand  is 
evidently  of  no  use  in  carrying  current,  because  one  break  opens  that 
strand  completely,  the  strand  being  insulated  from  its  neighbors. 

Specifications  for  radio  cable  should  therefore  state  not  only  the  size 
and  number  of  wires  to  be  used,  quality  of  enamel,  method  of  twisting, 
etc.,  but  should  also  call  for  a  c.c.  resistance  within  a  certain  percentage 
of  the  theoretical  value.  The  longer  the  pieces  of  cable  called  for,  the 
more  likely  are  breaks  to  occur,  for  this  reason  the  cable  is  generally 
obtained  in  lengths  of  a  few  hundred  feet  only.  If  two  pieces  of  radio 
cable  are  to  be  joined,  the  greatest  of  care  must  be  exercised  in  making 
the  joint;  if  only  half  the  strands  are  soldered  together  (quite  likely  unless 
each  individual  wire  is  separated  from  the  rest  and  properly  cleaned  before 
attempting  to  solder  the  joint)  then  the  resistance  of  the  whole  cable  is 
twice  as  much  as  it  should  be. 

Skin  Effect  in  Coils. — With  the  foregoing  analysis  of  skin  effect  in 
mind  it  is  at  once  evident  that  the  redistribution  of  current  throughout 
the  cross-section  of  a  conductor  will  be  greater  if  the  conductor  is  used 


SKIN  EFFECT  IN  COILS 


125 


in  making  a  coil  than  if  it  is  used  in  the  form  of  a  straight  wire.  The  dis- 
tribution of  magnetic  flux  inside  a  single  layer  solenoid  is  somewhat  as 
shown  on  Fig.  13;  the  flux  density  is  high  just  inside  the  solenoid  and 
practically  zero  at  the  outer  surface  of  the  coil.  Assuming  that  this  density 
decreases  to  zero  from  the  inner  surface  of  the  winding  to  the  outer  (nearly 


.Flux  density  =B 
FIG  13. — Approximate  flux  distribution  inside  a  short  solenoid. 


the  case  for  ordinary  coils)  it  is  evident  that  the  outer  filaments  of 
the  wire  are  linked  with  much  more  flux,  than  are  the  inner  filaments. 
Thus  an  imaginary  filament  on  the  outside  of  the  wire  as  at  6,  Fig.  13, 
will  be  linked  with  a  flux  in  excess  of  that  linked  with  filament  a  by  an 
amount  equal  to  B/2Xd  (where  B  is  the  flux  density  at  the  inner  surface 
of  the  winding  and  d  is  the 
radial  depth  of  the  wind- 
ing) per  unit  length  of  the 
wire.  It  is  apparent  that 
the  current  will  tend  to 
crowd  into  that  part  of  the 
wire  which  is  on  the  inside 
of  the  coil,  the  inductance 
reaction  being  less  for  the 
filaments  on  the  inner  side 
of  the  winding  than  for 
those  on  the  outer  side. 

But  besides  this  ten- 
dency of  the  current  to 
redistribute  itself,  there 

is  also  the  tendency  to  redistribution  about  the  axis  of  the  wire,  and  also 
each  conductor  exerts  a  certain  effect  on  its  neighbor — these  all  combine 
to  produce  a  current  distribution  about  as  indicated  in  Fig.  14,  the  density 
of  current  being  indicated  by  the  proximity  of  the  dots. 

In  constructing  variable  resistances  for  use  in  making  radio  measure- 


FIG.  14. — Distribution  of  current  in  the  conductors^of 
a  short  solenoid;  density  of  shading  corresponds  to 
current  density. 


"126  RESISTANCE— INDUCTANCE— CAPACITY  [CHAP.  II 

ments,  skin  effect  must  be  carefully  considered.  The  most  convenient  form 
of  variable  rheostat  is  a  cylindrical  one  with  a  sliding  contact,  the  almost 
universal  form  of  laboratory  rheostat  for  ordinary  c.c.  and  a.c.  measure- 
ments. But  this  type  of  winding  is  not  satisfactory  for  high-frequency 
currents  because  of  the  extra  skin  effect  caused  by  solenoidal  winding  and 
also  because  the  amount  of  self-induction  in  such  a  rheostat  is  too  great  to 
be  neglected  in  radio  circuits.  Radio  cable  cannot  be  used  with  sliding 
contact  rheostats  for  evident  reasons:  solid  wire  must  therefore  be  used 
and  still  the  skin  effect  and  self-induction  be  reduced  to  a  minimum.  This 
is  done  by  winding  on  a  porcelain  tube  a  bifilar  high-resistance  solid  wire; 
the  two  wires  making  the  bifilar  construction  are  wound  around  the  cylinder 
in  opposite  directions,  the  two  wires  crossing  each  other  twice  per  turn. 
Such  a  winding  has  a  self-induction  practically  zero,  and  hence  has  a 
minimum  skin  effect. 

The  increase  in  resistance  of  coils,  due  to  skin  effect,  is  a  very  difficult 
problem  to  analyze  mathematically;  only  the  simplest  cases  have  been 
considered,  and  even  then  assumptions  have  been  made  which  make  the 
validity  of  the  equations  obtained  doubtful. 

An  experimental  investigation  of  the  skin  effect  in  coils  was  carried 
out  by  the  author,  measurements  being  made  on  a  Wheatstone  bridge,  and 
the  results  are  given  herewith;  they  serve  to  indicate  how  much  increase 
in  resistance  from  skin  effect  may  be  expected  with  coils  similar  in  form. 
The  single  layer  coils  were  wound  on  dry  wood  reels  with  double  cotton- 
covered  wire,  the  wires  being  laid  as  closely  together  as  possible.  The 
length  of  the  winding  was  10  cm.  and  the  approximate  diameter  (the  cross- 
section  was  actually  octagonal)  was  10.5  cm.  The  datum  is  given  in  the 
accompanying  table,  both  self-induction  and  resistance  being  given,  the 
results  being  probably  accurate  to  within  1  per  cent  unless  otherwise  stated. 

There  are  two  effects  which  must  be  kept  in  mind  when  interpreting 
these  results;  there  is  an  actual  increase  in  resistance  due  to  redistribution 
of  current  in  the  conductor  of  which  the  coil  is  made,  and  there  is  an 
increase  in  the  measured  value  of  resistance  due  to  the  effect  of  internal 
capacity,  explained  in  the  previous  chapter  when  analyzing  resonance  in 
parallel  circuits. 

Every  coil  has  internal  capacity  due  to  one  part  of  the  winding  being 
equivalent  to  one  plate  of  the  condenser,  acting  with  every  other  part  to 
form  a  condenser.  It  was  shown  that  the  apparent  resistance  of  an  induc- 
tance, shunted  with  a  condenser,  increases  as  the  frequency  is  increased, 
in  accordance  with  Eq.  (48).  Although  this  equation  is  not  directly 
applicable  to  these  coils  (the  capacity  of  which  changes  with  frequency 
changes)  it  indicates  that  the  measured  value  of  resistance  may  be  expected 
to  increase  entirely  aside  from  any  skin  effect  which  may  be  present.  But 
this  effect  of  capacity  which  gives  an  apparent  increase  in  resistance  pro- 


SKIN   EFFECT  IN  SINGLE-LAYER  COILS 


127 


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Resistance 

128  RESISTANCE— INDUCTANCE— CAPACITY  [CHAP.  II 

duces  at  the  same  time  an  increase  in  the  apparent  inductance  of  the  coil, 
so  that  in  the  results  of  the  table  any  increase  in  resistance  which  occurs 
without  a  corresponding  increase  in  inductance  is  due  to  redistribution 
of  current  in  the  conductor  of  the  coil  (i.e.,  real  skin  effect) ;  for  frequencies 
high  enough  to  produce  an  increase  in  the  apparent  inductance  the  skin 
effect  is  not  alone  in  producing  the  increase  in  resistance,  the  internal 
capacity  contributing  its  effect  also  in  increasing  the  apparent  resistance. 

It  will  be  noticed  that  for  the  larger  wires  the  inductance  actually 
decreases  as  the  frequency  increases,  for  the  lower  values  of  frequency. 

Illustrating  this  effect  we  take  the  data  for  coil  No.  1  made  of  No.  11 
wire.  In  the  range  of  frequencies  used  the  inductance  decreased  with 
increase  of  frequency,  whereas  the  resistance  increased  from  .050  ohm  to 
.803  ohm.  The  radius  of  this  wire  is  .114  cm.  and  so  the  factor,  r\//  f°r 
2X105  cycles,  is  51.  Referring  to  Fig.  3  the  factor  m  is  found  to  be  4.2. 
If,  therefore,  the  wire  had  been  used  in  the  form  of  a  straight  conductor, 
we  might  have  expected  an  increase  in  resistance  from  .050  ohm,  the  c.c. 
resistance,  to  4. 2 X. 05  =  .21  ohm.  Actually  it  changes  from  .05  ohm  to 
.80  ohm,  thus  showing  how  the  skin  effect  is  augmented  when  the  wire  is 
used  in  the  form  of  a  coil.  The  superiority  of  the  radio  cable,  either 
42/36s  or  48/38s  is  at  once  evident  from  the  results  given  in  the  table. 

If  the  coil  used  has  more  than  one  layer,  the  magnetic  field  density  is 
much  greater  than  it  is  for  a  single  layer  coil,  hence  we  should  expect  a 
much  greater  skin  effect  for  multi-layer  coils  than  for  single-layer  coils  and 
the  experimental  results  of  Table  III  which  were  obtained  with  ten  layer 
coils,  prove  the  point.  Thus  the  single  layer  coil  of  No.  18  wire  showed  an 

2  18 
increase  in  resistance  of -^-  =  3.6  times  as  the  frequency  varied  from  zero 

to  100,000  cycles.     This  same  wire  wound  in  a  10-layer  coil  showed  an 

84 
increase  through  the  same  range  of  frequency  of  ---=48  times  so  that  the 

resistance  increase  is  13  times  greater  when  used  in  a  10-layer  coil  than 
when  used  in  a  single-layer  coil. 

It  must  be  noticed  also  that  this  great  increase  in  resistance  is  not 
due  to  the  internal  capacity  of  the  coil.  These  multilayer  coils  were 
built  on  wooden  reels  in  a  special  way  first  described  by  the  author;  the 
construction  was  such  that  a  considerable  air  space  (in  this  case  .16  cm.) 
was  used  between  consecutive  layers,  this  construction  giving  such  a  low 
internal  capacity  that,  up  to  the  highest  frequency  used  the  inductance 
of  the  coil  showed  but  slight  increase.  These  multilayer  coils  were  octag- 
onal in  form  and  had  10  layers  each,  wound  back  and  forth.  Each  layer 
was  2.6  cm.,  long  separated  from  the  next  layer  by  .16  cm.  air.  The 
inner  diameter  was  approximately  10.5  cm.  and  the  outside  diameter 
varied  with  the  size  of  wire  used,  being  greater  for  the  larger  wires. 


SKIN  EFFECT  IN  MULTILAYER  COILS 
TABLE  III 


129 


Coil 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

12 

18 

20 

22 

24 

26 

28 

30 

32 

34~ 

48/388 

Number  Turns.  .  .  . 

100 

197 

239 

300 

343 

410 

586 

719 

859 

898 

250 

Frequency  in 

Kilocycles 

.0          R 

.12 

1.74 

3.30 

6.7 

11.5 

21.3 

49 

96 

172 

300 

5.1 

R 

.48 

2.48 

3.40 

6.8 

11.7 

21.6 

50 

96.5 

173 

300 

5.2 

1.2          L 

1.46 

5.21 

8.10 

12.6 

16.7 

23.7 

48 

72 

102 

117 

9.2 

R/L 

.33 

.48 

.42 

.54 

.70 

.91 

1.0 

1.3 

1.7 

2.6 

.56 

R 

3.85 

6.27 

7.80 

11.4 

16.2 

27 

64 

122 

210 

345 

6.7 

10.5          L 

1.42 

5.18 

8.10 

12.6 

16.8 

24.0 

48 

73 

104 

120 

9.3 

R/L 

2.7 

1.2 

.96 

.91 

.96 

1.1 

1.3 

1.7 

2.0 

2.9 

.72 

R 

5.50 

10.2 

11.3 

15.4 

20.2 

32.0 

71 

126 

225 

370 

7.2 

15.4          L 

1.39 

5.20 

8.12 

12.7 

16.9 

24.0 

49 

74 

105 

124 

9.3 

R  L 

4.0 

1.9 

1.4 

1.2 

1.2 

1.3 

1.5 

1.7 

2.1 

3.0 

.77 

R 

7.40 

21.0 

22.3 

25.7 

28.5 

42 

97 

194 

360 

600 

8.5 

25            L 

1.37 

5.20 

8.14 

12.8 

17.1 

24.5 

51 

78 

116. 

138 

9.3 

R/L 

5.4 

4.0 

2.7 

2.0 

1.7 

1.7 

1.9 

2.5 

3.1 

4.3 

.91 

R 

10.9 

48.0 

63.5 

78 

82 

100 

200 

465 

1080 

1450 

15 

50           L 

1.37. 

5.22 

8.17 

13.2 

17.7 

25.3 

55 

87 

131 

150 

9.5 

R/L 

7.9 

9.1 

7.8 

5.9 

4.6 

4.0 

3.6 

5.3 

8.2 

9.7 

1.6 

R 

14.1 

73.0 

94 

155 

133 

172 

19 

75           L 

1.37 

5.23 

8.22 

13.6 

18.6 

27.5 

9.7 

R/L 

10.3 

14.0 

11.4 

11.4 

7.2 

6.2 

2.0 

R 

16.6 

84 

142 

267 

268 

415 

37 

100           L 

1.38| 

5.27 

8.55 

14.3 

20.3 

30.6 

10.4 

R  L 

12.0 

15.9 

16.6 

18.7 

13.2 

13.6 

3.6 

R 

18.8 

104 

190 

362 

462 

61 

125           L 

1.37 

5.32 

9.07 

15.1 

21.0 

10.8 

R/L 

13.7 

19.5 

21 

24 

22 

5.6 

R 

20.5 

124 

260 

550 

840 

115 

150            L 

1.38 

5.56 

9.30 

15.7 

22.0 

11.4 

R/L 

14.9 

32.3 

28 

35 

38 

10 

Size  of  wire  to  the  nearest  B.  &  S.  gage  number.  Inductance  given  in  millihenries. 

Resistance  given  in  ohms  and  ohms  per  millihenry. 

The  great  increase  in  resistance  of  coil  No.  16  for  example  is  really 
due  to  a  redistribution  of  current  throughout  the  cross-section  of  the  con- 
ductor. Although  the  resistance  increases  172  times  in  the  frequency 
range  used  the  inductance  is  lower  at  the  highest  frequency  than  at  the 
lowest.  There  are  cases  shown  in  which  the  increase  in  apparent  resist- 
ance increases  very  rapidly  for  the  higher  frequencies,  even  with  small- 


130  RESISTANCE— INDUCTANCE— CAPACITY  [CHAP.  II 

sized  wire.  Thus  the  10-layer  coil  wound  with  No.  26  wire  increased  its 
resistance  from  21.3  ohms  to  415  ohms,  but  at  the  same  time  the  induc- 
tance increased  from  23.7  X10~3  henries  to  30.6 X10~3  henries.  Hence 
for  this  coil  the  internal  capacity  was  making  itself  felt  so  that  the  actual 
increase  in  apparent  resistance  must  be  regarded  as  due  to  the  combined 
effect  of  redistributed  current  and  internal  capacity. 

Three  of  the  coils  were  wound  with  radio  cable;  in  two  of  them  there 
were  used  48  No.  38  enameled  strands  in  the  cable — three  twisted  cables, 
each  having  16  strands,  were  twisted  together  to  make  the  cable.  The 
solid  wire  most  nearly  approaching  this  cable  in  cross-section  was  No. 
22.  In  the  single-layer  coils  the  solid  wire  increased  its  resistance  by 
220  per  cent,  and  this  radio  cable  coil  increased  by  72  per  cent,  only  one- 
third  as  much  increase  as  for  the  solid  wire  over  the  same  range  of  fre- 
quency. In  the  multilayer  coil  the  solid  wire  increased  its  resistance  from 
6.7  ohms  to  267  ohms,  an  increase  of  40  times  as  the  frequency  was  varied 
from  zero  to  100,000  cycles  whereas  the  multilayer  coil  wound  with  the 
radio  cable  increased  (in  the  same  range  of  frequency)  from  5.1  ohms 
to  37  ohms,  an  increase  of  only  7.2  times,  that  is,  the  stranded  wire  coil 
showed  a  resistance  increase  due  to  skin  effect  only  one-sixth  as  great  as 
the  nearest  size  solid  wire.  In  this  resistance  increase  there  is  some  effect 
due  to  the  internal  capacity  of  the  coil,  and  if  this  effect  (which  is  approxi- 
mately the  same  in  amount  for  both  coils)  were  taken  into  consideration 
the  superiority  of  the  radio  cable  over  the  solid  wire  would  be  even  more 
striking. 

From  the  results  presented  in  Tables  II  and  III  there  was  calculated 
for  each  coil  the  "  ohms  resistance  per  millihenry  "  and  the  results  are 
presented  in  the  form  of  curves  in  Figs.  15  and  16.  The  most  interesting 
conclusion  to  be  drawn  from  these  curves  is  the  idea  that  the  higher  the 
frequency  the  smaller  the  wire  should  be  to  keep  the  ratio  of  resistance 
to  reactance  low.  Thus  in  the  single-layer  coil  it  is  evident  that  below 
40  kilocycles  No.  16  wire  is  better  than  No.  20  (such  factors  as  cost,  bulk, 
current-carrying  capacity,  etc.,  not  considered)  but  above  this  frequency 
No.  20  wire  is  better  than  No.  16. 

For  the  multilayer  coils  this  feature  is  shown  to  a  much  greater  degree 
and  at  lower  frequencies;  thus  at  1200  cycles  No.  34  wire  has  about  8 
times  as  many  ohms  per  millihenry  as  No.  12,  but  at  15  kilocycles  the 
No.  12  wire  has  more  resistance  per  millihenry  than  has  the  No.  34  wire. 

The  multilayer  coil  of  radio  cable  is  indicative  of  what  a  good  coil 
should  be;  its  reactance  at  75  kilocycles  is  220  times  as  much  as  its  resist- 
ance and  this  ratio  holds  over  a  wide  range  of  frequency.  Other  coils 
have  been  built  by  the  author,  using  better  stranded  wire,  more  of  it, 
keeping  the  radial  depth  of  conductor  low,  which  showed  a  reactance 
450  times  as  great  as  the  resistance  at  50  kilocycles.  The  ideas  to  be  kept 


SKIN   EFFECT   IN   MULTILAYER  COILS 


131 


in  mind  in  building  good  radio  coils  are  to  use  carefully  stranded  and 
insulated  cable,  keep  the  radial  depth  of  conductor  small,  keep  the  coil 
as  compact  as  possible  and  at  the  same  time  to  keep  the  internal  capacity 
low,  and  avoid  dielectric  losses. 

In  Fig.  17  is  shown  the  construction  of  a  coil'Vhich  has  about  10  milli- 
henries inductance  and  7  ohms  resistance  at  50,000  cycles;  sufficient  air 
space  was  used  between  layers  to  keep  the  internal  capacity  to  about 
120  micro-microfarads.  This  coil  operated  satisfactorily  when  carrying 


7        8        9      10       11      12      13      14      15 
Frequency  in  10    cycles  per  second 


16      17      18      19      20 


FIG.  15. — Variation  of  resistance  with  frequency  in  single  layer  solenoids  of  various 
wires.     Numbers  on  curves  indicate  size  of  wire,  B.  &  S.  gage. 

4  amperes  with  12,000  volts  across  its  terminals.  If  it  were  used  in  a  good 
insulating  oil  it  would  probably  be  satisfactory  when  carrying  200-300 
kilovolt  amperes,  although  in  this  case  its  internal  capacity  would  be  more 
than  doubled. 

To  illustrate  in  as  striking  a  manner  as  possible,  the  skin  effect  which 
may  be  present  in  poorly  designed  coils  tests  were  made  on  two  coils 
made  of  copper  strip,  wound  edgewise.  The  first  coil  had  29J  turns  of 
strip  1J  in.  wide  and  3^  in.  thick;  the  spacing  between  successive  turns 
was  nearly  T£  in. ;  its  inside  diameter  was  14|  in.  and  outside  diameter  was 
17f  in.  Its  resistance  for  continuous  current  was  .013  ohm  and  at  150 


132 


RESISTANCE— INDUCTANCE— CAPACITY 


[CHAP.  II 


kilocycles  it  had  3.44  ohms  resistance,  an  increase  of  285  times.  The 
second  coil  had  34J  turns  of  strip  1  in.  wide  and  r§-  in.  thick,  spacing 
between  turns  was  nearly  YQ  in.  The  c.c.  resistance  was  .020  ohm  and  at 
150  kilocycles  it  was  7.86  ohms,  an  increase  of  393  times.  These  two 
examples  bring  out  forcibly  the  fact  that  the  radial  depth  of  the  conductor 
in  a  coil  intended  for  radio  circuits  must  be  kept  small.  Further  data  on 
these  two  coils  are  given  in  Table  V,  p.  (147). 


32 


30 


28 


26 


24 


22 


c  20 

v 

J£ 

i  is 


a16 


14 


12 


10 


10  lay. 


26 


48-38  s 


0        1        2        34        5        6        7        8        9       10      11      12      13      14      15 
Frequency  in  10* cycles  per  second 

FIG.  16. — Variation  of  resistance  with  frequency  of  multilayer  coils;   short  coils  of  ten 
layers  each,  air  space  between  layers.    Numbers  on  curves  give  size  of  wire,  B.  &  S.  gage. 

Effect  of  Neighboring  Circuits  on  the  Resistance  of  a  Coil — Tuning 
These  Circuits. — It  has  been  shown  in  the  previous  chapter  that  the 
resistance  of  a  circuit  is  always  increased  by  the  presence  of  neighboring 
circuits  in  which  induced  currents  flow.  The  power  for  supplying  the 
losses  in  these  circuits  must  be  furnished  by  the  coil  inducing  the  current 
and  so  this  effects  an  apparent  increase  in  the  resistance  of  this  coil;  the 
amount  of  this  increase  is  given  by  Eq.  (73),  page  86.  This  increase  in 
resistance  evidently  depends  upon  the  tuning  of  this  second  circuit.  If  in 


RESISTANCE   AFFECTED   BY  NEIGHBORING   CIRCUITS 


133 


Eq.  (73)  the  reactance  of  the  second  circuit  is  put  equal  to  zero  the  apparent 
increase  in  the  resistance  of  the  first  circuit  may  be  very  great;  the  curves 
illustrating  this  effect  were  shown  in  Fig.  91,  Chapter  I. 

As  an  instance  of  the  losses  occurring  in  neighboring  circuits  it  is  inter- 
esting to  note  that  one  of  the  terminal  posts  of  the  coil  pictured  In  Fig. 


17  was  fastened  on  a  piece  of  hard  rubber,  and  this  rubber  block  was 
fastened  to  the  wood  end-piece  of  the  coil  with  small  iron  screws.  When 
operating  this  coil  with  four  amperes  at  50  kilocycles  flowing  in  the  wind- 
ing the  heat  generated  in  those  screws  was  such  that  they  burned  them- 
selves free  from  the  wood  after  the  coil  had  been  in  the  circuit  but  a 
short  time. 


134 


RESISTANCE— INDUCTANCE— CAPACITY 


[CHAP.  II 


Magnetizing  current 


' 

^ 

<v  Lamination 

c 

5 

c  "  _ 

_  _  _    y 

x. 

\ 

_y 

^ 

A    "ID 

^s 

Resistance  of  Iron-core  Coils. — It  was  at  first  thought  impossible  to 
use  iron-core  coils  for  the  high  frequencies  employed  in  radio  circuits,  but 
such  is  not  actually  the  case,  although  the  gain  in  using  iron  is  not  so  great 
for  radio  frequencies  as  it  is  for  ordinary  low  frequencies.  The  difficulty 
in  making  efficient  iron-core  coils  for  high-frequency  circuits  is  a  two- 
fold one,  the  apparent  permeability  of  the  iron  is  much  less  than  it  should 
be,  and  the  losses  in  the  iron  core  greatly  increase  the  effective  resistance 
of  the  coil.  Both  of  these  undesirable  effects  are  due  to  the  same  cause; 
the  increase  in  resistance  due  to  ijron  loss  is  mostly  caused  by  eddy  currents 
in  the  iron  laminae,  and  these  same  eddy  currents  serve  to  keep  the  mag- 
netic flux  from  penetrating  and  so  make  only  the  outer  parts  of  the  laminae 

useful  as  flux  carriers. 
There  is  also  some  iron 
loss  due  to  hysteresis, 
but  this  is  small  com- 
pared to  the  eddy-cur- 
rent loss. 

The  paths  of  the  eddy 
currents  in  the  laminae 
of  an  iron  core  are  indi- 
cated in  Fig.  18,  the  lam- 
inae being  shown  much 
thicker,  of  course,  than 
they  really  are.  The  di- 
rection  of  the  eddy  cur- 
rents, it  is  to  be  noticed, 

is  opposite  to  that  of  the  current  in  the  winding  hence  at  any  point  A  in  the 
center  of  a  laminae,  the  magnetomotive  force  acting  is  really  that  produced 
by  the  winding  diminished  by  a  certain  amount  due  to  these  eddy  currents. 
At  low  frequencies  the  back  m.m.f.  of  these  eddy  currents  is  negligible 
compared  to  that  of  the  main  magnetizing  coil,  so  that  the  flux  density 
in  the  lamina  is  nearly  constant  throughout  its  cross-section  and  is  about 
the  same  as  it  would  be  were  no  eddy  current  present.  At  higher  fre- 
quencies, however,  the  eddy-current  effect  becomes  increasingly  greater, 
so  that  at  radio  frequencies  the  full  value  of  magnetic  flux  exists  only 
on  the  outer  surface  of  the  iron ;  in  the  inner  parts  the  flux  density  decreases 
and  it  may  be  practically  zero  at  a  depth  only  a  small  fraction  of  a  milli- 
meter from  the  surface  of  the  iron. 

The  strength  of  the  eddy  currents  decreases  with  the  thickness  of  the 
laminations;  the  plates  used  for  the  cores  of  radio  coils  should  be  only 
a  few  hundredths  of  a  millimeter  thick.  To  get  the  benefit  of  lamination 
it  is  essential  that  the  plates  be  well  insulated  from  one  another,  either  by 
a  fine  quality  of  varnish  or  thin  paper,  or  both.  The  burred  edges  of 


Winding  carrying  the^ 
magnetizing  current 

,f 

FIG.  18. — Eddy  currents  occurring  in  a  laminated  iron 
core. 


IRON  CORE  COILS 


135 


the  plates,  caused  by  imperfect  fit  of  the  punch  and  die  used  in  making 
the  plates,  is  especially  bad  in  causing  eddy  currents. 

The  flux  density  in  the  steel  plates  has  about  the  distribution  shown 
by  Fig.  19,  the  penetration  of  magnetic  flux  into  an  iron  sheet  decreases 
as  frequency  increases,  increases  with  the  specific  resistance  of  the  Iron, 
etc.,  in  fact  follows  the  same  distribution  law  as  the  penetration  of  cur- 
rent itself  into  a  conducting  medium  given  in  Eq.  (3).  Because  of  this 
lack  of  penetration  the  apparent  permeability  of  the  iron  decreases  as 
the  frequency  increases,  resulting  in  a  decrease  in  the  self-induction  as 
the  frequency  increases.  The  curves  given  in  Fig.  20  show  how  the 
resistance  and  inductance  of  a  laminated  iron-core  coil  change  as  fre- 
quency changes.  It  will  be  noted  that  the  increase  in  resistance  is  practi- 
cally all  due  to  eddy-current  losses;  the  hysteresis  loss  is  nearly  negligible. 

Flux  density  at 


Lamina- 


Insulation->£ 


surface  of  lamina 


Flux  density  at 
center  of  lamina 


Flux  density 

FIG.  19. — Flux  density  variation  throughout  the  section  of  a  lamination  of  an  iron  core; 
the  higher  the  frequency  the  greater  is  the  variation  in  flux  density. 

It  is  evident  that  iron  of  the  quality  used  in  this  coil  must  be  used  in 
laminations  less  than  .0075  cm.  (the  thickness  of  those  in  the  test  coil) 
to  maintain  a  low  resistance  at  high  frequency.  The  decrease  in  induct- 
ance of  this  coil  is  comparatively  small  in  the  range  of  frequencies  used. 

In  Fig.  21  are  shown  the  variations  in  L  and  R  of  another  toroidal 
coil,  using  thicker  laminations.  Even  for  the  comparatively  low  frequen- 
cies used  in  this  test  the  decrease  in  inductance  is  very  pronounced. 

Iron  dust,  suitably  prepared,  makes  very  excellent  material  for  the 
cores  of  coils  intended  for  high-frequency  use,  having  very  low  eddy- 
current  loss.  It  has,  in  common  with  all  iron  cores,  the  disadvantage 
of  a  permeability  varying  with  magnetic  density.  A  dust-core  coil  (toroid) 
was  tested  to  show  this  effect  and  gave  the  results  shown  in  Fig.  22;  the 
measurements  were  carried  out  at  a  frequency  of  2000  cycles.  In  Fig. 
23  are  shown  the  characteristics  of  this  same  coil  measured  at  various 
frequencies.  The  ratio  of  reactance  to  resistance  brings  out  very  well 
the  fact  that  a  coil  is  always  most  efficient  at  some  certain  frequency. 

It  is  to  be  noticed  for  all  these  iron-core  coils  that,  at  radio  frequency, 


136 


RESISTANCE— INDUCTANCE— CAPACITY 


[CHAP.  II 


the  resistance  of  the  copper  wire  is  negligible  compared  to  the  resistance 
caused  by  iron  losses,  hence  it  is  of  little  use  to  employ  for  the  winding 
a  wire  as  large  as  those  used  in  winding  the  coils  whose  characteristics 
are  shown  in  the  foregoing  figures.  A  very  fine  wire  may  be  profitably 
used  for  the  windings  then  a  large  number  of  turns  (hence  high  L)  may  be 
put  on  a  very  small  core — using  an  iron-dust  toroidal  core,  the  outer  diam- 
eter of  the  toroid  being  5  cm.  and  the  core  itself  being  slightly  over  1  cm. 


700 
650 


6009 


£550 
§500 


^  450 

•2400 
o 

|  350 
•§300 
$250 

2 

150 


oo  I  - 


£- 


Iron  core  toroid 


180  plates 


re  toroid  _ 
.0075  [cm  thi 


st  v61tag( 


Jndu 


<jonl  yolt 


ctanCe 


dy  current  r 


es  stance 


0        5       10      15      20      25      30      35     40     45      50      55      60      65      70 
Frequency  in  Kilocycles 

FIG.  20. — Characteristics  of  a  toroidal  shaped  coil  having  laminated  iron  core. 

in  diameter,  winding  with  fine  wire,  it  is  possible  to  make  a  coil  with  an 
inductance  of  about  0.25  henry,  and  having  low  enough  internal  capacity 
to  be  efficient  at  60,000  cycles.  Such  coils  are  very  convenient  for  the 
plate  circuit  of  amplifying  tubes,  as  they  are  very  compact,  and  are  not 
subject  to  outside  disturbances,  a  toroid  having  practically  zero  mutual 
induction  with  any  other  circuit. 

Resistance  of  Spark  and  Arc. — In  radio  circuits  there  is  frequently 
used  an  arc,  or  a  spark  gap;  the  resistance  of  which  affects  the  operation 


IRON  CORE  COILS 


137 


of  the  set  and  must  be  considered  when  getting  decrement,  losses,  etc.  The 
resistance  of  a  spark  gap  varies  with  many  factors,  principally  the  length 
of  gap  and  magnitude  of  current  through  the  gap.  Within  the  ordinary 
range  of  currents  used  in  radio  circuits  the  resistance  of  an  arc  or  spark, 
for  constant  length  of  gap,  varies  inversely  with  the  current  to  some 


10 

I 

19 

co 

'S 


I' 


S5 

c 


Inductance 


n  core  toroid 


4  5  Plates!  .025cm.  thick 


finding  of  290  turns 


Impressed  errif.-=tlvlolt 


ota 


resistance 


10  12  14  16 

Frequency  in  Kilocycles 


18 


20 


22 


24 


FIG.  21. — Characteristics  of  a  toroidal  shaped  coil  having  laminated  iron  core,  lamina- 
tions being  much  thicker  than  those  of  Fig.  20. 

power  higher  than  the  first,  in  such  a  way  that  the  IR  drop  actually 
decreases  with  an  increase  of  current.  Other  factors  affecting  the  resist- 
ance of  the  gap  are  the  nature  of  the  gas  through  which  the  arc  or  spark 
is  passing  and  the  material  of  which  the  gap  terminals  are  made.  Silver 
and  copper  electrodes  give  a  higher  resistance  gap  than  such  metals  as 


138 


RESISTANCE— INDUCTANCE— CAPACITY 


[CHAP.  II 


12 


£11 


Impr 


essed 


freqi 


=  2000cj/ 


stanc 


Indu 


e  iron  dus 


winding  of  275  turns 


I6 

a  ' 
«  4 


of  \vindii 


'2cm. 


024 


8        10        12        14        16        18       20       22       24        2G       2b       30        32       34 
Excitation  current  10"2  amperes 


FIG.  22. — Variation  of  inductance  and  resistance  of  a  coil  having  iron  dust  core,  showing 
increasing  permeability  with  in  creasing  current. 


90 


100 


30  40  50  60  70 

Frequencies  in  Kilocycles 

FIG.  23. — Effect  of  frequency  upon  the  characteristics  of  a  toroidal  coil  having  a  core  of 

fine  iron  dust. 


RESISTANCE  OF  SPARK  AND  ARC  139 

zinc,  magnesium,  etc.;  hydrogen  and  illuminating  gas  give  a  higher  resist- 
ance than  air. 

Experiments  indicate  that  for  such  currents  and  gaps  as  are  used  in 
radio  sets  the  resistance  (effective)  of  a  spark  gap  is  not  more  than~l  ohm, 
and  is  generally  only  a  few  hundredths  of  1  ohm.  This  value  of  resistance 
is  obtained  from  the  heating  effect,  and  so  gives  a  kind  of  average  value 
of  the  resistance  during  the  cycle.  For  low  frequencies  the  resistance 
of  an  arc  or  spark  varies  a  great  deal  throughout  a  cycle  of  current,  and 
it  probably  does  (even  if  to  a  less  extent)  at  radio  frequencies. 

In  Fig.  24  is  shown  the  oscillogram  giving  the  form  of  voltage  across 
an  arc  and  the  current  through  the  arc;  if  the  resistance  is  defined  as  the 
ratio  of  volts  to  amperes  it  is  evident  that  the  resistance  varies  through 
widely  differing  values  during  the  cycle. 


FIG.  24. — A  sine  wave  of  e.m.f .  impressed  across  an  arc  in  series  with  an  iron  core  induct- 
ance gave  voltage  and  current  forms  as  shown. 

In  most  radio  circuits  the  resistance  which  assumes  importance  is  that 
offered  to  alternating  currents,  rather  than  the  continuous-current  resist- 
ance. Nearly  all  circuits  offer  a  greater  resistance  to  the  flow  of  alter- 
nating current  than  they  do  to  continuous  current,  but  the  arc  is  an  excep- 
tion to  this  rule.  The  relation  of  current  and  potential  difference  in  a 
certain  arc  is  shown  in  Figs.  25  and  26;  from  the  curves  it  is  evident  that 
increasing  current  requires  less  and  less  potential  difference  across  the 
arc.  The  resistance  of  the  arc  for  continuous  current  varies  from  50 
ohms  to  2  ohms,  according  to  conditions.  Now  the  alternating  current 
resistance  must  be  determined  by  the  ratio  of  the  voltage  change  to  the  current 
change,  i.e.,  R  =  dv/di,  and  from  these  curves  it  is  evident  that  when  dv 
is  positive  di  is  negative,  so  that  the  alternating-current  resistance  of 
the  arc  is  negative.  This  negative  resistance  for  alternating  currents  is 


140 


RESISTANCE— INDUCTANCE— CAPACITY 


[CHAP.  II 


characteristic  of  nearly  all  circuits  in  which  gas  of  some  kind  takes  part 
in  the  conduction  of  the  current;  in  some  special  cases  even  a  pure  electron 
stream  may  have  a  negative  resistance  for  an  alternating  current,  as  will 
be  explained  when  discussing  vacuum  tubes. 

The  magnitude  of  this  alternating  current  arc  resistance  varies  some- 
what with  frequency,  it  becoming  less  as  the  frequency  increases. 


456 
Amperes 


1  2  3 

FIG.  25. — Resistance  of  small  arc,  in  air. 


Resistance  of  an  Antenna. — An  antenna  is  a  circuit  consisting  of  a 
capacity,  inductance,  and  resistance  in  series,  the  resistance  being  fixed 
in  value  by  many  effects,  among  them  the  radiation  of  power  from  the 
antenna  in  the  form  of  electro-magnetic  waves.  The  surface  of  the  earth 
generally  forms  one  plate  of  the  condenser  and  the  over-head  wire  system 
the  other,  Fig.  27.  When  current  circulates  in  the  antenna,  losses  occur 


ANTENNA  RESISTANCE 


141 


in  the  network  of  wires  and  in  the  earth  due  to  actual  heat  loss  produced 
by  the  conduction  currents;  losses  occur  due  to  induced  currents  in  guy 
wires,  etc. ;  losses  occur  in  the  earth's  surface  and  any  other  dielectrics  in 
the  field  of  the  condenser  such  as  trees,  etc.,  and  power  is  radiated.  That 


50 


4  5 

Amperes 

FIG.  26. — Resistance  of  small  arc  in  illuminating  gas,  showing  also  the  effect  of  a  trans- 
verse magnetic  field. 

resistance  caused  by  radiation  is  the  only  useful  resistance;  the  other  fac- 
tors increase  the  resistance  of  the  antenna  but  perform  no  useful  function. 
The  resistance  of  an  antenna  varies  with  the  frequency  about  as  indi- 
cated in  Fig.  28.  With  very  high  frequencies  the  resistance  is  high;  it 
decreases  to  a  minimum  at  a  frequency  about  twice  that  of  the  natural 


142 


RESISTANCE— INDUCTANCE— CAPACITY 


[CHAP.  II 


oscillation  of  the  antenna  (without  any  added  inductance)  and  then  rises 
gradually,  the  amount  of  this  rise  being  determined  principally  by  dielec- 
tric losses  in  objects  located  in  the  electrostatic  field  of  the  antenna. 


Antenna  wires 


Condenser 


Loading 
Inductance 


%%Z^^ 

FIG.  27.  —  Antenna  with  loading  inductance. 


For  small  land  antennae  the  minimum  on  the  curve  may  be  20-30 
ohms,  for  aeroplane  antennas  perhaps  5-10  ohms;  for  ships'  antennas 
3-6  ohms,  and  for  the  large  antennae  used  for  long  distance  communica- 


Frequency  of  quarter 
wave  length  oscillation. 


High 


Low 


Frequency 
FIG.  28. — Typical  resistance  curve  for  an  antenna,  showing  variation  with  frequency. 

tion  the  minimum  value  may  be  1-2  ohms.     The  more  complete  discus- 
sion of  antennas  and  their  characteristics  will  be  given  in  Chapter  IX. 

Resistance  due  to  dielectric  loss  and  corona  loss  will  be  treated  in  the 
section  dealing  with  capacity. 


COEFFICIENT  OF  SELF-INDUCTION  143 

INDUCTANCE 

Self-induction 

Coefficient  of  Self-induction.  Units. — The  ordinary  unit  of  self- 
induction,  the  henry,  is  much  too  great  to  serve  for  radio  work;  instead 
there  are  used  the  millihenry  (10~3  henry)  the  microhenry  (10~6  henry) 
and  infrequently  the  centimeter  (10~9  henry).  The  microhenry  is  most 
commonly  used. 

The  fundamental  viewpoint  from  which  to  consider  the  self-induction 
of  a  circuit  is  that  of  the  amount  of  energy  stored  in  the  magnetic  field 
of  the  circuit.  This  energy  is  given  by  the  well-known  formula,  Energy 
=  L/2/2,  where  the  energy  is  measured  in  joules,  the  current  in  amperes 
and  L  is  the  coefficient  of  self-induction  in  henries.  From  this  equa- 
tion we  can  get  the  definition  that  the  coefficient  of  self-induction  of  a 
circuit  in  henries,  is  numerically  equal  to  twice  the  number  of  joules 
stored  in  the  magnetic  field  when  the  current  in  the  circuit  is  one  ampere. 
Hence  any  conditions  which  affect  the  magnetic  energy  in  a  circuit,  the 
current  staying  fixed,  must  affect  the  coefficient  of  self-induction. 

A  piece  of  iron  introduced  into  the  magnetic  field  decreases  the  reluc- 
tance of  the  magnetic  path,  increases  the  flux  and  hence  the  magnetic 
energy,  and  therefore  increases  the  L  of  the 
circuit.  If  a  neighboring  closed  circuit  is  so 
placed  that  current  is  caused  to  flow  in  it  by 
an  alternating  current  in  the  coil  in  question, 
this  induced  current  will  be  nearly  in  phase 
opposition  to  the  current  in  the  first  circuit. 
Flux  which  is  produced  by  A  (Fig.  29)  and 
which  threads  circuit  B  is  opposed  by  the 
m.m.f.  of  the  current  induced  in  B,  and 
hence  the  reluctance  of  this  part  of  the 
magnetic  path  of  coil  A  is  increased.  This 

decreases    the    flux    produced    by   a    given     FIG.  29 -When  the  current  in 

/  circuit  A  is   varied   current 

current  in  A  and  so  proportionately  decreases        will  flow  in  circuit  B)  affect. 

the  L  of  coil  A.  It  is  evident  that  the  ing  thereby  the  resistance 
closer  circuit  B  is  placed  to  circuit  A,  the  and  inductance  of  circuit  A. 
more  effect  will  its  counter  m.m.f.  have  on  the 

amount  of  flux  produced  by  A,  and  hence  the  more  effect  it  will  have  in 
decreasing  the  L  of  coil  A. 

If  by  any  means  the  current  in  B  is  made  to  lead  the  induced 
voltage  of  coil  2  by  90°  (as  may  be  nearly  done  by  putting  a  suitable 


144  RESISTANCE— INDUCTANCE— CAPACITY  [CHAP.  II 

condenser  in  series  with  the  circuit)  then  the  m.m.f.  produced  by  B 
occurs  in  such  phase  as  to  help  the  m.m.f.  of  coil  A  and  hence  produce 
an  increase  in  the  magnetic  energy  of  A  for  a  given  current,  thus  the 
presence  of  coil  B  actually  increases  the  effective  self-induction  of  coil  A. 
These  effects  were  analyzed  in  the  previous  chapter  and  are  calculable 
from  Eqs.  (85),  etc.,  pages  91  et  seq. 

It  is  evident,  therefore,  that  the  L  of  a  circuit  may  vary  with  frequency, 
current  amplitude,  current  distribution,  etc.,  and  that  its  changes  can 
best  be  predicted  by  examining  in  each  case  the  distribution  and  density 
of  the  magnetic  field  produced  by  one  ampere  of  current  in  the  circuit; 
the  value  of  L  (in  henries)  of  the  circuit  is  equal  to  twice  the  number 
of  joules  of  energy  stored  in  this  field.  The  derivation  of  the  amount  of 
the  magnetic  energy  is  difficult  and  tedious  except  in  the  most  simple 
cases;  it  will  not  be  attempted  here,  but  the  formulae  themselves  for  the 
circuits  most  generally  used  in  radio  work  will  be  given  in  comparatively 
simple  form,  the  accuracy  being  for  most  cases  better  than  1  per  cent. 
For  exact  formulae  the  student  should  consult  the  various  publications  on 
the  subject,  notably  those  of 'the  Bureau  of  Standards. 

Self-induction  of  a  Single  Straight  Vertical  Wire  Distant  from  all 
Other  Conductors — 


4y»*a (7) 

where  I  =  length  of  wire  in  cm. ; 

r  =  radius  of  wire  in  cm. ; 
L  =«=  coefficient  of  self-induction  in  cm. ; 
log  =  logarithm  to  the  base  e,  as  it  is  for  all  the  suc- 
ceeding formulae. 

Eq.  (7)  assumes  the  material  of  the  wire  to  have  a  permeability  of 
unity.  For  uniform  current  distribution,  and  permeability  differing  from 
unity, 


m  ........     (8) 

where  M  =  the  value  of  the  permeability. 

For  a  Single  Horizontal  Wire— 

(9) 


where,  I  =  length  in  cm.  ; 

r  =  radius  of  wire  in  cm.  ; 

h  =  height  of  wire,  above  earth,  in  cm. 


COEFFICIENT  OF  SELF-INDUCTION 
For  a  Single  Circular  Turn  of  Round  Wire.— 

8#  ,     r2 


where, 


cm, 


R  =  radius  of  turn,  to  center  of  conductor,  in  cm.  ; 
r  =  radius  of  cross-section  of  conductor. 


145 


.     .     (10) 


For  a  Single  Layer  Solenoid,  Closely  Wound.— 

L=4ir2R2m2lK  cm., 


where 


(ID 


R  =  radius  of  coil,  to  center  of  wire,  in  cm. ; 

m  =  number  of  turns  of  wire  per  cm.  length; 
/  =  length  of  winding  in  cm. 

K  =  summation  of  a  certain  series,  which  series  depends 
upon  the  form  of  the  coil.  These  series  have  been 
summed  by  H.  Nagaoka  and  are  given  in  Table 

97? 
IV.     The  value  of  K  is  given  in  terms  of  -y-,  i.e., 

the  ratio  of  the  coil  diameter  to  the  coil  length. 


TABLE  IV 


Diameter 

Diameter 

Length 

K 

Length 

K 

.00 

1.000 

.95 

.700 

.05 

.979 

.00 

.688 

.10 

.959 

.10 

.667 

.15 

.939 

.20 

.648 

.20 

.920 

.40 

.611 

.25 

.902 

.60 

.580 

.30 

.884 

1.80 

.551 

.35 

.867 

2.00 

.526 

.40 

.850 

2.50 

.472  . 

.45 

.834 

3.00 

.429 

.50 

.818 

3.50 

.394 

.55 

.803 

4.00 

.365 

.60 

.789 

4.50 

.341 

.65 

.775 

5.00 

.320 

.70 

.761 

6.00 

.285 

.75 

.748 

7.00 

.258 

.80 

.735 

8.00 

.237 

.85 

.723 

9.00 

.219 

.90 

.711 

10.00 

.203 

146  RESISTANCE— INDUCTANCE— CAPACITY  [CHAP.  II 

The  values  of  K  given  in  the  table  assume  a  current  distribution 
uniform  throughout  the  conductor,  and  so  give  too  large  a  value  of  L, 
if,  due  to  skin  effect,  the  current  concentrates  in  the  inner  side  of  the 
winding.  The  decrease  in  induction  due  to  this  effect  is  shown  in  Table 
V,  in  which  are  tabulated  the  experimentally  determined  inductances 
and  resistances  of  the  two  edgewise-wound  ribbon  coils  referred  to  on 
p.  132,  and  pictured  in  Fig.  30.  It  may  be  found  by  calculation  from  the 
figures  given  that  at  high  frequencies  the  current  is  Dractically  concen- 
trated in  the  inner  side  of  the  coil. 


Coil^l    DfUfc       D2  =  17%'  Turns  =  29.6 
Coil*2    Drl4%"     D2=16?4"Turns=  34.5 


FIG.  30.  —  Short  solenoid  made  of  edgewise-  wound  copper  ribbon. 

Best  Form  of  Solenoid.  —  It  may  be  seen  from  a  few  calculations. 
using  Eq.  (11),  that  a  given  amount  of  wire,  to  be  wound  into  a  single 
layer  solenoid,  should  have  a  certain  form  if  the  maximum  inductance  is 
to  be  obtained.  This  occurs  when  the  diameter  is  2.45  times  the  coil  length. 
The  variation  of  L  with  departure  from  this  form  is  not  great,  however; 
thus  if  the  ratio  is  made  as  low  as  1.5  or  as  high  as  4.5  the  decrease  in  L 
(for  fixed  length  of  wire),  is  only  3  per  cent. 

Two  layer  solenoids,  one  layer  wound  directly  on  the  other,  are  not 
feasible  for  radio  work,  as  the  internal  capacity  is  so  high.  They  are 
sometimes  used,  the  turns  being  arranged  in  a  so-called  "  banked  "  wind- 


COEFFICIENT  OF  SELF-INDUCTION 


147 


ing.     Multilayer  coil  are,  however,  preferable,  but  they  must  be  built  in 
such  a  way  as  to  keep  the  internal  capacity  low,  as  described  on  p.  133. 

TABLE  V 

RESISTANCE  AND  INDUCTANCE  OF  EDGEWISE-WOUND  RIBBON  COILS 

Coil  No.  1 


Frequency  in  103 
cycles  

.043 

.088 

.128 

.248 

338 

.4 

50 

.731 

) 

1.250 

3.50 

L  in  10~6  henry.  .  .  . 

489 

485 

482 

476 

472 

4 

70 

46( 

3 

464 

460 

Rin  10-3ohm  

13 

15 

19 

26 

31 

3 

5 

46 

72 

176 

Frequency  in  10  3 
cycles              .  .    . 

7  00 

16  4 

25.2 

50. 

f) 

75 

0 

1 

00 

125 

150 

L  in  10  ~6  henry.  .  .  . 

458 

455 

452 

451 

45 

4 

4 

57 

456 

460 

R  in  10~3  ohm  

295 

725 

945 

1345 

17 

75 

2 

205 

2745 

3440 

Coil  No.  2 


Frequency  in  103 
cycles   

043 

.100 

.150 

.200 

300 

400 

fi 

00 

1  0 

00 

1  6(1 

2  44 

L  in  10~6  henry.  .  .  . 

613 

608 

604 

602 

598 

595 

5 

92 

58 

5 

585 

583 

R  in  10~3  ohm  

23 

25 

26 

30 

40 

45 

49 

7 

0 

100 

145 

Frequency  in  10  3 
cycles  

3.50 

6.46 

15.3 

21.5 

50 

75 

1 

00 

1?5 

150 

L  in  10~6  henry.  .  .  . 

581 

578 

574 

572 

570 

56 

8 

5 

68 

570 

572 

R  in  10-3ohm  

245 

495 

1095 

1345 

2640 

294 

0 

37 

30 

6 

280 

7860 

Inductances  of  a  Flat  Spiral,  of  Ribbon  Conductors,  Wound  Flatwise, 
Turns  Close  Together.— 

b2 


• 


Y2]  cm.  .     (12) 


where 


/2  =  mean  radius  of  coil  (see  Fig.  31); 

n  =  total  number  of  turns; 

6  =  width  of  strip  =  axial  length  of  coil; 

d  =  radial  depth  of  coil  =  outside  radius  —  inside  radius; 


148 


RESISTANCE— INDUCTANCE— CAPACITY 


[CHAP.  II 


Ci  and  €2  are  constants  depending  on  the  shape  of  the  spiral  for  their 
values.     They  are  given  in  Table  VI. 

TABLE  VI 
CONSTANTS  Ci  AND  C2  FOB  EQ.  (12) 


Ratio  b- 

Ci 

d 

.00 

.500 

.125 

.05 

.549 

.127 

.10 

.592 

.133 

.15 

.631 

.142 

.20 

.665 

.155 

FIG.  31. — Spiral  coil  of  ribbon  wound  flat  wise. 


Eq.  (12)  gives  incorrect  values  if  the  turns  are  not  close  together;  the 
values  obtained  from  the  equation  must  be  increased  as  much  as  5  per 
cent  for  the  spacing  used  in  ordinary  transmitting  coils  in  spiral  form. 
Fig.  32  shows  how  the  value  of  L  for  a  given  spiral  varies  with  the  number 
of  turns  used. 

It  As  interesting  to  note  that  the  same  length  of  wire  will  give  about 
the  same  inductance  whether  wound  into  a  flat  spiral  or  a  single-layer  sole- 
noid, provided  that  the  mean  radius  of  the  spiral  has  the  same  value  as 
the  radius  .of  the  solenoid. 


COEFFICIENT  OF  SELF-INDUCTION  149 

Toroidal  Coil  of  Rectangular  Cross-section.     (Fig.  33.) — 

L  =  2n2l  log  ~  cm (13) 

tii 


30 


£20 


10 


456789 
Number  of  turns,  counted  from  inside 


10 


FIG.  32 — Inductance  of  a  spiral  similar  to  that  shown  in  Fig.  31. 


where 


Toroid 
FIG.  33. — Toroidal  coil  of  rectangular  cross-section. 

n  —  total  number  of  turns; 
I  —  axial  length  of  coil; 
#2  =  outer  radius; 
RI  =  inner  radius. 


150 


RESISTANCE— INDUCTANCE— CAPACITY 


[CHAP.  II 


Toroidal  Coil  of  Circular  Cross-section  (Torus).     (Fig.  34.)— 


-r     cm., 


(14) 


where 


n  =  total  number  of  turns; 

R  =  mean  radius  of  ring; 

r  =  radius  of  cross-section  of  winding. 


The  great  advantage  of  a  toroidal  coil  is  that  it  has  practically  no 
external  magnetic  field  and  so  gives  but  little  mutual  induction  with  other 
circuits.  Also  a  toroidal  coil  will,  for  similar  reasons,  not  be  affected  by 
mutual  induction  from  other  circuits  or  sources.  Used  as  a  tuning  coil 
in  a  receiving  set  it  will  not  pick  up  any  strays  or  other  disturbing  fields 
unless  they  be  of  excessively  short  wave  length. 


Torus 
FIG.  34. — Toroidal  coil  of  circular  cross-section. 

Single  Layer  Square  Coil.  (Fig.  35.)— 

L  =  8an2f  log  |+.72G+.223^j  -San  [A  +  B]  cm.,      . 


.     (15) 


in  which  a  =  side  of  square,  measured  to  center  of  wire; 

n  =  number  of  turns ; 
D  =  pitch  of  winding,  center  to  center; 
6  =  axial  length  of  coil=  (n—  l)D. 

A  and  B  are  constants  depending  upon  number  of  turns,  pitch,  etc., 
and  are  given  in  Tables  VII  and  VIII,  d  being  the  diameter  of  the  wire 
used.  Coils  wound  with  rectangular  conductor  have  slightly  different  con- 
stants than  those  given  here. 


COEFFICIENT  OF  SELF-INDUCTION 
TABLE  VII  TABLE  VIII 


151 


1 

d 
D 

A 

Number  of 
Turns,  n 

B 

557 

.18 

1.16 

I 

.000 

452 

.16 

1.28 

2 

.114 

334 

3 

.166 

2CO 

.14 

1.41 

4 

.197 

046 

.12 

1.56 

6 

.233 

136 

.10 

1.75 

8 

.253 

356 

.08 

1.97 

10 

.266 

443 

.06 

2.26 

20 

.297 

647 

.04 

2.66 

40 

.315 

830 

.02 

3.36 

60 

.322 

05 

100 

.328 

i 

• 

X 

x 

\ 

\ 

c 

: 

\ 

\ 

FIG.  35. — Single  layer  square  coil,  such  as  is  used  for  a  coil  antenna. 

Flat  Square  Coil.     (Fig.  36.)— 

For  this  case  Eq.  (15)  is  applicable  providing  a  is  taken  as  ao—  (n—  l)D 

where         ao  =  side  of  square,  outside  wire ; 
n  =  number  of  turns ; 
D  =  distance  between  turns,  center  to  center. 

The  value  of  b  is  obtained  from  the  depth  of  the  winding,  i.e.,  it  is 
equal  to  (n— 1)7). 


152  RESISTANCE— INDUCTANCE— CAPACITY  [CHAP.  II 

Multilayer  Coils  of  Rectangular  Cross-section.1     (Fig.  37.)— 

(2irRn)2 


where 


PF"  cm., 


R  =  mean  radius  of  coil  in  cm. ; 
n  =  total  number  of  turns  in  coil; 
b  —  axial  length  of  coil; 
t  —  radial  depth  of  winding. 


(16) 


FIG.  36 


FIG.  37. 


FIG.  36. — Flat  square  coil,  used  as  coil  antenna  for  short  wave  lengths. 
FIG.  37. — Multilayer  coil  of  rectangular  cross-section;  the  cross-hatched  area  shows  the 

cross-section  of  the  winding. 

F'  and  F"  are  correction  factors 

106+13£+2# 


F'  = 


106+10.7/4-1.4/2 


"  =  1.15  log, 


For  accurate  results  with  this  lormula  the  distance  between  wires 
must  be  small  compared  to  the  diameter  of  the  wire. 

A  multilayer  coil  of  very  ingenious  construction  is  being  made  at  pres- 
ent, using  a  so-called  honeycomb  construction.  A  picture  of  such  a  coil 

1An  excellent  article  on  the  design  of  multilayer  coils  was  published  in  Univ.  of 
California  Publications  in  Engineering  Vol.  147,  by  F.  E.  Pernot. 


VARIABLE   INDUCTANCE 


153 


is  shown  in  Fig.  38.  The  coil  is  self-supporting,  in  this  respect  being 
superior  to  the  multilayer  coils  described  on  p.  133  and  although  its  internal 
capacity  is  greater  than  that  of  the  type  shown  in  Fig.  17,  it  is  still  suffi- 
ciently low  to  make  it  an  excellent  coil  for  radio  circuits,  especially  those 


FIG.  38. — "Honey  comb"  construction  of  multilayer  coil. 

calling  for  many  millihenries  of  inductance.     The  constants  of  one  of 
these  coils  is  shown  in  Table  IX. 

TABLE  IX 
CONSTANTS  OF  A  HONEYCOMB  COIL 


Frequency  in  103 
cycles 

R  in  ohms 

L  in  10  ~  3  henries 

Reactance  Divided 
by  Resistance 

0 

9.39 

26.5 

12.4 

17.75 

238 

53 

23.8 

17.85 

250 

79.5 

53.0 

18.70 

176 

106 

102.0 

20.25 

120 

The  dimensions  of  this  coil  were  internal  diameter =5  cm.,  external 
diameter=10  cm.,  cross-section  of  winding  2.5  cm.  by  2.5  cm. 

Variable  Inductances. — It  is  many  times  desirable  to  have  a  continu- 
ousty  variable  inductance  for  tuning  a  circuit;  two  such  types  have  been 
used,  one  a  long  solenoid  with  a  sliding  contact  and  the  other  a  pair  of 
coils  connected  in  series,  one  rotatable  inside  the  other,  an  inductance  of 
this  type  being  generally  styled  a  variometer. 

The  solenoid  with  sliding  contact  is  not  good,  because  the  sliding 
contact  frequently  lies  on  two  turns  at  the  same  time,  thus  producing  a 
short-circuited  turn,  decreasing  very  appreciably  the  self-induction  from 


154 


RESISTANCE— INDUCTANCE— CAPACITY 


[CHAP.  II 


its  proper  value  for  the  position  of  the  contact,  and,  due  to  the  current 
in  the  short-circuited  turn,  increasing  the  effective  resistance  of  the  coil. 
Also  there  is  not  much  useful  variation  of  inductance  obtainable  by  this 
method;  for  long  solenoids  the  value  of  L  increases  with  the  first  power 
of  the  length  only  and  the  coil  cannot  be  used  effectively  with  the  con- 
tact set  to  connect  in  only  a  small  portion  of  the  coil  because  of  the  losses 
occurring  in  the  long  unused  portion.  This  part  of  the  coil  (generally 
called  a  "  dead  end  ")  is  excited  like  the  secondary  of  a  step-up  auto  trans- 
former; the  charging  current  circulating  in  the  dead  end  produces  losses 
and  so  increases  the  effective  resistance  of  that  part  of  the  coil  which  is 


a 

6 


OOOOOOOOGOOOOOOQ.  _       _  _ 


OOOOOOOOOOOOOOCT 


0       10      20     30      -40      50     60      70      80      90     100    110    120    loO    140    150    160    170    180 
Setting  of  rotating  coil,  in  degrees 

FIG.  39. — Calibration  curve  of  a  variable  inductance  commonly  known  as  a  variometer. 

used.  Long  solenoids  intended  to  be  used  in  steps  should  be  divided  up 
into  a  number  of  completely  insulated  sections,  these  being  connected 
in  series  as  required. 

The  variometer  type  of  inductance  is  very  convenient  and  useful,  it 
being  continuously  variable;  the  calibration  curve  of  such  an  inductance 
is  shown  in  Fig.  39,  from  which  the  probable  range  in  inductance  can  be 
seen.  If  the  ends  of  the  stationary  coil  and  rotating  coil  are  brought  out 
to  separate  terminals,  the  combination  forms  a  very  convenient  scheme  of 
magnetically  coupling  two  independent  circuits,  a  so-called  "  coupler." 

A  rather  convenient  scheme  (even  though  inefficient)  for  making  a  con- 
tinuously variable  inductance  out  of  a  short  solenoid,  is  to  fix  a  copper 


MUTUAL  INDUCTANCE 


155 


disk  on  a  shaft  inside  the  solenoid,  so  that  the  axis  of  the  disk  may  be 
made  parallel  or  not  to  that  of  the  coil.  The  eddy  currents  in  the  disk, 
with  parallel  axes,  will  very  materially  reduce  the  inductance  of  the  sole- 
noid. 

The  effect  of  such  a  solid  disk  placed  inside  a  short  solenoid  is  given 
in  Table  X.  The  coil  was  a  single  layer  solenoid  12  cm.  in  diameter  and 
of  2  cm.  axial  length;  the  various  disks  were  11  cm.  diameter  and  were 
placed  inside  the  coil,  centrally,  with  the  plane  of  the  disk  perpendicular 
to  the  axis  of  the  coil.  It  is  evident  that  a  copper  disk  very  materially 

TABLE  X 
EFFECT  OF  METAL  DISK  INSIDE  SOLENOID 


Frequency  in 
Kilocycles 

Coil  alone 

^-in.  Copper 
Disk 

^-in.  Brass 

^j-in.  Brass 

^j-in.  Tinned 
Iron 

L 

10~3 

henry 

R 

ohms 

L 

R 

L 

R 

L 

R 

L 

R 

1 

1.060 

3.03 

.807 

3.49 

.895 

3.77 

1.025 

3.53 

1.055 

3.25 

5.35 

1.052 

3.20 

.762 

4.18 

.785 

5.13 

.870 

6.40 

.970 

6.40 

50 

1.058 

3.35 

.751 

.5.79 

.756 

8.13 

.783 

12.6 

.865 

18.6 

149 

1.092 

5.08 

.760 

9.17 

.765 

13.5 

.792 

17.8 

.861 

44.3 

affects  the  inductance  without  prohibitive  increase  in  resistance.  By 
having  the  plane  of  the  disk  rotatable  this  scheme  of  varying  the  induc- 
tance of  a  coil  may  be  useful,  e.g.,  in  heterodyne  reception,  where  but 
slight  changes  in  inductance  are  desired  (to  change  signal  note),  and  an 
increase  in  resistance  of  the  coil  is  not  of  serious  consequence. 

The  best  adjustable  inductance  is  a  multilayer  coil,  with  each  layer 
(or  every  other  one  after  the  first  four  perhaps)  separate  from  the  others, 
equipped  with  the  proper  switch  to  connect  in  the  circuit  as  many  layers 
as  desired. 

Mutual  Induction. — The  coefficient  of  mutual  induction  of  two  coils 
may  be  expressed  in  terms  of  energy  in  the  same  way  as  is  self-induction. 
If  two  coils,  so  situated  with  respect  to  one  another  that  part  of  the  mag- 
netic field  of  each  is  linked  with  the  other,  are  connected  electrically  in 
series  in  such  a  way  that  their  m.m.f.'s  add,  the  total  energy  associated 
with  the  magnetic  field  of  the  circuit  is  i/2(Li  +  L2+2M)  and  if  the  elec- 
trical connection  is  reversed,  it  is  i-/2(Li-f-L2  —  2M).  Any  change  in  the 
circuit  which  changes  that  portion  of  the  magnetic  energy  due  to  M  has 


156 


RESISTANCE— INDUCTANCE— CAPACITY 


[CHAP.  II 


i, 


*— d- 


a  corresponding  effect  on  the  value  of  M.     The  value  of  M  may  also  be 

considered  as  fixed  by  the  voltage  induced  in  one  coil  by  current  in  the 

other  as  given  in  Eq.  (6)  Chapter  I. 

The  M  of  the  two  coils  is  determined  by  their  relative   position;    it 

may  be  changed,  however,  even  if  the  rela- 
tive position  of  the  two  coils  stays  fixed,  if 
a  third  circuit  is  brought  into  the  mutual 
field  of  the  two  coils.  Thus  two  equal 
coaxial  coils,  placed  with  their  ends  close 
together  may  have  a  value  of  M  about  .7  as 
large  as  LI,  but  if  a  copper  sheet  is  inserted 
between  the  two  coils  the  value  of  M  may 

FIG.  40.-Cross-section  through  be  brought  nearly  to  zero, 
two  single  turns  placed  co-         The  values    of   M    for    a    few    ordinary 
axially.  arrangements  are  given  below,  the  formulae 

being  approximations  as  were  those  for  L, 

the  values  obtained  from  the  formulae  being  accurate  to  better  than  1  per 

cent  in  most  of  the  cases. 

Two  Single  Turns,  Coaxial.     (Fig.  40.) — 


When  the  circles  have  nearly  the  same  radii  and  the  distance  between 
coils  is  small  compared  to  the  radius,  the  simpler  form  may  be  used, 


cm., 


(18) 


in  which  Ri  =  radius  of  smaller  circle. 


Experimental  results  showing  how  M  varies  for  the  case  shown  in 
Fig.  40  are  shown  in  Fig.  41.  The  coils  used  were  not  actually  single 
tarns,  but  the  cross-section  of  the  winding  was  so  small  compared  with 
the  radius  of  the  coil  that  they  approximated  single  turns  geometrically. 

Mutual  Induction  of  Two  Coaxial,  Circular  Coils  of  Rectangular 
Cross-section.  (Fig.  42.)  —  An  approximate  formula  for  this  case  (error 
for  most  practical  cases  less  than  1  per  cent)  is 

M=NiN2M0  cm.,       .......     (19) 


COEFFICIENT  OF   MUTUAL  INDUCTION 


157 


where  M0  is  the  mutual  induction  between  the  central  turns  of  the  two 
coils  (by  Eq.  (17)).  The  curves  of  Figs.  43  and  44  show  the  experimentally 
determined  values  of  M  for  two  typical  cases. 


8 

en 

1     1     1 

1 

1     1     1     1 

Eacl 

i_cjoil|  lids  80  t 

urns  of  copper  r 

ibl 

.on, 

.02 

5cfn; 

<  1 

27 

yaL  ihsi 

lal 

10 

ib 

et^ 

^e 

en 

tu 

rm 

Mutual  induction  in  10's  henrit 

(-.toco*>cnc5^i_ 

^ 

of 

w 

w 

d 

pa 

oei     1 

S^ 

|     1 

x 

D 

tern. 

D2 

=  6 

8.7 

cm 

. 

k 

— 

1.2 

ten 

i. 

s 

^ 

s 

;N 

I,. 

"N 

;<, 

*-•• 

-»^ 

••—  < 

***** 

1  —  , 

Con' 

ta 

nb 

of  et 

Cll 

c< 

>il 

~* 

F 

requenc 

v 

| 

R 

1°  1 

00828 

[80 

8000 

00834 

4.0 

14000 

00846| 

7.0 

1 

1     1 

1 

I 

r 
Separatioa 


34567 
Separation  in  cm. 


10 


FIG.  41. — Variation  in  mutual  inductance  of  two  coaxial  coils  with  separation;  the  two 
coils  approximated  single  turns. 

Mutual  Induction  of  Two  Coaxial  Solenoids.— The  formulae  to  cover 
the  various  cases  which  may  arise  in  this 
class  are  long;  the  reader  is  referred  to  the 
Bureau  of  Standards  Bulletin  No.  74  for  dis- 
cussion of  the  case.  In  Fig.  45  are  shown,  how- 
ever, three  curves  for  coils  of  different  dimen- 
sions; from  these  curves  M  for  other-shaped 
coils  can  be  approximated. 

Mutual  Induction  of    Two    Overhead    Par- 
allel Wires,   Grounded,  at  Same  Height  from 

Ground. — 

/d2+4h2\ 

\     d2     / 
where  d  =  separation  of  the  two  wires; 

h  =  height  of  wires  above  ground  (same  units  as  d)  ; 
I  =  length  of  one  wire  in  cm. 
a  Two-wire  Antenna,  Made  up  of  Two  Parallel 


cm., 


Central  turns 
FIG.  42. — Two  coaxial 
multilayer  coils. 

(20) 


Self-induction  of 
Wires  at  Same  Height  from  Ground.— 

L+M 


(21) 


L'  =  inductance  of  the  antenna; 
L  =  self-induction  of  one  wire  by  Eq.  (9) ; 
M  =  mutual  induction  of  the  two  wires  by  Eq.  (20). 


158 


RESISTANCE— INDUCTANCE— CAPACITY 


[CHAP.  II 


Mutual  Induction  between  Two  Concentric  Coils,  as  One  Rotates. 

(Fig.  46.) — This  combination  of  coils  is  frequently  used  in  radio  work, 
either  to  make  a  variable  self-inductance  or  to  couple  two  circuits  together. 


•2.07 

c 
o 

I-06 

.2  .05 

1      ' 
*2.04 


3.03 
5.02 


.01 


If  nduc 


each 


coil 


tiqnof 


.206  ienry 


Separation 


10 


20  30 

Separation  in  cm. 


40 


50 


FIG.  43. — Variation  of  mutual  inductance  of  two  multilayer  circular,  coaxial,  coils; 
separation  measured  between  nearest  sides. 

The  exact  expression  for  M  has  not  been  calculated,  but  an  experimentally 
determined  value  of  M  for  a  certain  combination  is  shown  in  Fig.  46. 
In  case  the  two  coils  are  connected  in  series  the  self-induction  of  the  com- 


Mutual  induction  in  henries 

10 

X. 

^ 

12 

\ 

%%^%% 

% 

W^^ 

T 

1 

% 

^ 

"*-•» 

L(OL 

te 

r  coil)  =.0400 

"*^ 

-•v. 

^. 

L(in 

ne 

r  coil)=. 

5295 

*"-. 

-^ 

*•*- 

^ 

•^ 

^ 

^^ 

•^ 

a 

"  — 

;;..;<x;.-; 

%%%% 

^ 

> 

r 

N 

Sejpacation 

\ 

)       .2        .4       .6       .8       1.0      .2        .4       .6       .8      2.0      .2 
Separation  in  inches 

.4       .6       ,8 

FIG.  44. — ^Variation  in  mutual  induction  of  two  multilayer  circular,  coaxial,  telescoping 

coils. 


bination  is  Li  +  L2±2M.  In  such  variable  inductances  it  is  feasible  to 
get  a  maximum  value  of  L  about  12  times  as  large  as  the  minimum  value 
of  L.  This  range  is  determined  by  the  manner  in  which  the  coils  are 


COEFFICIENT  OF   MUTUAL   INDUCTION 


159 


.«  18 

C 


.2 
£  14 


12 


§   10 

B 

'Z    8 
a 

3 

I   6 

4 
2 


A 
110 

100 
90 
80 
70 
60 
50 
40 
30 
20 
10 


\ 


3 


Curv 


V 


5S 


K 


ej^ 


-^ 


3*W 

144  x 


10"°  henry 


33  x  10 


#, 


1.37 


^.52 


345 
Separation  in  inches 


FIG.  45. — Variation  in  mutual  induction  of  various  single  layer  solenoids  placed  coaxially. 


z.o 

0    t 

0  0 

^^ 

—  J 

~*4 

)  — 

^* 

^ 

9  0 

s 

/ 

s 

Sin 

^ 

/ 

x 

1C 

i 

^x 

^ 

/ 

c  1  4 

/\ 

/ 

0 
C    1   9 

/ 

« 

y 

! 

/ 

-- 

.^ 

"2  i  n 

, 

/ 

> 

f 

\ 

/ 

if 

^ 

/ 

\ 

<S 

/ 

/ 

A 

e 

) 

3 

/ 

/ 



-/- 

— 

^_ 

/ 

S06 

/ 

(^ 

> 

/x 

/ 

\ 

y 

S 

/ 

0  4 

/ 

/ 

\ 

'\ 

s 

S 

j 

^*, 

^x 

> 

0  2 

/* 

/ 

/ 

s 

20 


70 


0  10 

FIG.  40. — Mutual  inductance  of  two  coils,  one  rotating  inside  the  other. 


30  40  50  60 

Value  of  angle  0,  in  degrees 


160 


RESISTANCE— INDUCTANCE— CAPACITY 


[CHAP.  II 


fitted  into  one  another.  When  both  coils  are  wound  in  straight  cylin- 
drical form  (short  solenoids)  the  range  in  L  will  not  be  as  great  as  when 
both  coils  are  wound  on  spherical  surfaces,  making  a  closer  fit  possible. 
A  typical  calibration  of  such  an  inductance  is  given  in  Fig.  39,  the  form 
of  the  coils  being  shown  on  the  curve  sheet. 

Mutual  Induction  between  Two  Coaxial  Spirals. — A  tedious  calcu- 
lation is  necessary  to  calculate  the  value  of  M  for  two  flat  spirals  arranged 
coaxially  but  an  idea  of  what  may  be  expected  is  indicated  in  the  experi- 
mentally determined  curves  of  Fig.  47. 


5        6        7        8        9       10      11      12 


FIG.  47. — Mutual  induction  of  the  two  flat  spiral  coils  of  an  oscillation  transformer. 

Two  ribbon-wound  spirals  of  the  dimensions  given  on  the  curve  sheet 
were  used;  the  number  of  turns  in  one  spiral  was  fixed  at  12,  while  the 
sliding  contact  on  the  other  was  used  to  vary  its  number  of  turns  as  indi- 
cated on  the  curve  sheet — the  value  of  M  was  measured  for  various  sepa- 
rations of  the  two  spirals.  The  results  shown  in  Fig.  41  indicate  the 
higher  values  of  M  obtainable  when  the  radial  depth  of  the  winding  of 
the  spiral  is  smaller. 


CAPACITY  OF  OVERHEAD  WIRES  161 


CAPACITY 

General  Idea  of  Capacity.  —  The  electrostatic  capacity  of  a  body  may 
may  be  thought  of  either  in  terms  of  the  quantity  of  electricity  stored 
for  a  given  potential  difference  between  the  two  surfaces  constituting  the 
condenser  or  in  terms  of  the  energy  in  the  electrostatic  field,  the  value 
of  this  capacity,  in  farads,  being  equal  to  twice  the  energy  of  the  field, 
measured  in  joules,  when  the  potential  difference  is  one  volt. 

There  may  be  still  another  idea  of  capacity  when  looking  at  a  circuit 
from  the  standpoint  of  electrical  reactions,  just  as  there  is  for  inductance 
and  resistance.  When  a  current  flows  in  a  circuit  the  circuit  will  generate 
counter  forces  called  reacting  forces  or  reactions.  If  the  current  flowing 
is  one  ampere  the  amount  of  reacting  force  set  up  in  phase  opposition  to 
the  current,  in  volts,  is  the  resistance  of  the  circuit  in  ohms  —  the  reacting 
force  set  up  in  phase  with  the  current  is  the  negative  resistance  of  the  cir- 
cuit, the  reacting  force  set  up  90°  behind  the  current  is  the  inductance 
reaction  in  volts,  and  the  reacting  force  set  up  90°  ahead  of  the  current 
is  the  capacity  reaction.  The  capacity  and  inductance  are  calculated  from 

their  respective  reactions,      frt  and  2irfL,  f  being  known.     The  reactions 


may  be  caused  by  ordinary  coils,  condensers,  and  wires,  but  it  must  be 
remembered  that  in  special  cases  a  circuit  may  give  capacity  reaction  when 
there  are  no  condensers,  and  it  may  give  inductance  reaction  when  there 
are  no  coils  present.  Thus  an  overexcited  synchronous  motor  is  electrically 
equivalent  to  a  condenser;  a  tuned  electrostatic  telephone  when  excited 
at  certain  frequencies  develops  (due  to  its  motion)  an  inductance  reaction 
and  there  are  no  coils  used  in  the  telephone. 

It  must  also  be  remembered  that  the  capacity  of  a  body  in  general 
changes  with  the  frequency.  Not  only  does  the  viscous  action  of  the 
dielectric  decrease  the  effective  specific  inductive  capacity  constant  as 
the  frequency  is  increased,  but  in  many  circuits,  the  capacity  of  which 
is  under  consideration,  the  potential  distribution  changes  with  frequency, 
and  as  the  electrostatic  energy  (hence  capacity)  depends  upon  the  potential 
distribution,  the  capacity  may  be  expected  to  change  with  frequency. 

The  formulae  given  herewith  are  good  only  for  stationary  charges;  if 
the  circuit  considered  is  electrically  long,  the  values  obtained  from  these 
formulae  are  not  correct  except  at  very  low  frequencies.  The  capacity 
calculated  from  these  formulae  is  in  centimeters;  to  change  to  micro- 
micro-farads  (MM/)  the  values  obtained  must  be  divided  by  0.9  and  to  get 
milli-micro-farads  the  values  must  be  divided  by  900.  Where  the  abbrevi- 
ation log  is  used  the  natural  logarithm  (to  base  e)  is  intended. 


162  RESISTANCE—  INDUCTANCE—  CAPACITY  [CHAP.  II 

Capacity  of  a  Conducting,  Isolated,  Sphere  in  Air.— 

C  =  rcm.,     .........     (22) 

where  r  =  radius  of  sphere  in  cm. 

Capacity  of  Two  Flat,  Circular  Parallel  Plates  in  Air.— 

m'>     '    '     (23) 


r  =  radius  of  plates  in  cm.; 
t  =  thickness  of  plates  in  cm.; 
d  —  separation  of  plates  in  cm. 

• 

Capacity  of  Two  Flat  Plates  (approximate  Formula).  — 


K  =  specific  inductive  capacity  of  dielectric ; 
A  =area  of  one  side  of  one  plate  in  sq.  cm.; 
d  =  separation  of  plates  in  cm. 

Single  Vertical  Wire,  Proximity  to  Earth  Neglected. — 

I 


(25) 


7 

2  log  --r 

» 

1  =  length  in  cm.; 
r  =  radius  in  cm. 

In  several  experiments  with  the  lower  end  of  the  wire  close  to  the 
earth,  the  measured  capacity  exceeded  that  calculated  from  the  formula 
by  about  10  per  cent. 


Single  Horizontal  Wire,  Earth  for  Other  Plate.— 


(26) 


2  log 

1  =  length  of  wire  in  cm.; 

h  =  height  of  wire  above  earth; 

r  =  radius  of  wire,  same  units  as  used  for  h. 

This  formula  assumes  the  charge  in  the  wire  distributes  itself  uniformly 
over  the  periphery.     Actually  the  lower  side  of  the  wire  has  a  slightly 


CAPACITY  OF  OVERHEAD  WIRES 


163 


greater  density  of  charge  than  the  upper  side,  resulting  in  a  formula  in 
hyperbolic  functions. 

I 


cm. 


127) 


2  cosh'1  - 
r 


When  /i/r  =  5  Formula  (27)  gives  a  result  15  per  cent  greater  than  does 
(26).  For  greater  values  of  h/r  the  discrepancy  between  the  two  is  less. 
In  general  whenever  two  wires  are  so  close  together  that  the  separation 
is  not  more  than  5  times  their  diameter,  hyperbolic  functions  are  required 
for  precise  results,  rather  than  the  ordinary  logarithmic  formulae,  for  either 
the  inductance  or  capacity.  In  practice  the  ratio  of  h/r  is  much  greater 
than  5  except  for  one  or  two  cases,  such  as  the  wires  of  a  telephone  cable,  etc. 
Mutual  Capacity  of  Two  Horizontal  Wires,  Such  as  Two  Wires  of 
an  Antenna. — 


c=z 


d2 


22 


cm., 


.    .    (28) 


where 


1  =  length  of  one  wire; 
h  =  height  of  each  wire; 
r  =  radius  of  wire; 
d  =  distance  between  wires. 


The  mutual  capacity  is  not  the  same  as  the  capacity  of  the  two  wires 
regarded  as  the  two  plates  of  a  condenser,  one  charged    positively  while 
the   other  is    charged   nega- 
tively.    It   really  represents 
a  decrease   in    the    capacity 
of  one  of  the  wires  with  re- 
spect to  earth  caused  by  the 
presence  of  the  field  of  the 
other.     In  Fig.  48  this  point 
is    illustrated;      the    normal 
field  of  wire  a    to   earth    is 
shown  by  the  full  lines  and    FIG.  48.— Diagram  illustrating  the  "overlapping" 
that    of  wire  b  is  shown  by          of  the  electric  fields  of  two  antenna  wires, 
dotted  lines,   and  it  is  evi- 
dent that  the  two  fields  overlap.      The  total  capacity  of  these  two  wires, 
to  earth,  is  diminished  to  some  extent  by  this  overlapping   of   the  two 
individual  fields,  and  a  measure  of   the  decrease  in  capacity  is  given  by 
the  value  of  M  from  Eq.  (28). 


Earth 


164  RESISTANCE—  INDUCTANCE—  CAPACITY  [CHAP.  II 

Capacity  of  Two  Horizontal  Overhead  Wires  with  Respect  to  Each 
Other.  —  This  is  the  case  of  using  the  two  wires  of  Fig.  48,  one  as  one  side 
of  a  condenser  and  the  other  one  for  the  other  side  of  the  condenser. 


4  l°9  ~ 


(29) 


where  I  =  length  of  one  wire  in  cm.  ; 

d  =  separation  of  the  two  wires; 
r  =  radius  of  the  wire  hi  same  unit  as  d. 

This  formula  supposes  the  distance  between  the  wires  is  small  compared  to 
the  height  aboye  the  earth;  for  wires  close  to  the  earth,  compared  to  their 
separation,  this  formula  gives  values  of  C  too  low. 

Capacity  of  Two-wire  Antenna.  —  This  is  the  case  of  the  two  wires  of 
Fig.  48  being  connected  together  and  their  capacity  with  respect  to  earth 
being  determined.  It  is  equal  to  twice  the  capacity  of  one  wire  with 
respect  to  ground  (Eq.  (26))  diminished  by  the  mutual  capacity  of  the  two 
wires  (Eq.  (28)). 

In  case  the  two  wires  are  far  apart  the  value  of  capacity  is  twice  that 
of  one  wire,  and  as  the  wires  approach  each  other  the  capacity  decreases, 
until  when  the  two  wires  touch,  their  combined  capacity  is  not  greatly 
in  excess  of  that  of  a  single  wire. 

It  is  interesting  to  note  that  the  self-induction  of  a  pair  of  wires  (the 
two  wires  of  an  antenna,  for  example)  increases  as  the  wires  approach, 
whereas  the  capacity  of  the  pair  diminishes.  In  fact  the  variation  is 
nearly  reciprocal,  so  that  the  product  of  L  and  C  of  the  pair  is  independent 
of  the  spacing  of  the  two  wires. 

The  foregoing  formulae  for  capacity  of  wires  with  respect  to  earth  are 
not  very  accurate,  not  being  corrected  for  end  effects,  etc.  It  does  not 
seem  worth  while  to  use  more  elaborate  formulae,  however,  because  the 
presence  of  foreign  bodies  in  the  electrostatic  fields  of  antennae,  such  as 
trees,  masts,  stays,  etc.,  influences  the  value  of  capacity  to  a  large  extent. 
Also  the  height  of  a  wire  is  ambiguous;  this  height  is  really  to  be  measured 
to  conducting  earth  (wet)  and  the  height  of  the  wires  above  wet  earth 
may  not  be  easy  to  determine. 

Recently  Austin1  has  given  an  empirical  formula  for  the  capacity 
of  an  antenna,  the  formula  apparently  being  fairly  accurate  (say  within 
10  per  cent)  for  any  ordinary  form  of  antenna.  It  is 


(29a) 


A  =area  of  the  antenna  in  sq.  meters; 
h  =  mean  height  of  the  antenna,  in  meters. 
1  Louis  W.  Austin,  Calculation  of  antenna  capacity,  Proc.  I.  R.  E.,  Vol.  8,  No.  2. 


VARIABLE  CONDENSERS  165 

In  case  the  length  of  the  antenna  is  more  than  eight  times  the 
breadth  a  slight  additional  correction  is  necessary,  this  increase  being 

equal  to  ,-       ,,u  X 1  •  5  per  cent, 
breadth 

In  calculating  A}  the  length  of  the  antenna  is  multiplied  by  its 
breadth,  the  area  thus  obtained  being  of  course  much  greater  than  the 
actual  surface  of  the  antenna  wires.  With  the  ordinary  antenna  a  spac- 
>  ig  of  one  meter  between  wires  will  give  a  capacity  about  90  per  cent  of 
>hat  which  would  be  obtained  if  sufficient  wires  were  used  to  completely 
fill  the  space  occupied  by  the  antenna,  so  that  neighboring  wires  touched 
each  other. 

Capacity  of  a  Multiplate  Condenser. — 

C-^-^em (30) 

A  =  area  of  one  side  of  one  plate  in  sq.  cm. ; 

n  =  total  number  of  plates; 

d  =  separation  of  plates  in  cm. ; 
K  =  specific  inductive  capacity  of  dielectric. 

Various  Forms  of  Variable  Condenser. — It  is  in  genera?  more  con- 
venient to  make  a  condenser  continuously  variable  than  to  make  an 
inductance  of  that  kind,  hence  the  tuning  of  a  radio  circuit  is  generally 
accomplished  by  using  fixed  steps  of  inductances  and  a  continuously  vari- 
able condenser.  These  variable  condensers  are  made  with  either  sliding 
plates,  one  set  of  plates  moving  in  groves  in  insulating  blocks,  or  with 
rotating  plates,  one  set  of  plates  being  mounted  on  a  shaft. 

If  the  sliding  plates  are  rectangular  (and  move  parallel  to  one  side) 
or  the  rotating  plates  are  circular  (with  shaft  on  which  they  rotate  in  the 
center),  then  the  amount  of  capacity  in  the  condenser  will  vary  directly 
with  the  amount  of  movement  (sliding  or  rotation)  of  the  moving  plates 
and  the  calibration  curve  will  be  a  straight  line.  This  straight  line  will 
not  pass  through  the  zero-zero  point,  because  even  with  zero  scale  setting 
there  is  still  an  appreciable  capacity  in  the  condenser. 

It  is  many  times  convenient  to  have  the  capacity  vary  with  the  setting 
to  some  other  power  than  the  first;  thus  if  it  is  used  in  a  wave  meter 
(see  Chapter  X)  it  is  convenient  to  have  the  capacity  vary  as  the  square  of 
the  setting  and  the  wave  length  scale  will  then  be  a  straight  line.  For 
other  purposes  it  is  convenient  to  have  a  logarithmically  varying  capacity 
so  that  a  scale  division  everywhere  represents  the  same  percentage-  change 
in  capacity.  Both  of  these  variations  of  capacity  are  obtainable  in  rotat- 
ing plate  condensers  by  properly  shaping  the  rotating  plates  and  suitably 
placing  the  shaft  in  which  they  turn. 


166 


RESISTANCE— INDUCTANCE— CAPACITY 


[CHAP.  II 


Two  typical  calibration  curves  are  shown  in  Fig.  49,  for  semicircular 
plates  with  central  shaft,  and  for  specially  formed  plates,  with  displaced 
shaft.  In  the  first  the  capacity  varies  directly  as  the  angle  of  the  movable 
plates  and  in  the  second  the  scale  reading  is  proportional  to  the  logarithm 
of  the  capacity. 

Losses  Occurring  in  Condensers. — When  a  condenser  is  used  in  a  high- 
frequency  circuit  there  are  various  losses  which  occur,  all  of  which  are 
detrimental  and  to  be  avoided  if  possible.  The  losses  may  be  due  to 
actual  leakage  from  one  plate  to  the  other  through  or  around  the  dielec- 


6 

5 

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plstef  dj'cij'emet^r 

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r 

a 

2 

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x^ 

X 

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x 

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x 

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10      20     30      40      50      GO      70      80      90     100    110    120    130    140    150    1GO    170   18C 
Setting  of  rotating  plate,  in  degrees 

FIG.  49. — Calibration  curves  of  typical  condensers  used  in  radio  apparatus. 

trie,  to  dielectric  hysteresis,  to  PR  loss  in  the  conducting  plates  of  the 
condensers,  and  due  to  corona  losses  from  the  edges  of  the  plates.  When 
a  condenser  is  used  in  a  receiving  circuit  (low  voltage)  only  the  first  three 
sources  of  loss  exist. 

For  an  air  condenser  constructed  with  rugged  plates  of  negligible 
resistance  all  of  the  losses  in  the  condenser  properly  are  negligible  except 
at  voltages  high  enough  to  give  corona  loss.  However,  the  supports, 
terminals,  etc.,  of  the  air  condenser  must  be  mounted  on  very  good  insu- 
lators, otherwise  an  appreciable  resistance  may  be  incurred  due  to  the 
dielectric  hysteresis  and  leakage  at  these  points.  Quartz  or  high-grade 
porcelain  should  be  used  at  these  points. 


PROPERTIES  OF  DIELECTRICS 


167 


Condensers  using  glass,  paper,  rubber,  or  mica  for  the  dielectric  have 
some  dielectric  losses,  although  this  loss  in  a  well-constructed  mica  con- 
denser (air  and  moisture  excluded)  seems  to  be  very  small;  the  dielectric 
losses  in  paper  and  some  grades  of  glass  are  high.  Dry  oil  is  in  general  a 
very  good  dielectric  with  very  low  losses;  the  oil  has  an  added  advantage 
over  a  solid  dielectric,  in  that  a  disruptive  breakdown  does  not  spoil  the 
condenser,  the  oil  repairing  itself  with  no  deleterious  effects  unless  sufficient 
arcing  occurs  in  the  oil  to  produce  considerable  carbonization.  A  good 
grade  of  mineral  oil  is  generally  used,  but  the  author  has  found  castor 
oil  to  be  excellent,  having  a  high  dielectric  strength,  low  losses,  and  having 
such  a  high  specific  inductive  capacity  as  to  give  about  twice  as  much 
capacity  as  the  same  amount  of  mineral  oil.  The  value  of  K  for  various 
dielectrics  is  shown  in  Table  XI. 

TABLE  XI 

SPECIFIC  INDUCTIVE  CAPACITY  OF  MATERIALS  USED  MORE  GENERALLY  IN  RADIO 
CONDENSERS  (MEASUREMENTS  AT  Low  FREQUENCY) 


Material 

Value  of  K 

Material 

Value  of  K 

Ebonite  

2  5-3  5 

Porcelain 

4  38 

Ebonite 

1  9  at  about  4X107  cycles 

Quartz 

4  50 

Glass,  density: 

Resin  

2.50 

2.5-4.5  

5-10 

Shellac  

3  0-3.7 

Glass,  density: 

Castor  oil 

4  7 

2  .  5-4  5  

2  7  Sit  about  5  X  107  cycles 

Olive  oil 

3  1 

Gutta  percha  .... 
Mica  ;  

3.3-4.9 
4.6-8.0 

Petroleum  oil  ... 
Vaseline 

2.1 
2  2 

Paraffin  wax 

2  0-2  5 

Formica,  bakelite,  bakelite-dilecto,  and  such  compounds  have  a  value  of  K  of  about 
5,  generally  lying  between  5  and  6. 

It  must  be  remembered  when  using  solid  dielectric  condensers  that 
practically  all  such  materials  as  glass,  rubber,  paper,  wax,  etc.,  very  rapidly 
lose  their  insulating  properties  as  the  temperature  increases.  In  fact  the 
operation  of  most  solid  dielectric  condensers  becomes  unstable  above  a 
certain  voltage;  above  this  critical  voltage  the  condenser  will  soon  break 
down  if  left  connected  to  the  circuit.  This  is  due  to  the  cumulative  effect 
of  the  losses  in  causing  temperature  rise,  the  higher  the  temperature  the 
higher  the  losses  become,  thus  again  increasing  the  temperature.  Some 
special  paper  condensers  passed  a  puncture  test  of  4000  volts  successfully, 
but  upon  being  connected  to  a  2000  volts  60-cycle  line  every  one  out  of 
the  twelve  tested  broke  down  in  less  than  twenty  minutes.  The  same 
experience  was  had  to  an  even  more  marked  degree  with  a  lot  of  mica 
condensers. 


168 


RESISTANCE— INDUCTANCE— CAPACITY 


[CHAP.  II 


It  must  also  be  remembered  that  a  condenser  passing  a  voltage  test 
successfully  when  tested  in  a  60-cycle  line  may  break  down  after  a  few 
minutes'  operation  on  a  high-frequency  circuit  with  a  voltage  only  a  small 
fraction  of  the  60-cycle  voltage  which  it  withstood  successfully.  In 
certain  parts  of  a  vacuum  tube  the  glass  (as  dielectric)  is  subjected  to 
high-potential  gradients  at  high  frequency  and  it  shows  losses  many 
times  as  great  as  might  be  expected  from  low-frequency  tests. 

Even  quartz,  which  is  one  of  the  best  dielectrics,  shows  this  effect; 
a  certain  piece  required  46,000  volts  to  puncture  when  the  voltage  was 
continuous,  whereas  it  broke  down  at  18,000  volts  (effective)  after  being 
connected  to  a  500-cycle  line  for  a  few  minutes. 

Equivalent  Series  or  Shunt  Resistance  of  a  Condenser. — All  of  the 
losses  in  a  condenser  can  be  grouped  together  and  represented  by  a  certain 
hypothetical  series  resistance;  the  value  of  this  resistance  will,  in  general, 
be  different  for  different  frequencies.  Thus  in  Fig.  50  let  a  represent  a 


Equivalent 
series  resistance 


Faulty 
dielectric : 


(a) 


(6) 


Equivalent 

shunt 
'resistance 
r 


FIG.  50. — A  condenser  with  imperfect  dielectric  may  be  represented  by  one  having  per- 
fect dielectric  in  series  with,  or  shunted  by,  a  suitable  resistance. 


condenser  which  is  drawing  a  current  of  2  amperes  at  a  certain  frequency, 
and  has  a  total  power  loss  due  to  all  causes  of  7.5  watts.  Then  this 
faulty  condenser  can  be  well  enough  represented  by  a  perfect  condenser 
6  (of  the  same  capacity  as  a)  having  no  losses,  but  having  in  series  with 
itself  a  non-inductive  resistance  R,  such  that  the  charging  current  of  con- 
denser 6,  flowing  through  this  resistance,  will  dissipate  the  same  amount  of 
power  as  is  lost  in  the  faulty  condenser  a.  For  the  case  cited  above  we 

7  5 
shall  have  R  =  ~^~  1.88    ohms.     The    faulty    condenser   might    also    be 

replaced  by  a  perfect  condenser  and  a  suitable  leak,  or  shunt,  resistance. 
If  the  voltage  in  the  condenser  is  E,  the  loss  in  a  shunt  resistance  is  E2/r, 
so  in  c,  Fig.  50,  is  shown  this  arrangement  and  for  the  case  cited,  if  the 
voltage  is  5000  volts  the  proper  shunt  resistance  is  obtained  by  putting 


7.5  or  r  =  =  3.34  X  106  ohms. 

7.5 


CONDENSERS   FOR   HIGH-VOLTAGE   CIRCUITS 


169 


These  simple  calculations  hold  only  for  condenser  of  low  power  factor, 
say  0.02  or  less,  but  as  all  good  radio  condensers  have  a  lower  power  factor 
than  this  the  method  outlined  above  is  accurate  enough.  The  relation 
between  the  equivalent  series  resistance  and  equivalent  shunt  resistance 
is  obtained  from  the  relations  (which,  it  must  be  remembered,  hold  good 
for  low  power  factor  condensers  only) 

E2 


or 


>2C2R' 


(31) 


R  being  the  series  resistance  and  r  the  shunt  resistance. 

For  most  dielectrics  the  equivalent  series  resistance  varies  inversely 
with  the  frequency,  indicating  a  constant  energy  loss  per  cycle. 

Characteristics  of  Ordinary  Power  Condensers. — Tests  made  by 
L.  W.  Austin  on  various  condensers  used  for  the  transmitting  circuits  of 
radio  sets  gave  results  as  shown  in  Table  XII.  The  tests  were  made  at 
14,500  volts  and  300,000  cycles  with  damped  wave  excitation  of  120  sparks 
per  second. 

TABLE  XII 


Kind  of  Condenser 

Power  Factor 

Capacity  in  10  —  9 
farads 

Equivalent  series 
resistance  in  ohms 

Compressed  air  

.001 

5  8 

14 

Leyden  jar  in  oil  (glass) 

003 

6  0 

28 

Composition  Murdoch  
Glass  plates  in  oil  

.004 
.005 

5.4 

4  2 

.41 
58 

Moscicki  condenser  
Leyden  jar  in  air  

.006 
.016 

5.5 
6  1 

.57 
1  4 

Molded  micanite  

.023 

4  1 

2  9 

Paper 

024 

5  8 

2  2 

In  the  case  of  the  compressed-air  condenser  it  is  probable  that  practi- 
cally all  of  the  loss  was  attributable  to  dielectric  losses  in  the  insulated 
lead-in  wire.  At  the  voltages  used  it  seems  that  the  ordinary  Leyden 
jar  used  in  radio  sets  has  considerable  corona  or  leakage  loss,  because 
immersion  in  oil  cut  the  losses  to  about  20  per  cent  of  the  value  in  air. 
Mica  condensers  were  not  tested  at  this  time,  but  recent  tests  give  them 
an  efficiency  rating  nearly  equal  to  the  compressed  air. 

Test  made  by  E.  F.  W.  Alexanderson,  using  a  high-frequency  alternator 
for  source  of  power,  shows  power  factors  greatly  in  excess  of  the  values 
given  by  Austin's  results.  Some  of  the  values  obtained  by  Alexanderson 
are  given  in  the  accompanying  table;  the  frequency  used  varied  from 


170  RESISTANCE— INDUCTANCE— CAPACITY  [CHAP.  II 

20  kilocycles  to  90  kilocycles,  and  the  potential  gradient  from  5000  volts 
per  cm.  to  20,000  volts  per  cm.  The  power  factor  for  most  of  the 
dielectrics  tested  increased  somewhat  with  frequency  increase,  the  amount 
of  increase  begin  small  for  the  better  dielectrics;  thus  the  power  factor 
for  mica  was  constant  within  the  range  of  frequency  used,  while  glass 
increased  from  .013  to  .016.  All  of  the  samples  showed  an  increase  of 
power  factor  with  increased  potential  gradients,  a  slow  increase  at  first, 
then  more  rapidly  until  rupture  occurred;  glass,  e.g.,  increased  its  power 
factor  from  .013  to  .015  with  a  change  in  potential  gradient  from  5000 
to  12,000  volts  per  cm.,  and  when  the  gradient  was  further  increased  to 
19,000  volts  per  cm.  the  power  factor  rose  to  .054. 

For  a  gradient  of  10,000  volts  per  cm.  and  frequency  of  50,000  cycles 
the  results  obtained  were  as  follows: 


Material 

Power  Factor 

Watts  loss  per  cm. 

cube 

Built-up  mica  

.019 

.15 

Glass      

.014 

.25 

Paper 

.021 

.26 

Varnished  cambric  

.031 

.35 

The  mica  used  was  built  up  from  small  mica  sheets  and  some  binding 
cement;  it  seems  likely  that  the  losses  in  the  cement  and  possible  small 
air  cavities  caused  more  loss  than  did  the  mica  itself;  the  small  temperature 
rise  in  a  good  mica  condenser  built  especially  for  radio  work  would  indicate 
that  a  comparatively  small  part  of  the  loss  found  by  Alexanderson  was 
due  to  losses  in  the  mica  itself,  unless  a  poor  grade  had  been  used.  He 
found  some  samples  of  built-up  mica  with  a  power  factor  as  high  as  .07; 
it  would  seen  likely  that  a  lot  of  air  was  trapped  in  this  sample.  Some 
recent  tests  have  indicated  a  power  factor  in  mica  as  low  as  .0003. 

It  will  be  noticed  that  there  is  a  considerable  difference  between  Austin's 
results  and  those  of  AJexanderson;  e.g.,  glass  gave  power  factors  of  .005 
and  .014,  in  the  different  measurements.  The  difference  is  probably 
attributable  to  the  different  quality  of  glass  used  and  also  to  the  fact  that 
different  methods  of  experimentation  were  used ;  in  one  case  the  material 
was  subjected  to  the  loss  continuously  and  in  the  other  for  only  a  small 
fraction  of  the  time.  Alexanderson  used  continuous  wave  excitation  and 
Austen  a  120-cycle  spark;  the  resulting  temperature  rise  was  undoubtedly 
different  in  the  two  tests. 

Most  of  the  solid  dielectrics  using  bakelite  for  base  have  a  power  factor 
(at  radio  frequencies)  of  about  4  per  cent.  Some  show  a  power  factor, 
increasing  with  age  of  the  material,  the  power  factor  of  some  of  them 
increases  with  increase  in  frequency  and  in  others  a  decrease  of  power 
factor  occurs. 


PHASE  DIFFERENCE  IN  CONDENSERS  171 

Phase  Difference  of  a  Condenser. — In  a  good  condenser  the  angle  of 
current  lead,  </>,  is  very  nearly  90°;  the  power  factor  of  the  condenser  is 
the  cosine  of  this  angle,  0,  or  it  may  be  put  equal  to  sin  \f/,  where  \f/  =  90°  —  </>. 
This  angle  \[/  is  called  the  phase  difference  of  the  condenser,  and  it  is  evi- 
dent that  if  ^  is  only  1°  or  2°  that  the  power  factor  of  the  condenser, 
cos  0  =  sin  \t/=\l/,  hence,  the  power  used  in  a  condenser  is  readily  given 
in  terms  of  $. 

Power  used 

=  El  cos  <{>  =  EIt=uCE2t (32) 

The  power  factor  of  the  condenser 

Resistance 


Reactance 


RuC (33) 


The  phase  difference  of  a  condenser  to  be  used  for  radio  work  should  never 
exceed  0.2°;  a  greater  value  indicates  excessive  dielectric  loss. 

Phase  Difference  Caused  by  Dielectric  loss  is  Constant  for  a  Given 
Material. — The  dielectric  loss  in  most  dielectrics  varies  with  the  square 
of  the  potential  gradient  in  the  dielectric,  other  quantities  being  fixed; 
this  merely  states  the  fact  that  the  power  factor  of  the  condenser  is  inde- 
pendent of  the  voltage.  Such  has  been  found  to  be  true  for  most  materials, 
for  voltages  well  below  the  rupturing  strength  of  the  dielectric.  If  then 
we  have  a  condenser  (of  certain  capacity),  made  with  a  certain  dielectric, 
it  will  produce  a  certain  loss,  no  matter  how  much  or  how  little  of  the 
dielectric  we  use.  Thus  if  we  double  the  thickness  of  the  dielectric 
(cutting  the  gradient  in  half)  we  must  increase  the  area  of  the  dielectric 
by  two,  thus  using  four  times  the  volume  of  the  dielectric  as  before.  With 
the  gradient  cut  in  two  the  dielectric  loss  per  unit  volume  is  cut  to  one- 
fourth,  but  as  we  have  four  times  the  volume  the  total  loss  is  the  same. 

It  seems  then  that  the  efficiency  of  a  condenser  cannot  be  improved 
by  using  more  or  less  dielectric;  a  better  dielectric  must  be  substituted 
if  the  phase  difference,  \f/,  is  to  be  reduced.  Fig.  51  serves  well  to  illus- 
trate this  point,  the  curves  showing  the  experimentally  determined  resist- 
ance and  capacity  of  a  variable  condenser  having  ebonite  for  the  dielectric. 
The  condenser  showed  the  product  #C=14X10~9  everywhere  through- 
out the  scale;  the  test  was  performed  at  25,000  cycles,  giving  a  value 
for  ^=.0022.  In  this  condenser,  therefore,  the  current  leads  the  voltage 
by  an  angle  of  89.874°. 

Internal  Capacity  of  a  Two-layer  Solenoid. — A  certain  single-layer  sole- 
noid had  an  inductance  of  1000  ph  at  600  meters;  another  solenoid  was 
at  hand  which  had  the  same  dimensions  as  the  first,  but  it  had  two  layers  of 
wire  instead  of  one,  giving  it  twice  as  many  turns.  Tested  at  1000  cycles 
it  showed  an  inductance  slightly  more  than  four  times  as  great  as  the  single- 


172 


RESISTANCE— INDUCTANCE— CAPACITY 


[CHAP.  II 


layer  solenoid,  as  it  should,  but  when  tested  at  500,000  cycles  it  acted  like 
a  condenser,  not  like  an  inductance ;  in  fact  it  ceased  to  act  like  an  induc- 
tance for  frequencies  above  200,000  cycles.  This  peculiar  behavior  was 
caused  by  the  internal  capacity  of  the  coil;  this  internal  capacity  may 
be  represented  to  a  certain  degree  of  approximation,  as  a  condenser 
connected  in  parallel  with  the  terminals  of  the  coil.  It  is  then  evident 
that  above  a  certain  frequency  the  current  taken  to  charge  the  condenser 


20 


18 


16 


14 


10 


Is 

C 


•1 

a  4 


Equivalen 


Condenser 


stance 


viU 


ebonit 


•lee 


Capacity 


0123456789  10 

Position  of  rotating  plates 

FIG.  51. — Variation  of  equivalent  series  resistance  of  a  radio  condenser  having  ebonite 

dielectric. 

will  be  greater  than  the  current  through  the  coil  itself,  making  the  com- 
bination circuit  act  like  a  condenser,  of  capacity  varying  with  the  frequency. 
The  calculation  of  the  internal  capacity 1  of  a  coil  is  most  conveniently 
carried  out  by  calculating  the  electrostatic  energy  stored  in  the  coil  for 
a  given  voltage;  the  value  of  C  is  then  at  once  obtained.  The  capacity 
of  the  two-layer  solenoid  referred  to  above  will  first  be  calculated.  Fig. 
52  depicts  the  arrangement  of  the  electrostatic  and  magnetic  fields  of  the 
coil  when  current  is  flowing  through  it;  when  the  impressed  e.m.f.  is 
continuous,  the  difference  in  potential  between  the  two  layers  varies 

1  In  Phys.  Rev.,  Aug.  1921,  Breit  publishes  a  note  in  which  he  says  that  for  a  short 
single  layer  solenoid  the  internal  capacity  (in  /x/x/)  is  nearly  equal  to  7  per  cent  of  the 
axial  length  of  the  coil,  in  centimeters. 


INTERNAL  CAPACITY  OF  COILS 


173 


directly  as  the  distance  from  the  end  where  the  two  layers  connect  together, 
being  zero  at  this  point.  When  the  impressed  e.m.f.  is  alternating,  this 
potential  difference  between  the  two  layers  is  no  longer  a  straight  line 
variation  but  varies  more  rapidly  in  the  center  of  the  coil  ;  the  exact  form 
of  this  potential  difference  curve  varies  with  the  frequency  and  with  the 
shape  of  the  coil. 

End  where  layers  are 
connected  together 




Electro  static  field 


FIG.  52.  —  Magnetic  and  electric  fields  in  an  ordinary  two-layer  solenoid. 


It  is  noticed  that  the  capacity  of  the  coil  is  essentially  that  of  two 
concentric  cylinders,  the  separation  of  these  two  cylinders  being  determined 
by  the  average  separation  of  the  wire  on  the  two  layers  of  the  coil,  being 
perhaps  four  times  the  thickness  of  insulation  of  the  wire,  for  wire  and 
insulation  with  relative  proportions  as  shown  in  Fig.  53;  this  is  about 
the  right  scale  for  No.  26  double  cotton-covered  wire.  With  such  wire 


Cotton  insulation 


between  layejsT 


FIG.  53. — Electric  field  between  neighboring  conductors  of  a  two  layer  solenoid. 

then  we  can  calculate  the  capacity  by  replacing  the  actual  coil  by  two 
conducting  cylinders  having  the  same  diameter  and  length  as  the  coil, 
and  separated  by  a  distance  equal  to  four  times  the  thickness  of  insula- 
tions of  the  wire.  As  the  separation  of  the  cylinders  is  so  small  compared 
to  the  diameter,  the  capacity  may  be  calculated  by  using  the  formula  for 
flat  plates.  Hence  we  get 

rlK 

-cm (34) 


174 


RESISTANCE— INDUCTANCE— CAPACITY 


[CHAP.  II 


where     r  =  mean  radius  of  coil  in  cm.  ; 
1  =  length  of  coil  in  cm.; 
t  =  thickness  of  insulation  in  cm.; 
K  =  specific   inductive   capacity  of  dielectric. 
If  the  coil  is  impregnated  with  shellac, 


Eq.  (34)  gives  the  capacity  for  static  charges,  the  two  cylinders  being 
insulated  from  one  another;  in  the  coil,  however,  the  two  cylindrical 
surfaces  are  actually  connected  together  at  one  end.  The  problem  then 
resolves  itself  in  one  of  determining  the  equivalent  capacity  of  two 
cylinders  having  a  potential  difference  of  zero  at  one  end  and  E  volts  at 


Electric  field 


FIG.  54. — Variation  in  potential  difference  between  the  layers  of  a  two  layer  solenoid, 

at  low  frequency. 

the  other.     The  diagram  in  Fig.  54  gives  the  elements  of  the  problem; 
two  plates,  capacity  per  unit  length  =-or  with  potential  difference  as 

represented  by  the  e  curve  in  the  upper  part  of  Fig.  54.    The  energy 
stored  in  an  element  of  length  of  the  condenser  is, 

rKe2 


The  total  work  stored  in  the  electrostatic  field, 


1?jfH)! 


w --- 


dx* 


rKE2  I 
IQt   3* 


Now  we  define  capacity  in  a  problem  like  this  by  putting  the  total 
energy  stored  in  the  field  equal  to  — ~-  where  C'  is  the  capacity  we  desire 

to  calculate. 

C'E2_rKE2l       r,_rKl 
^O     o  /ic/     ®*  ^       ft  At ("5) 


By  comparison  with  Eq.  (34)  we  see  that  the  equivalent  capacity  of 
such  a  coil,  assuming  uniform  change  in  the  potential  gradient  from  one 


INTERNAL  CAPACITY  OF  COILS 


175 


end  to  the  other,  is  equal  to  one-third  of  the  static  capacity  of  the  two 
surfaces. 

The  actual  distribution  of  potential  differences  between  the  two  layers 
is  more  nearly  as  shown  in  the  curve  of  Fig.  55;  such  a  distribution  will 
result  in  Cf  being  somewhat  smaller  than  the  value  obtained  in  Eq.  (35). 

Internal  Capacity  of  a  Multiple-layer  Coil. — A  multilayer  coil  con- 
structed with  an  air  space  between  each  layer  may  have  a  comparatively 
small  internal  capacity  in  spite  of  the  fact  that  it  has  10  or  20  layers  of 
winding;  a  short  analysis  shows  that  the  internal  capacity,  as  a  matter 
of  fact,  decreases  with  an  increase  in  the  number  of  layers.  If  the  capacity 


Curve  of  potential  difference 


FIG.  55. — Potential  difference  between  the  two  layers  of  a  two  layer  solenoid  at  high 

frequencies. 


between  two  adjacent  layers  of  the  coil  is  C  then,  the  internal  capacity 
of  a  coil  having  N  layers  is  nearly  C/N,  as  will  be  shown. 

The  electrostatic  field  in  such  a  coil  has  a  distribution  about  as  shown 
in  Fig.  56,  which  represents  a  cross-section  through  the  winding  of  an  air- 
spaced  coil,  having  8  layers.  The  cross-section  is  shown  through  one  side 
of  the  coil  only,  the  other  side  of  the  coil  would  be  similar. 

If  a  voltage  of  E  volts  is  impressed  across  the  terminals  of  the  coil, 
the  voltage  between  adjacent  layers  (at  the  ends  where  the  two  layers 
are  not  connected)  is  E-t-N/2. 

Let  the  normal  geometrical  capacity  between  two  adjacent  layers  be 
C,  this  is  the  capacity  between  two  cylinders,  insulated  from  one  another, 
of  same  dimensions  as  the  layers  of  wire,  and  spaced  by  the  space  between 
the  two  layers  of  wire.  If  the  potential  gradient  between  two  adjacent 
layers  is  assumed  to  vary  uniformly  from  a  maximum  at  one  end  to  zero 
at  the  other  (where  the  two  layers  connect  together)  as  illustrated  in  Fig. 
54  the  energy  between  two  adjacent  layers  is  found  by  integration  to  be 

9  77*2 

^  olvnr     ^s  there  are  N—l  spaces  between  layers  where  this  much  energy 
oiV 

O  J?2(^t 

is  stored  the  total  energy  stored  is  (N—l)  -o2~- 


176 


RESISTANCE— INDUCTANCE— CAPACITY 


[CHAP.  II 


Now  if  we  consider  a  condenser  made  up  of  two  cylinders  having  the 
same  dimensions  and  spacing  as  the  inner  and  outer  layers  of  the  coil,  its 

C 
capacity  would  be  equal  to  ^ — j,  the  thickness  of  dielectric  being  (N—  1) 


Axis  of  th-e  coll 


FIG.  56. — Electric  field  distribution  in  a  multilayer  coil. 

times  as  thick  between  the  innermost  and  outermost  layers  as  it  is  between 
two  adjacent  layers.     The  stored  energy  in  such  a  condenser  would  be 

/    C    \E2 
\~N-l    2' 


But  from  the  previous  paragraph  the  stored  energy  in  the  coil  is  actu- 


ally 


C 


v-Vwr*Fir)  TO- 


INTERNAL  CAPACITY   OF   COILS  177 

from  which  it  follows  that  the  equivalent  internal  capacity  of  a  multilayer 

4  /N—  1\2 
coil  is  equal  to  «  (     „    J   X  the  capacity  between  the  inner  and  outer 

layers,  that  is 


(36) 


where    Co  =  capacity  from  inside  to  outside  layer. 


This  capacity  calculation  neglects  the  "  edge  effect  "  which  may 
increase  the  actual  capacity  over  that  given  by  Eq.  (36)  by  as  much  as 
100  per  cent,  depending  upon  the  shape  of  coil. 

In  calculating  the  separation  of  the  inner  and  outer  layers  the  thick- 
ness of  wire  in  the  intermediate  layers  must  not  be  included;  thus  if  the 
space  between  the  surfaces  of  the  wires  of  two  adjacent  layers  is  0.5  mm. 
and  there  are  ten  layers,  the  space  between  the  inner  and  outer  layers  is 
4.5  mm. 

To  keep  the  capacity  low  it  is  very  necessary  to  keep  the  adjacent 
layers  separated  by  an  appreciable  air  space;  if  this  space  is  too  small 
the  internal  capacity  is  high,  and  the  coil  cannot  be  used  at  as  high  a 
frequency  as  it  is  possible  with  a  coil  of  equal  inductance  having  a  low 
internal  capacity.  If  paper,  oiled  cloth,  wax,  shellac,  or  similar  dielectric 
is  used  to  separate  the  different  layers  there  will  be  an  appreciable  dielec- 
tric loss  in  this  material  (thereby  decreasing  the  efficiency  of  the  coil) 
and  the  internal  capacity  will  be  increased  by  a  factor  equal  to  the  specific 
inductive  capacity  of  the  material  used.  The  bad  effects  of  the  dielectric 
used  between  layers  increase  as  the  amount  of  external  tuning  capacity 
is  decreased. 

It  might  seem  from  the  previous  reasoning  that  a  large  air  space  would 
be  advisable,  but  such  is  not  the  case;  as  the  air  space  is  increased  the 
value  of  inductance  for  a  given  amount  of  wire  is  decreased,  the  ratio  of 
L  to  R  being  greater  the  more  compact  the  coil.  Just  what  air  space  is 
best  the  author  has  not  determined,  but  with  a  coil  made  of  well-stranded 
radio-cable  an  air  space  equal  to  the  diameter  of  the  cable  has  seemed 
suitable. 

Natural  Period  of  Multilayer  Coils.  —  It  is  possible  to  calculate  the 
natural  period  of  the  air-spaced  coils  with  a  fair  degree  of  precision,  per- 
haps within  10  per  cent.  The  capacity  to  be  used  in  making  the  cal- 
culation is  considerably  greater  than  the  value  given  in  Eq.  (36)  because 
of  the  edge  effects  and  a  redistribution  of  potential  in  the  coil.  For 
some  coils  having  a  square  cross-section  of  winding,  outer  radius  about 
30  per  cent  greater  than  the  inner  radius,  the  natural  period  could  be 
determined  by  using  for  L  its  low-frequency  value  and  for  C  just  twice 


178 


RESISTANCE— INDUCTANCE— CAPACITY 


[CHAP.  II 


the  value  calculated  from  Eq.  (36).     As  examples  of  how  well  the  pre- 
diction may  be  made  the  data  for  two  coils  are  given  herewith. 


Coil  No.  1. 

Coil  No.  2. 

Inner  radius  

4.7  cm. 

4.7 

Outer  radius  

5  5  cm. 

6.3 

Axial  length  of  coil 

2  5  cm. 

2.5 

Number  of  layers  

10 

18 

Number  of  turns  (total)  

736 

740 

Air  space  between  layers  
Calculated  capacity  Eq   (36) 

.060  cm. 
14  2X10~12 

.033  cm. 
16.2X10-12 

Low  frequency  inductance  

66.2X10-3 

72.2X10-3 

Calculated  natural  frequency 

1.09X105 

1.11X105 

Measured  natural  frequency  

1.16X105 

1.05X105 

The  natural  period  of  a  multilayer  coil  does  not  increase  rapidly  with 
increase  in  inductance.  Thus  if  the  number  of  layers  in  such  a  coil  is 
doubled,  the  inductance  is  increased  nearly  four  times,  but,  as  the  capacity 
has  been  decreased  to  only  half  its  previous  value,  the  natural  period  has 
been  increased  only  about  40  per  cent. 


CHAPTER  III 
GENERAL  VIEW  OF  RADIO  COMMUNICATION 

Wave  Motion. — Since  the  transmission  of  intelligence  by  radio  is 
brought  about  by  sending  out  so-called  electromagnetic  waves,  and  since 
the  transmission  of  these  waves  is  somewhat  similar  to  that  of  other  kinds 
of  waves,  such  as  light,  sound,  heat,  water,  etc.,  we  will  first  discuss  wave- 
motion  in  a  simple  manner  and  then  apply  this  to  electromagnetic  wave- 
motion. 

In  wave-motion  a  stress  is  transmitted  from  one  point  to  another  in  an 
elastic  medium  without  any  permanent  displacement  of  the  medium  itself 
in  the  direction  in  which  the  stress  is  transmitted.  Thus,  if  a  pebble  be 
dropped  in  a  still  pond  at  A,  an  up-and-down  motion  of  the  water  will 
be  set  up  at  A,  which  will  be  transmitted  to  a  point  at  B,  without  any 
motion  of  the  water  itself  in  the  direction  A-B,  as  evidenced  by  the  fact 
that  a  float  placed  between  A  and  B  will  not  be  displaced  toward  B.1 

In  the  case  of  water  waves  the  pebble  dropped  at  A,  Fig.  1,  will  dis- 
place the  water  directly  under  A  to  the  right  and  left  (in  fact  in  all  direc- 

Pebble  dropped  here 


Surface  of  water 


FIG.  1. — Cross-section  through  surface  of  water,  immediately  after  pebble  has  been 

dropped  at  A. 

tions)  towards  B  and  C,  and  will  produce  the  bulges  at  B  and  C  known 
as  "  crests."  These  bulges  are  due  to  the  fact  that  the  water  displaced  from 
A  tends  to  raise  the  level  all  around  A,  but,  on  account  of  inertia,  this 
cannot  be  done  quickly  enough,  with  the  result  that  the  level  is  raised 
most  at  B  and  C,  and  hence  the  "  crests." 

Considering  the  disturbances  to  the  right  of  A  alone,  the  particles  of 
water  in  the  space  EBD  will,  because  of  gravitational  forces,  seek  the 
average  level  of  the  water,  and,  in  so  doing,  the  bulge  EBD  will  be  made  to 

1  If  a  wave  is  so  high  as  to  "  break,"  i.e.,  an  impure  wave,  this  statement  is  not 
quite  true. 

179 


180  GENERAL  VIEW  OF  RADIO  COMMUNICATION        [CHAP.  Ill 

disappear,  and  a  depression  will  be  created  thereat  due  to  the  fact  that, 
on  account  of  inertia,  the  particles  move  beyond  the  average  "  level  posi- 
tion." Not  only  is  this  the  case,  but  the  particles  to  the  right  of  D  will, 
one  after  the  other,  be  urged,  as  if  elastically  tied  together,  to  perform 
motions  similar  to  those  of  the  particles  within  EBD,  so  that  a  crest  will 
presently  appear  to  the  right  of  D  at  the  same  time  that  a  depression  or 
"  trough  "  is  created  in  the  region  EBD.  The  result  is  that  a  "  trough  " 
and  a  "  crest "  of  a  wave  will  appear  to  move  in  all  directions,  away  from 
the  center  of  disturbance  at  A,  and  with  a  definite  velocity. 

It  must  be  understood  that  the  motion  of  the  particles  is  limited  to 
a  small  region  around  their  positions  of  equilibrium,  and  that  the  wave 
is  propagated  by  imparting  this  motion  to  one  particle  after  the  other, 
while  each  particle,  after  the  disturbance  has  passed,  remains  in  practically 
the  same  position  as  it  originally  occupied. 

An  exact  analysis  of  the  motions  of  the  particles  is  extremely  complex 
and  will  not  be  attempted  here,  but  we  will  give  certain  well-known  ele- 
mentary facts  regarding  it  because  of  the  analogy  between  certain  points 
regarding  water  waves  and  electromagnetic  waves. 

Theory  indicates  and  experiment  corroborates  that  the  water  particles 
within  the  path  of  a  wave  execute  motions  which  are  in  the  simplest  cases 
circular.  Taking  this  case  of  circular  motion  of  the  particles  and  con- 
sidering Fig.  2,  at  C  a  particle  of  water  will  just  be  passing  through  the 

^.  Direction  of  wave^travel 


FIG.  2. — Motion  of  the  water  associated  with  a  wave. 

undisturbed  level  and  moving  with  a  velocity  Vi  in  a  downward  direction, 
while  at  B  another  particle  will  be  moving  with  a  velocity  ¥2  in  a  horizontal 
direction.  Thus,  at  every  point  within  the  volume  of  the  water  involved 
in  the  wave  propagation  each  and  every  particle  will  be  executing  a  cir- 
cular motion  in  a  clockwise  direction,  and  the  formation  of  a  crest  or 
trough  is  the  result  of  various  particles  being,  at  any  time,  at  different 
stages  of  their  circular  motions.  Thus  where  the  particles  are  moving 
horizontally  in  the  same  direction  as  that  in  which  the  wave  is  being  prop- 
agated we  obtain  a  crest,  since  a  large  number  of  particles  are  then  at 
or  near  the  top  of  the  circle;  where  the  particles  are  moving  horizon- 
tally, but  in  a  direction  opposite  to  that  of  the  propagation  of  the  wave  a 


WATER  WAVES 


181 


trough  is  obtained,  since  a  large  number  of  particles  are  then  at  or  near 
the  bottom  of  the  circles  representing  their  respective  motions. 

Consider  now  the  question  of  energy  of  a  particle  at  B ;  it  has  a  velocity 
in  the  direction  of  the  propagation  of  the  wave,  and,  furthermore,  it  is 
displaced  vertically  upward  with  respect  to  the  undisturbed  level  ~of  ~the 
water;  such  a  particle  has  kinetic  energy  in  the  direction  of  the  wave  prop- 
agation plus  potential  energy  with  respect  to  the  average  level.  As  the 
particle  rotates  the  vertical  displacement  from  the  average  level  becomes 
less  and  less  and  so  does  the  component  of  its  velocity  in  the  direction  of 
propagation  of  the  wave;  so  that  when  it  occupies  the  position  B\,  its 
potential  energy  has  become  zero  and  so  has  the  kinetic  energy  in  the 
direction  of  the  wave  propagation.  As  it  moves  still  further  it  suffers 
a  negative  displacement  and  its  velocity  acquires  a  component  parallel 
to  direction  of  propagation  of  the  wave  but  opposite  thereto,  so  that  by 
the  time  it  has  reached  the  point  #2  its  potential  and  kinetic  energy  are 
equal  and  opposite  in  sense  to  those  which  it  had  while  at  the  point  B. 

It  may  be  shown  that  the  potential  energy  of  a  particle  at  any  point 
is  exactly  equal  to  the  kinetic  energy  in  the  direction  of  propagation  of 
the  wave,  provided  that  the  wave  is  not  changing  shape  Because  of 
this  there  must  be  a  fixed  relation  between  the  displacement  of  a  particle 
above  or  below  the  undisturbed  level  of  the  water  and  the  component  of 
the  velocity  of  the  same  particle  parallel  to  the  direction  of  propagation 
of  the  wave. 

Again,  the  total  energy  of  a  particle  of  water  (potential  and  kinetic 
in  the  direction  of  propagation  of  the  wave)  is  continually  changing  as 
the  wave  progresses,  the  particle  in  question  passing  its  energy  along  to 
the  particle  adjacent  to  it,  in  the  direction  of  the  wave  propagation;  this 
transfer  of  energy  from  one  particle 
to  another  is  the  underlying  principle 
of  all  wave  motion  in  water. 

Electromagnetic  Waves.  —  These 
are  due  to  a  disturbance  of  an  electro- 
magnetic nature  and  are  such  that 
they  produce  at  points  all  around  the 
center  of  disturbance  a  varying  mag- 
netic field  and  a  varying  electric  field. 
Thus,  if  a  wire,  such  as  A  B  (Fig.  3) 
in  space,  has  an  alternating  current 
flowing  through  it  for  a  short  interval 
of  time  it  will  set  up  an  alternating  FIG.  3. — Electric  and  magnetic  fields  set 
magnetic  field  and  an  alternating  elec-  UP  at  p  by  wire  A~B- 

trie  field  all  around  itself,  which  fields, 
starting  from  the  vicinity  of  the  conductor,  will  travel  away  from  it  with 


Direction  of 
wave  travel 


182  GENERAL  VIEW  OF  RADIO  COMMUNICATION       [CHAP.  IIJ 

the  velocity  of  light.  In  so  far  as  to  set  up  a  magnetic  field  or  an  electric 
field  requires  energy,  it  follows  that  a  certain  amount  of  energy  must 
be  detached  from  that  available  in  the  conductor  in  order  that  the  electro- 
magnetic disturbance  be  created  at  all.  Thus  energy  is  said  to  be  "  radi- 
ated," and  the  phenomenon  itself  is  known  as  "  electromagnetic  radiation  " 
or  simply  "  radiation." 

The  electric  and  magnetic  fields  of  radiation,  at  any  one  point,  are  in 
space  quadrature,  but  they  are  at  all  times  in  time  phase  with  each  other. 
And  not  only  is  this  the  case,  but  there  is  a  fixed  relation  between  the 
values  of  the  electric  and  magnetic  fields  at  any  instant;  this  relation  is 
based  upon  the  fact  that,  in  order  for  the  wave  of  electromagnetic  dis- 
turbance to  exist  in  space  the  energy,  per  unit  volume  of  the  medium, 
possessed  by  the  electric  field,  must  be  equal  to  that  possessed  by  the 
magnetic  field.  Thus  the  total  amount  of  energy  at  any  one  point  and 
instant  is  equal  to  twice  that  possessed  by  either  field.  The  value  of  this 
energy  is  changing  as  the  intensity  of  the  two  fields  changes,  and,  as  a 
tnatter  of  fact,  the  energy  is  being  transferred  from  one  point  to  the  next 
by  the  elastic  properties  of  the  medium  in  which  the  disturbance  travels. 
{The  discussion  of  electromagnetic  waves  here  given  uses  the  idea  of  a 
medium  as  a  carrier  of  the  disturbance;  to  make  this  medium  fill  the  role 
it  is  supposed  to  play  in  modern  electron  theory  it  must  be  considered  as 
the  superimposed  electric  fields  of  all  the  electric  charges  in  the  universe.) 
The  reader  will  note  that  this  is  analogous  to  the  case  of  water  waves, 
where,  at  any  point,  the  potential  energy  per  unit  volume  is  equal  to  the 
kinetic  energy  in  the  direction  of  propagation  of  the  wave,  and  the  total 
amount  of  energy  is  transferred  from  point  to  point  within  the  medium, 
thus  bringing  about  the  conditions  of  wave  motion. 

In  the  case  of  water  waves  or  electromagnetic  waves  if,  at  any  point, 
some  of  the  energy  in  one  of  the  two  forms  (potential  and  kinetic  for  water, 
and  electric  and  magnetic  for  electromagnetic  waves)  be  withdrawn  from 
the  space  wherein  the  wave  exists,  part  of  the  energy  in  the  other  form 
will  be  immediately  transformed  into  the  former,  with  the  result  that 
equality  of  the  two  forms  of  energy  will  still  apply,  but  the  crests  and 
troughs  of  the  water  waves  will  not  be  as  high  as  before,  nor  will  the 
amplitude  of  the  electric  and  magnetic  field  intensities  be  as  large  as 
before. 

It  must  be  noted  that  this  phenomenon  is  different  from  that  of  the 
creation  of  the  ordinary  magnetic  or  electric  field  around  the  conductor, 
which  field  never  reaches  far  from  the  conductor  (with  appreciable  inten- 
sity), and  does  not  represent  energy  permanently  removed  from  the  con- 
ductor, since  the  variation  of  this  field  induces  electromotive  forces  in 
the  conductor,  and  thus  an  exchange  of  energy  is  kept  up  between  the  con- 
ductor and  the  field.  This  field  is  known  as  "  induction  field  "  to  dis- 


ELECTROMAGNETIC  WAVES 


183 


tinguish  it  from  the  "  radiation  field,"  wherein  we  arc  more  vitally  inter- 
ested. 

In  the  case  of  the  "  radiation  field  "  at  any  point  such  as  P,  Fig.  3, 
the  magnetic  field  would  act  along  PD  and  the  electric  field  along  the 
line  PC  at  right  angles  to  PD,  while  the  disturbance  would  traveHn-the 
direction  of  the  arrow  at  right  angles  to  both  PC  and  PD.  Both  fields 
change  in  value  and  in  direction  in  accordance  with  the  variations  of  the 
current  in  the  conductor  producing  the  disturbance;  if  this  is  harmonic 
the  two  fields  will  change  harmonically.  At  some  other  point  such  as 
P\  the  disturbance  will  arrive  a  little  later  than  at  P  with  the  result  that 
the  fields  at  P  and  P\  are  out  of  phase,  the  phase  difference  depending 
upon  the  frequency  and  the  velocity  of  propagation. 

Considering  one  of  the  two  fields,  say  the  magnetic,  and  plotting  the 
instantaneous  value  of  the  field  against  distance  from  the  conductor  of 
Fig.  3  we  would  obtain  a  curve  such  as  A  in  Fig.  4,  which  applies  to  any 


FIG.  4. — Illustrating  one  "wave  length." 

particular  instant  of  time.  A  little  later  the  plot  of  the  field  would  be 
given  by  the  curve  B  in  so  far  as  the  intensity  at  every  point  in  space 
will  by  then  have  varied  so  as  to  make  the  new  curve  possible.  The  wave 
has  thus  been  shifted  in  the  direction  of  the  arrow  by  the  amount  C.  If 
we  plot  a  number  of  such  curves  we  would  find  that  the  wave  has  shifted 
the  distance  X,  by  the  time  the  magnetic  field  has  completed  a  cycle.  We 
thus  have  that  if: 

X  =  wave  length  in  cms. ; 

v  =  velocity  of  propagation  of  wave  in  cms./sec.; 

/=  frequency  of  the  field  in  cycles/sec.; 


Time  for  one  cycle =7- 


and 


or 


(1) 


which  is  the  fundamental  relation  for  any  wave  propagation. 


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GENERAL  VIEW  OF  RADIO  COMMUNICATION       [CHAP.  Ill 


Velocity  of  Propagation.  —  For  electromagnetic  waves  this  is  equal, 
as  already  stated,  to  the  velocity  of  light  when  the  wave  is  being 
propagated  through  air,  but  in  general,  for  any  medium,  we  have  the 
following: 

V  =  velocity  of  light  in  vacuum; 

v  =  velocity  of  propagation  of  wave  in  any  homogeneous  medium; 

/t  =  magnetic  permeability  of  the  medium; 

k  =  specific  inductive  capacity  (inductivity  of  medium). 

..........    (2) 


since  for  air  ju  =  1  and  k  =  1,  v  =  V. 

This  formula  neglects  any  possible  effect  on  the  velocity  of  propagation, 
of  any  losses  occurring  in  the  medium,  due  to  conduction,  hysteresis  or 
dielectric  losses,  etc. 

As  shown  by  Eq.  (2)  the  velocity  of  propagation  is  dependent  only 
upon  the  nature  of  the  medium  through  which  the  wave  is  moving  (its 
magnetic  and  electric  constants),  and  is  not  effected  by  the  wave  length 
or  by  the  frequency.  Thus,  in  considering  the  conductor  AB  of  Fig.  5, 


Radiation  from  a  ships 
antenna  near  a  shore 


On  striking  the  mountain  at  A,  part  of  the  energy 
is  reflected  and  part  transmitted  into  the  earth, 
with  low  velocity  and  high  attenuation 

FIG.  5.  —  Energy  radiated  from  an  antenna  is  subject  to  the  same  laws  of  reflection, 
refraction,  and  absorption  as  ordinary  light. 

as  the  source  of  an  electromagnetic  wave,  this  wave  would  spread  out  in 
the  direction  of  C  with  the  velocity  of  light,  but  in  passing  through  the 
mountain  to  the  left  the  velocity  would  be  lower.  If  instead  of  a  mountain 
we  should  have  a  sheet  of  metal  for  which  the  value  of  k  is  infinitely  large, 
then: 


that  is,  the  wave  would  stop  completely;  1  the  energy  of  the  wave  would 

1  This  conclusion  is  not  strictly  accurate;  the  velocity  hi  such  a  case  would  be  much 
less  than  the  velocity  of  light,  but  would  not  be  zero.  The  discrepancy  arises  from 
the  very  elementary  viewpoint  from  which  wave  motion  is  here  considered. 


TYPES  OF  WAVES  USED  IN  RADIO  185 

be  partly  absorbed  by  the  metal  in  the  production  of  electric  currents 
therein  and  partly  reflected  back.  Not  only  would  the  wave  travel  in 
the  direction  C  and  Z>,  but  in  every  other  direction,  up  into  the  air  ui 
the  direction  of  F  and  J,  and  into  the  water  and  earth  in  the  direction,  of 
L  and  G. 

As  the  wave  travels  outward  some  cf  the  energy  is  absorbed  by  the 
medium  if  this  be  other  than  air;  even  in  air  there  is  some  absorption  of 
energy,  especially  in  daylight,  due  to  ionization  making  it  partially  con- 
ducting; and,  in  other  materials,  losses  are  produced  by  the  varying  electric 
and  magnetic  fields  which  absorb  energy  from  the  wave  itself.  The  result 
of  this  is,  of  course,  that  a  distance  is  soon  reached  where  practically 
no  more  energy  is  available  and  the  disturbance  ceases  to  be  communi- 
cated (in  measurable  intensity)  any  further.  The  distance  over  which 
a  certain  amount  of  energy  will  travel  through  air,  even  in  daylight,  before 
being  absorbed  is,  of  course,  much  greater  than  through  solid  matter  or 
even  liquid,  due  to  the  fact  that  the  losses  (eddy  currents,  magnetic  hys- 
teresis, dielectric  hysteresis,  etc.)  are  greater  than  in  air. 

In  cases  where  a  wave  travels  in  the  direction  of  C  (Fig.  5)  through 
the  air  there  are  parts  of  the  wave  which  are  close  to  the  water  (or  earth, 
as  the  case  may  be) ;  it  follows  (from  Eq.  (2))  that  these  parts  cannot  travel 
as  fast  as  the  rest  and,  therefore,  lag  behind,  and  the  surface  bounding 
the  advancing  wave  in  the  air  is  distorted,  the  parts  nearer  the  water 
reaching  a  given  distance  from  the  transmitting  station  later  than  some 
other  part  of  the  wave  which  is  more  distant  from  the  absorbing  medium 
(earth,  or  sea).  This  makes  the  wave  front  "  lean  over  "  as  the  wave 
advances. 

Various  Types  of  Waves. — While  the  discussion  given  above  has  been 
of  a  purely  theoretical  nature,  the  reader  will  understand  that  in  radio 
communication  it  is  by  means  of  electromagnetic  waves  that  the  trans- 
mission of  intelligence  is  effected,  and  that  these  waves  are  produced  by 
sending  suitable  currents  through  one  or  more  suitably  arranged  wires 
forming  what  is  known  as  the  "  antenna,"  or  "  radiating  system."  Thus, 
an  operator  at  the  transmitting  station  will,  on  depressing  a  key,  send 
through  the  radiating  system  a  current  which  will  start  an  electromagnetic 
disturbance  and  cause  an  electromagnetic  wave  to  be  "  radiated."  Such 
a  wave  will  travel  in  air  with  the  velocity  of  light  and  produce  all  around 
the  radiating  system  an  alternating  electric  field  and  an  alternating  mag- 
netic field  which  may  be  made,  at  a  suitable  receiving  station,  to  actuate 
suitable  instruments  for  the  detection  of  such  a  wave;  and  in  this  manner 
the  pressing  of  the  key  at  the  transmitting  station  will  be  signaled  to  the 
receiving  station.  The  details  of  a  transmitting  and  receiving  set  are 
given  later  on  in  this  chapter  and  further  discussed  in  other  chapters. 

Various  types  of  electromagnetic  waves  may  be  sent  out  by  a  radiating 


186 


GENERAL  VIEW   OF  RADIO   COMMUNICATION        [CHAP.  Ill 


system,  depending  upon  the  kind  of  current  used  to  produce  the  waves. 
Thus,  two  systems  of  radio  transmission  are  at  present  in  use,  which  are 
distinguished  by  two  different  kinds  of  waves.  These  are  known  as 
"  Undamped  wave  "  and  "  Damped  wave  "  systems.  In  the  former  the 
current  which  is  made  to  flow  through  the  antenna  when  the  operator 
presses  his  key  is  an  alternating  current  of  constant  amplitude  (undamped), 
so  that  the  waves  produced  are  such  that  at  any  point  in  space  the  maxi- 
mum value  of  the  intensity  of  the  electric  field  and  of  the  magnetic  field 
is  constant  as  long  as  the  wave  is  passing. 

In  the  "  Damped  wave  "  system,  on  the  other  hand,  the  current  sent 
into  the  antenna  at  the  pressing  of  the  key  may  be  represented  by  the 
graph  of  Fig.  6,  from  which  it  may  be  seen  that  the  waves  are  sent  out  in 
"  trains,"  each  train  consisting  of  a  number  of  waves  of  diminishing  ampli- 
tude; so  that  at  any  point  in  space  the  maximum  value  of  the  intensity 
of  the  electric  and  magnetic  fields  will  not  be  constant  but  will  be  damped. 


Frequency  of  wave  trains  fixed 
by  time  from  C  to  D 


Time- 


Frequency  of  antenna  current 
A    B      fixed  by  time  from  A  to  B 


FIG.  G. — Type  of  antenna  current  in  a  spark-  station. 


The  frequency  used  in  radio  transmission  either  for  the  undamped  or 
for  the  damped  waves  is  very  high,  because  more  power  is  radiated  by 
an  antenna  at  high  than  at  low  frequencies.  If  the  currents  used  for  radio 
transmission  were  passed  through  the  coil  of  a  telephone  receiver,  no  audible 
sound  would  be  produced,  because  the  diaphragm  could  not  vibrate  at 
such  a  high  frequency  and,  even  if  it  did  vibrate,  the  human  ear  would  be 
unable  to  detect  any  sound.  Such  frequencies  are  said  to  be  beyond 
the  limit  of  audibility  and  are  known  as  "  radio-frequencies/'  while  the 
frequencies  which  may  be  "  heard  "  are  known  as  "  audio-frequencies." 
There  is  no  distinct  line  of  demarkation  between  these  two  frequencies, 
but  it  may  be  stated  in  a  broad  manner  that  the  audio-frequency  range 
is  between  40  and  10,000  cycles  per  second  while  the  radio-frequency 
range  is  between  10,000  and  3,000,000  cycles  per  second  or  over. 

In  view  of  the  fact  that  in  radio-transmission  the  frequency  is  a  large 
number  it  is  more  customary  to  speak  of  the  wave-length  of  a  wave  rather 
than  of  its  frequency.  The  wave-length  is  generally  expressed  in  meters, 
Eq.  (1)  of  p.  183  states 


DAMPED   WAVES  187 


or  X  =  T. 

If  v  is  in  meters  per  sec.  and  /  in  cycles  per  sec.,  then  X  is  in  meters._ 

Since  v  =  3  X  108  meters  per  second  the  wave-length   for  10,000  and 
3,000,000  cycles  per  sec.  may  easily  be  found  to  be 


X  =  =  30,000  meters 

oy  irjg 

and  X  =  -  =  100  meters. 


Thus  the  wave-length  range  for  radio-transmission  is  30,000  to  100  meters. 
The  wave-lengths  which  have  been  found  most  suitable  for  various 
kinds  of  work  at  present  are  as  follows: 

10,000  to  20,000  meters  for  trans-oceanic  comm     ication; 
1000  to  10,000  meters  for  distances  between  30C     id  1000  miles; 
450  to  1000  meters  for  distances  between  50  an        0  miles; 
Less  than  450  meters  for  short  distances.  h*sr 

Spark  Telegraphy.  —  In  the  past  the  production  of  high-frequency 
currents  required  for  radio-transmission  has  been  largely  accomplished 
by  utilizing  the  high-frequency  oscillatory  discharge  of  a  condenser  associ- 
ated with  a  suitable  radiating  circuit.  As  the  energy  initially  stored  in 
the  condenser  is  dissipated  in  the  primary  circuit  and  associated  circuits, 
the  condenser  must  again  be  charged  and  the  cycle  repeated.  In  order 
that  the  condenser  may  be  charged  to  the  high  potentials  required  for 
large  energy  storage,  and  to  permit  its  discharge  in  a  suitable  closed  cir- 
cuit of  low  resistance,  that  circuit  must  contain  an  element  whose  resistance 
is  very  high  during  the  charging  period,  but  whose  resistance  decreases 
instantaneously  when  the  condenser  discharges  and  remains  at  a  very  low 
value  during  the  period  of  discharge.  This  requirement  is  fulfilled  by 
the  ordinary  spark  gap,  the  resistance  of  the  gap  being  very  high  before 
breakdown  occurs,  but  decreasing  to  a  very  small  value  when  the  gap  has 
broken  down  under  the  increasing  potential  impressed  across  its  terminals. 
The  spark  gap  and  spark  are  thus  essential  to  transmitters  generating 
high-frequency  oscillations  by  means  of  condenser  discharges,  and  this 
system  is  therefore  designated  as  "  spark  telegraphy."  The  connections 
of  such  a  transmitter  are  indicated  in  Fig.  7. 

The  detailed  action  of  this  transmitter  is  discussed  in  Chapter  V,  and 
is  therefore  omitted  here.  By  operating  the  switch,  or  key,  in  the  alter- 
nator circuit,  the  radiated  energy  may  be  interrupted,  and  if  this  is  done 
in  accordance  with  a  prearranged  code,  signals  may  be  transmitted  to 


188 


GENERAL  VIEW  OF  RADIO  COMMUNICATION       [CHAP.  Ill 


the  distant  receiving  station.  For  low-powered  stations  a  storage  battery 
^nd  small  induction  coil  take  the  place  of  the  alternator  and  transformer. 

Spark  telegraphy  is  distinguished  by  the  fact  that  the  high-frequency 
oscillations  are  damped,  successive  oscillations  decreasing  in  amplitude 
to  zero.  The  series  of  oscillations  occurring  with  each  discharge  con- 
stitute a  train  of  waves,  and  the  number  of  such  trains  produced  per 
second  is  known  as  the  group,  or  wave-train,  frequency,  which  in  practice 
may  be  from  100  to  1000  per  second. 

Continuous  Wave  Telegraphy. — Transmission  of  signals  by  means  of 
undamped  high-frequency  oscillations  possesses  several  advantages,  and 
this  system  is  rapidly  superseding  the  spark  system  for  large  stations  of 


Key 


Antenna 


Oscillation  transformer,, 

transfers  high  frequency 

energy  from  closed 

circuit  to  antenna 


Low  frequency  iron  core 

transformer  increases 

alternator  voltage 

about  100  times 


Ground 


FIG.  7. — Typical  connection  scheme  of  a  spark  transmitting  station. 


high  power,  long  range,  and  utilizing  the  lower  radio  frequencies.     Chief 
among  the  advantages  obtained  are: 

1.  A  given  amount  of  power  in  the  form  of  a  continuous  wave  signal 

will  in  general  give  a  louder  response  in  the  telephone  receivers 
than  would  the  same  amount  of  power  in  the  form  of  spark 
signal  (due  to  the  characteristics  of  the  receiving  circuits). 

2.  Due  to  the  scheme  of  reception  the  interference  between  stations 

is  much  less  for  continuous  waves  than  for  spark  waves. 
8.  To  radiate  a  given  amount  of  power  requires  less  voltage  on 
the  antennae  (hence  cheaper  antennae  construction)  for  con- 
tinuous waves  than  for  spark  waves,  due  to  the  fact  that  in 
one  case  energy  is  being  continuously  radiated,  and  in  the 
other  case  for  a  small  fraction  of  the  time  only. 

Undamped  oscillations  may  be  generated  by  the  high-frequency  alter- 
nator (Alexanderson  and  Goldschmidt  types),  the  Poulsen  arc,  a  scheme 
utilizing  saturated  iron  cores,  or  the  oscillating  vacuum  tube;  all  act  to 
send  through  the  antenna  circuit  an  undamped  high-frequency  current. 
This  current  may  be  varied  by  means  of  a  key,  which  may  interrupt  the 
supply  to  the  antennae,  or  change  the  frequency  of  the  oscillations 


Antenna 


CONTINUOUS  WAVES  189 

slightly  by  varying  the  inductance  of  the  circuit.  Both  methods  are 
not  equally  applicable  to  all  means  of  generation.  (See  Chapter  VII.) 

Radiotelephony. — The  war  very  greatly  stimulated  the  development 
of  the  radio  telephone  because  of  the  necessity  which  arose  of  providing 
a  rapid  and  direct  communication  between  aeroplanes  and  the  ground  at 
all  times,  vessels  of  a  group  of  submarine  chasers,  etc.  This  need  could 
be  fulfilled  satisfactorily  only  by  the  radio  telephone,  and  its  development 
on  a  practical  basis  was  accordingly  greatly  accelerated.  This  refers  par- 
ticularly to  small  power  sets  of  low  range.  In  1917  radiophone  messages 
had  been  successfully  transmitted  to  land  stations  at  Honolulu  and  Paris 
from  Arlington,  U.  S.  A.,  and  in  1919  successful  radiophone  communica- 
tion was  established  between  Washington  and  steamships  while  the  latter 

were  still  several   hundred  miles  at  sea,  ^ 

and  also  between  ground  stations  and 
flying  aeroplanes  many  miles  distant. 

To  transmit  radiophone  messages 
between  distant  stations  requires  the 
same  equipment  utilized  in  continuous 
wave  telegraphy,  i.e.,  a  generator  of  un- 
damped  oscillations  and  associated  an-  /  the  high  frequency  power 

tenna,      plus    a      "  modulating  "     element          @       High  frequency  generator 

whose  function  it  is  to  vary  the  amplitude 
of  this  high-frequency  current  in  accord- 

ance  with  the  sound  waves  of  the  voice,  ^  . 

_'  .       .        FIG.    8. — Illustrating    possibility    of 

Fig.  8  shows  the  fundamental  idea  clearly;      varying  the  ampiitude  of  the  high 

the     amplitude     of    the    high-frequency       frequency  current  in  an  antenna, 
current     flowing    in    the    antenna    (and       b7  the  voice  waves, 
therefore   the  power  radiated)  is  varied 

in  accordance  with  variations  in  the  transmitter  resistance,  which  in  turn 
is  dependent  on  the  sound  vibrations,  as  sent  out  by  the  speaker,  impinging 
on  its  diaphragm. 

The  problems  of  radiotelephony  are  those  met  in  connection  with  the 
generation  of  undamped  high-frequency  alternating  currents  and  the 
modulation  of  their  amplitude  in  accordance  with  speech  waves. 

Receiving  Station. — The  receiving  station  consists  of  an  antenna  and 
associated  equipment,  which  may  be  tuned  so  as  to  absorb  a  maximum 
amount  of  the  energy  of  the  incident  electromagnetic  waves  radiated  by 
the  transmitting  station. 

Coupled  to  the  antenna  is  a  secondary  circuit,  also  tuned  to  the  incom- 
ing wave  length,  and  to  which  is  connected  the  rectifier  and  phones  required 
to  make  the  incoming  signal  audible  to  the  receiving  operator.  The  com- 
plete connections  of  a  receiving  station,  consisting  of  the  foregoing  elements, 
are  shown  in  Fig.  9. 


190  GENERAL  VIEW  OF  RADIO   COMMUNICATION       [CHAP.  Ill 

As  previously  mentioned,  by  tuning  the  antenna  and  secondary  cir- 
cuits to  the  frequency  of  the  received  oscillations,  using  the  variable  con- 
denser or  inductance,  or  both,  as  required,  a  maximum  amount  of  the 
power  transmitted  by  the  incident  electromagnetic  waves,  will  be  trans- 
ferred to  the  receiving  circuits.  Under  these  conditions  a  maximum 
current  flows  in  the  secondary  circuit  and  hence  a  maximum  voltage  will 
exist  across  the  terminals  of  the  inductance  (£2). 

The  detecting  circuit,  consisting  of  the  rectifier  and  phones,  and  con- 
nected across  the  coil,  will  thus  have  a  maximum  flow  of  current  through 

it.     The  rectifier  so  acts  as  to 
permit  current  to  flow  in  only 
_      .  _,  one  direction,  having  a  much 

Detector  or  rectifier.,  J 

permits  flow  of  current       higher  resistance  in  one  direc- 

in  one  direction  only  .  ,  .  . 

tion  than  in  the  other.     For 

Telephone  receivers  One    gTGUp    of    WaVCS,     a     Uni- 

directional  pulse  of  current  is 
thus  sent  through  the  phones. 
FIG.  9.— Typical  receiving  station  circuit,  for     Therefore,  as  the  wave  trains 
reception  cf  spark  signals.  strike  the   antennae,  pulses  of 

current     flow     through     the 

phones,  the  diaphragm  of  which  is  thus  impulsed  at  group  frequency. 
These  pulses,  following  one  another  with  the  same  rapidity  as  the 
sparks  occur  at  the  transmitting  station,  give  in  the  telephone  a  musical 
note,  the  duration  of  which  depends  upon  how  long  the  operator  at  the 
transmitting  station  holds  down  his  sending  key. 

The  receiving  circuit  described  above  will  receive  only  damped  wave 
signals  or  radiotelephone  messages.  For  undamped  wave  signal  reception 
a  special  receiver  is  necessary,  as  the  pulse  effect  obtained  with  damped 
waves  is  absent,  and  radio  frequencies  are  too  high  to  be  able  to  move 
the  phone  diaphragm,  due  to  its  inertia.  Even  if  an  appreciable  move- 
ment of  the  diaphragm  were  obtained,  no  signaling  could  be  accomplished, 
as  the  radio  frequencies  used  are  above  audibility. 

The  reception  of  undamped  wave  signals  is  at  the  present  time  most 
successfully  accomplished  by  producing  "  beats  "  of  audible  frequency, 
as  is  done  by  the  "  heterodyne  "  receiver,  embodying  a  local  high-frequency 
generator  combined  with  a  rectifying  device.  The  dual  functions  of  this 
receiver  are  admirably  fulfilled  by  the  vacuum  tube  and  its  associated 
circuits  as  illustrated  in  Fig.  127,  p.  514.  Various  arrangements,  as 
described  in  Chapter  VIII,  have  been  used  to  mechanically  break 
up  the  steady,  high-frequency  oscillations  into  groups  occurring  at 
audio  frequency,  the  most  prominent  of  these  devices  being  the 
Goldschmidt  tone  wheel.  Due  to  its  greater  selectivity,  simplicity,  and 
sensitiveness,  the  heterodyne  receiver  .using  a  vacuum  tube  as  the  gener- 
ating and  detecting  element  is  rapidly  superseding  these  earlier  forms. 


SELECTIVITY  AND  INTERFERENCE  191 

Selection  of  the  Desired  Signal. — Since  a  number  of  other  transmitting 
stations,  within  range,  may  be  sending,  simultaneously  with  the  station 
the  signals  of  which  it  is  desired  to  receive,  the  receiving  circuit  must 
possess  the  ability  to  "  tune  out  "  these  other  signals  which  are  reaching 
the  station,  and  "  select "  that  signal  sent  by  the  transmitting  station 
with  which  it  is  desired  to  communicate.  Without  this  means  of  selecting 
a  desired  signal  to  the  exclusion  of  others  which  would  be  received  at  the 
same  time,  the  operator  would  hear  only  a  confusion  of  dots  and  dashes 
sent  by  all  the  different  stations. 

It  has  already  been  shown  in  Chapter  I  how  the  current  in  a  circuit 
containing  inductance,  capacity,  and  resistance,  is  made  a  maximum, 
when  the  natural  frequency  of  the  circuit  is  adjusted  to  coincide  with 
the  frequency  of  the  impressed  e.m.f.  This  effect  is  graphically  indicated 
by  the  resonance  curve  plotted  in  Fig.  53,  Chapter  I.  The  adjustment  of 
the  antenna  circuit  to  the  frequency  of  the  incoming  oscillations,  repre- 
sents an  analogous  operation,  and  is  called  "  tuning  "  the  antenna  cir- 
cuit. Thus,  by  tuning  to  the  frequency  of  the  signals  which  it  is  desired 
to  receive,  the  current  due  to  this  signal  is  made  the  maximum,  while 
the  currents  flowing  in  the  antenna  due  to  signals  sent  out  from  other 
stations,  which  have  a  frequency  different  than  that  of  the  signal  being 
received,  are  relatively  much  weaker. 

The  secondary  circuit,  being  also  "  tuned  "  to  the  frequency  of  the 
signal  desired,  will  still  further  diminish  those  currents  due  to  the  inter- 
fering transmitting  stations,  while  the  current  of  signal  frequency  will  be 
a  maximum.  This,  as  pointed  out  previously,  results  in  a  maximum 
voltage  being  impressed  on  the  detector-phone  circuit,  resulting  in  maxi- 
mum rectified  current  in  that  circuit,  and  maximum  strength  of  the  signal 
which  it  is  desired  to  receive. 

Interference. — The  confusing  and  clouding  of  the  desired  signal  due 
to  signals  simultaneously  received  from  undesired  stations  within  whose 
range  the  receiving  station  is  operating,  is  called  "  interference/'  and,  as 
pointed  out,  this  "  interference  "  is  eliminated  in  practice  by  careful 
tuning  of  the  several  circuits.  Several  factors  determine  the  extent  of 
this  interference  and  the  completeness  with  which  it  may  be  tuned  out. 

First.  The  amount  by  which  the  radio  frequency  of  the  desired  signal 
differs  from  the  radio  frequencies  at  which  the  interfering  stations  are 
sending.  If  they  are  widely  different,  tuning  will  effectively  eliminate 
the  interfering  signals.  Where  the  frequencies  are  nearly  the  same  or 
are  the  same,  it  is  impossible  to  tune  them  out  completely  and  differenti- 
ation must  then  be  accomplished  by  means  of  the  characteristics  mentioned 
below;  viz.,  relative  loudness,  pitch  of  the  signal  note,  or  by  using  a 
directional  antenna. 

Second.  The  relative  strength  of  the  desired  signal  and  signals  received 
from  interfering  stations.  When  the  interfering  station  is  relatively 


192  GENERAL  VIEW  OF  RADIO  COMMUNICATION         [CHAP.  Ill 

close  to  the  receiving  station,  thus  producing  heavy  interference,  the 
reception  of  the  desired  signal  may  be  extremely  difficult,  even  though 
the  frequency  of  the  interfering  station  may  differ  to  a  considerable  extent 
from  that  for  which  the  circuit  is  tuned. 

Third.  The  pitch  of  the  signal  note  heard  in  the  phones,  as  deter- 
mined by  the  group  frequency  of  the  several  transmitters  in  operation. 
If  the  pitch  note  of  the  desired  signal  is  distinctive,  as  compared  to  the 
notes  of  the  interfering  stations,  then  the  signals  may  be  read  "  through 
the  interference  "  and  the  message  obtained.  This  would  be  the  only 
feature  whereby  the  signal  could  be  distinguished  if  the  radio  frequencies 
of  the  several  stations  agreed  closely  and  the  interfering  stations  were 
relatively  close  to  the  receiving  station. 

Fourth.  If  the  transmitting  stations  are  in  different  directions  from 
the  receiving  station,  the  directional  properties  of  a  coil  antenna  may 
be  used  to  eliminate  interference;  this  property  of  the  coil  antenna  is 
described  in  pages  766  et  seq. 

Simultaneous  Sending  and  Receiving. — In  the  development  of  radio- 
telephony  one  of  the  problems  to  be  met  was  the  elimination  of  the  necessity 
of  any  action  on  the  part  of  the  subscriber,  required  to  change  over  from 
sending  to  receiving  -and  vice  versa.  A  simple  method  of  duplex  oper- 
ation, as  described  by  E.  F.  W.  Alexanderson,1  is  included  at  this  point 
to  show  the  possibility  of  using  radio  communication  in  exactly  the  same 
way  ordinary  telephone  communication  is  carried  on. 

The  arrangement  utilizes  separate  sending  and  receiving  antennae, 
located  sufficiently  far  apart,  and  having  natural  frequencies  differing 
from  one  another  a  sufficient  amount,  to  make  the  operation  stable.  The 
general  arrangement  is  indicated  in  Fig.  10,  wherein  it  will  be  noted  that 
the  radio  system  has  the  same  relation  to  the  subscriber  as  the  toll  line 
in  wire  telephoney. 

A  radio  telephone  current  set  up  in  the  receiving  antenna,  due  to 
excitation  from  the  distant  transmitter,  is  transformed  into  a  current  flow- 
ing in  the  closed  circuit  between  the  subscriber's  instrument  and  the  trans- 
mitting station.  The  same  path  is  followed  by  a  telephone  current  origi- 
nating in  the  local  subscriber's  station.  Therefore  the  current  set  up  in 
the  local  receiving  station,  due  to  a  signal  from  the  distant  transmitting 
station,  will  be  retransmitted  by  the  local  sending  station  in  the  same 
way  as  the  current  set  up  by  the  local  subscriber  station, '.and  consequently, 
both  sides  of  the  conversation  are  transmitted  by  each  station  and  could 
be  overheard  by  a  third  party  tuned  to  either  of  the  two  wave  lengths  used. 

If  the  amplification  of  the  received  signal  were  made  too  great,  so 
that  the  telephone  current  set  up  by  the  speaker  came  back  to  him  in 
intensified  form,  a  cumulative  reflective  action  would  be  created,  which 

1  E.  F.  W.  Alexanderson,  "  Simultaneous  Sending  and  Receiving,"  Proceedings  of 
the  Institute  of  Radio  Engineers,  August,  1919. 


ATMOSPHERIC  DISTURBANCES 


193 


would  result  in  self-exciting  inarticulate  oscillations  being  set  up.  Any 
trouble  from  this  source  may  be  effectively  eliminated,  however,  by  keep- 
ing the  amplification  within  a  certain  critical  value,  whereby  the  retrans- 
mission becomes  effectively  damped. 

Static,  Strays,  or  X's. — In  addition  to  the  interference  which  may  be 
produced  by  the  operation  of  other  transmitting  stations  as  described 
above,  natural  electrical  disturbances  occurring  in  the  atmosphere  also 
cause  serious  interference  in  the  reception  of  signals.  These  disturbances 
set  up  electromagnetic  waves,  which,  upon  striking  the  receiving  antennae, 
set  up  troublesome,  interfering  sounds  in  the  phones,  to  which  the  name 


Transmitting 
antenna 


Scheme  for  two  way 
radio  telephone 


The  two  antennae  are  several 
miles  apart  and  are  tuned 
to  different  wave  lengths 


frequency  (Q) 


generator. 


Amplifier 

jn,dt 


CI  — 


J-M/J-2A& 


Subscribers 
phone 


T¥ 


Local 
Exchange 


Transmitting  antenna  at  distant  station 
tuned  to  same  wave  length  as  this 
receLving  antenna,  and  vica  versa 


FIG.  10. — Modern  scheme  for  two-way  radio  telephone  communication. 

static,  strays,  or  X's  have  been  variously  applied.     These  strays  have  beer 
arbitrarily  placed  by  De  Groot 1  in  the  following  classes: 

(a)  Loud  and  sudden   clicks.     These  do  not  interfere  seriously 
when  no  other  interference  effects  are  present,  and  have  been 
shown  to  originate  in  nearby  or  distant  lightning  discharges. 

(b)  A  constant  hissing  noise  in  the  receivers,  giving  the  impression 

of  a  softly  falling  rain,  of  the  noise  of  water  running  through 
tubes.  This  type  occurs  occasionally  when  there  are  dark, 
low-lying  electrically  charged  clouds  near  the  antennae,  and 
is  apparently  caused  by  intermittent,  unidirectional  currents 
in  the  antennae.  Charges  of  electricity  come  upon  the  antennae 


1  "On  the  Nature  and 


of  Strays."     Proc.  I.  R.  E.,  April,  1917. 


194  GENERAL  VIEW  OF  RADIO  COMMUNICATION        [CHAP.  Ill 

from  the   atmosphere    through  direct  physical  contact,  and 
thence  discharge  to  ground,  producing  a  current, 
(c)  This  type  produces  a  continuous  rattling  noise  in  the  telephone, 
something  like  the  tumbling  down  of  a  brick  wall,  and  are 
usually  present  to  a  greater  or  less  extent.     In  the  tropics, 
where  interference  from  static  is  especially  severe,  this  type 
predominates,   and   is   always   present.     It   is   frequently   so 
severe  as  to  prevent  entirely  the  reception  of  signals.     Strays 
are 'most  prominent  at  night,  but  are  not  so  troublesome  at 
that  time,  due  to  the  great  increase  of  signal  strength. 
Their  intensity  and  character  is  a  function  of  the  time  of  day,  the  sea- 
son of  the  year  and  the  location  of  the  station;   thus,  in  the  tropics,  De 
Groot  found  the  most  unfavorable  time  was  that  of  the  trade  wind.     In 
general,  the  worst  trouble  is  experienced  when  the  sun's  altitude  is  highest. 
Their  intensity  is  probably  dependent  somewhat  on  the  dryness  of  the 
air  and  wind   conditions,   increasing  dryness  and  high-wind  velocities 
increasing  interference  due  to  this  cause. 

Elimination  of  Strays. — It  has  been  described  how  interference,  due 
to  simultaneous  operation  of  other  transmitting  stations  within  range, 
may  be  minimized  or  eliminated  by  selective  tuning,  provided  the  wave 
lengths  are  not  too  closely  in  agreement,  and  the  signals  received  from 
the  interfering  station  are  not  too  strong.  This  means  also  fails  if  their  de- 
crements are  high.  It  may  be  noted  that  very  powerful  or  strongly  damped 
waves  act  like  an  impact  excitation  of  the  receiving  circuits,  which  are 
set  into  oscillation  at  their  own  natural  frequency.  This  response  is 
secured  regardless  of  the  wave  length  of  the  incoming  highly  damped 
oscillation;  for  this  reason  the  circuit  is  not  selective  to  these  waves. 
Stray  waves  are  always  highly  damped,  and  may  be  very  much  stronger 
than  the  incoming  signal  waves.  Therefore,  their  elimination  cannot  be 
satisfactorily  accomplished  by  selective  tuning,  but  some  other  arrange- 
ment must  be  used  which  results  in  their  neutralization. 

A  neutralization  scheme,  suggested  by  De  Groot,  is  shown  in  Fig.  11; 
many  similar  arrangements  have  been  recommended. 

Antennae  No  1  and  No.  2  are  similar,  but  the  former  is  tuned  to  the 
radio  frequency  of  the  incoming  signal,  while  No.  2  is  practically  untuned 
because  the  detector  Z>2  is  inserted  directly  in  the  circuit;  the  circuit  is 
made  nearly  aperiodic  and  signals  from  distant  stations  are  impossible 
of  reception  by  this  antenna.  The  reception  of  static  signals  is  just  as 
strong,  however,  as  are  obtained  with  the  tuned  antenna. 

The  receiving  circuits  of  both  antennas  are  coupled  together  and  to 
a  third  circuit  containing  the  phones  and  condenser  (this  condenser  is 
used  for  tuning  the  phone  circuit  to  the  audio-frequency),  this  coupling 
being  arranged  so  that  the  static  currents  tend  to  neutralize  one  another, 
onlv  the  received  signal  current  to  act  on  the  third  circuit. 


ELIMINATION  OF  DISTURBANCES 


195 


A  later  arrangement,  as  developed  by  R.  A.  Weygant,1  is  based  on 
the  inventor's  belief  that  static  disturbances  of  the  third  type  specified 
above  are  propagated  in  a  direction  perpendicular  to  the  earth's  surface, 
whereas  the  signal  waves  are  transmitted  parallel  to  the  earth's  surface 
(horizontally).  Two  loop  aerials  were  used  in  the  experimental  work, 
located  about  5000  feet  apart,  the  plane  of  the  loops  being  vertical.  The 
waves  due  to  static  cut  both  loops  in  phase,  whereas  the  signal  waves, 
traveling  horizontally,  induced  e.m.f.'s  in  the  two  loops,  which  were  out 
of  phase  by  an  amount  depending  on  the  separation  between  the  two 


FIG.  11. — One  of  the  early  attempts  to  eliminate  "strays." 

loops  expressed  as  a  fraction  of  the  signal  wave  length.  By  coupling 
the  two  circuits  to  a  third  receiving  circuit,  the  static  effects  are  elimi- 
nated, while  the  signal  currents  combined  vectorially  to  give  a  resultant 
which,  in  turn,  is  rectified  by  means  of  a  vacuum-tube  detector. 

A.  H.  Taylor  reports  very  successful  results  in  the  elimination  of  static 
by  suitably  balancing  the  signals  received  by  an  under-water  (or  buried) 
single-wire  antenna  with  that  received  from  an  overhead  antenna,  gener- 
ally of  the  coil  type.  His  results  would  indicate  that,  using  his  scheme, 
transatlantic  radio  communication  is  assured  under  any  condition  of  static 
to  be  expected. 

Probably  one  of  the  most  promising  lines  of  development  in  the  elimi- 
nation of  static  interference  has  to  do  with  a  vacuum  tube  detector  which, 
even  with  the  heaviest  static,  can  give  but  limited  response  in  the  telephone 
receiver ;  if  this  response  is  not  more  than  two  or  three  times  as  loud  as  the 
signal  a  good  operator  can  read  the  signal  right  through  the  interfering  noises. 

Even  at  the  present  time,  when  many  devices  have  been  gotten  up 

1  Roy  A.  Weygant,  "Reception  through  Static  and  Interference,"  Proceedings  of 
the  Institute  of  Radio  Engineers,  June,  1919. 


196  GENERAL  VIEW  OF  RADIO  COMMUNICATION         [CHAP.  Ill 

for  eliminating  the  effects  of  atmospheric  interference,  it  is  the  one  factor 
which  limits  the  rate  of  transmission,  high  speed  sending  cannot  be  carried 
out  and  because  of  the  many  repeats  required  the  present  commercial  speed 
of  transoceanic  communication  is  between  five  and  ten  words  per  minute. 

Attenuation  of  Propagated  Waves. — The  electromagnetic  waves  set 
up  by  the  transmitter  are  propagated  in  all  directions  through  the  ether 
at  a  velocity  corresponding  to  that  of  light,  as  discussed  in  the  earlier 
portions  of  this  chapter.  As  the  distance  from  the  transmitter  increases 
their  amplitude  or  intensity  decreases,  due  to  the  wave  spreading  out  in 
ever-widening  circles  and  energy  absorption  by  the  different  media  through 
or  over  which  the  wave  may  be  propagated.  This  decrease  in  intensity, 
expressed  in  terms  of  the  initial  intensity  at  the  source,  is  called  the  attenu- 
ation of  the  wave. 

Many  investigations  have  been  made  to  determine  the  attenuation 
of  these  waves,  among  the  more  important  of  which  may  be  mentioned 
those  carried  out  by  L.  W.  Austin  l  in  1909-1910,  using  the  station  at 
Brant  Rock,  Mass.,  as  the  receiver  and  the  transmitting  sets  on  U.  S. 
cruisers  for  sending.  His  results  cover  one  special  case  only,  namely, 
transmission  during  daylight  over  sea  water.  The  variation  of  currents 
flowing  in  the  receiving  antennae  is  indicated  in  Fig.  12.  The  dotted 
curve  is  plotted  to  show  what  the  results  would  be  if  no  absorption  of 
energy  had  occurred,  in  which  case  the  received  current  would  have  been 
nearly  inversely  proportional  to  the  distance  from  the  source.2 

Through  the  points,  obtained  from  the  experiments,  the  full-line  curve 
was  drawn,  as  shown  by  Fig.  12,  the  equation  of  which  as  deduced  by 

Austin,  is  as  follows  L  L  d 

T      AT    nsnr    -  0.0015—= 
Ir  =  AIS'  -rr-'€  VX 

where  A  is  a  constant; 

I sis  the  effective  current  in  the  transmitter  antenna; 
Ir  is  the  effective  current  in  the  receiver  antenna; 
hs  is  the  height  of  the  transmitting  antennae ; 
hr  is  the  height  of  the  receiving  antennae; 
d  is  the  distance  between  the  two  stations; 
X  is  the  wave  length  of  transmission. 
All  lengths  are  expressed  in  kilometers. 
For  the  ranges  covered  by  Austin's  investigation,  namely: 

7S  =  7.0  to  30.0  amperes 
hr  and  hs=  12  to  40  meters 

X  =  300  to  3750  meters 
d=up  to  1500  kilometers 
the  constant  A  was  found  to  be  equal  to  4.25. 

1  L.W.  Austin:  Bull.  Bureau  of  Standards,  vol.  7,  p.  315, 1911  and  vol.  11,  p.  69, 1914. 

2  More  recent  tests  by  Vallauri  on  the  strength  of  signals  received  at  Leghorn  from 
Annapolis  indicate  that  the  attenuation  is  much  less  than  Austin's  formula  predicts. 
Vallauri's  measurements  gave  a  field  strength  at  his  receiving  station  about  ten  times  as 
creat  as  the  value  calculated  from  Austin's  formula. 


VARIATIONS  IN  ATTENUATION  OF  WAVES 


197 


The  receiving  antenna  resistance  was  25  ohms. 

Day  and  Night  Variation  in  Signal  Strength. — The  foregoing  inves- 
tigation considered  day  conditions.  At  night,  due  to  variations  in  atmos- 
pheric conditions,  affecting  the  conductivity  of  the  upper  strata,  the 
energy  losses  in  transmission  are  decreased,  and  the  attenuation  of  the 
wave  is  correspondingly  diminished.  In  practice  it  is  generally  found 
that  transmission  is  very  much  more  effective  at  night  than  in  the  day- 


600 


100 


400          500 
Distance  in  Miles 


900       1000 


FIG.  12. — Calculated  and  experimental  values  of  current  in  receiving  antenna,  as  dis- 
tance from  transmitter  is  increased. 

time,  the  range  of  transmission  being  sometimes  increased  two  and  one-half 
times  or  more.  The  transmission,  however,  is  very  much  more  uncertain, 
the  range  sometimes  being  only  slightly  greater  than  in  the  daytime.1 

The  electromagnetic  waves  are  generally  believed  to  be  propagated 
through  the  layer  of  atmosphere  immediately  adjacent  to  the  earth's  sur- 
face, this  layer  being  considered  about  30  to  40  miles  thick.  Above  this, 

^See  article  by  J.  H.  Bellinger » Proc.  Washington  Academy  of  Sciences,  January, 
1921,  on  the  Fading  of  Signals.^ 


198  GENERAL   VIEW  OF  RADIO   COMMUNICATION       (CHAP.  Ill 

the  atmosphere,  due  to  this  low  density,  and  the  ionizing  action  of  the 
sun's  rays,  rapidly  increases  in  conductivity,  and  forms  a  bounding  plane, 
of  high  conductivity,  for  the  layer  of  atmosphere  adjacent  to  the  earth, 
whose  resistance  is  comparatively  high. 

During  the  day,  however,  this  layer  adjacent  to  the  earth  is  also  ionized 
to  a  small  extent,  increasing  its  conductivity  and  decreasing  the  efficiency 
of  transmission  of  the  electromagnetic  waves,  which  is  a  maximum  for 
a  dielectric  possessing  zero  conductivity.  With  the  removal  of  the  sun 
and  its  ionizing  effects  on  this  transmitting  layer  of  atmosphere,  this 
efficiency  is  increased  and  thus  also  the  range  of  transmission.  During 
daylight  the  refracting  effects  of  the  upper  ionized  portion  of  the  trans- 
mitting layer  cause  the  waves  to  bend  over,  so  that  when  they  reach  the 
receiving  antennae  they  may  be  bent  at  such  an  angle  as  to  have  very 
little  effect  on  the  aerial.  This  effect  is  diminished  at  night,  when  the 
ionization  of  this  transmitting  belt  is  largely  reduced,  as  already  described. 

Another  interesting  fact  concerned  with  the  diurnal  variation  in  trans- 
mission is  the  fact  first  recorded  by  Marconi  in  his  early  transatlantic 
experiments.  When  the  line  of  sunrise  or  sunset  is  between  the  two 
stations  transmission  is  almost  impossible,  according  to  Marconi's  results. 
It  seems  as  though  the  twilight  line  acts  as  either  a  reflector  or  absorber 
of  the  radio  waves. 

Seasonal  Variation  in  Signal  Strength. — The  strength  of  received 
signals  varies  also  with  the  seasons,  and  in  1912,  an  investigation  cf  this 
effect  was  made  by  L.  W.  Austin,1  signals  being  received  at  Washington, 
D.  C.,  from  the  radio  stations  in  the  Philadelphia  and  Norfolk  Navy  Yards. 
The  results  obtained  are  shown  in  Fig.  13. 

The  reason  for  this  seasonal  variation  of  signal  strength  is  ordinarily 
considered  as  being  due  to  the  absorption  of  the  waves  by  vegetation, 
thus  causing  a  marked  decrease  in  intensity  during  the  summer  months. 
This  seems  to  be  a  reasonable  conclusion,  in  view  of  the  fact  that  trees 
have  been  successfully  used  as  antennae,  thus  demonstrating  their  energy- 
absorbing  qualities.  It  was  found  that  rainfall  had  no  appreciable  effect 
of  the  signal  intensity. 

Amount  of  Power  Sent  Out  and  Received. — Hertz  showed  that  the 
electric  and  magnetic  forces  in  the  radiated  wave  varied  inversely  as  the 
distance  from  a  small  Hertzian  oscillator.  The  same  relation  is  true  for 
an  ordinary  grounded  antennae  if  the  distance  assumed  does  not  exceed  a 
few  hundred  miles.2  The  energy  thus  decreases  inversely  as  the  square 
of  the  distance,  while  the  amplitude  varies  inversely  as  the  distance.3 
(See  dotted  curve  shown  in  Fig.  12.) 

1  L.  W.  Austin  "  Seasonal  Variation  in  the  Strength  of  Radiotelegraphic  Signals." 
Proc.  Institute  of  Radio  Engineers,  June,  1915. 

2  See  Chapter  IX,  page  707. 

3  It  is  interesting  to  note  that  a  recent  report  by  a  British  radio  commission  points 


AMOUNT  OF  POWER  USED  IN  RADIO 


199 


Duddell  and  Taylor  *  wore  the  first  to  investigate  the  decrease  of 
field  as  the  distance  from  the  transmitter,  increases,  and  a  few  of  their 
results  are  given  in  the  following  table;  the  transmission  was  over 
land,  but  it  is  likely  that  for  such  short  distances  as  were  used  in  their 


1OA 

1 

WaLhin 

gto 

i  to 

Phi 

ladelph 

a 

Received  current  in  10"  amp. 

£§  £  §  §  8  S 

x 

-- 

--V, 

V\a 

shiri 

gto 

i  to 

Noi 

folk 

^_ 

'  V 

/ 

2 

s 

x\ 

/ 

\ 

\ 

// 

\ 

\ 

/ 

/ 

/ 

V 

\ 

/ 

2 

\ 

A 

1 

/ 

\ 

\ 

t 

/ 

^ 

-X 

\ 

\ 
v    \ 

/ 

\ 

-  — 

^ 

/ 

' 

^, 

,  ' 

s 

ease 

nal 

var 

atic 

nin 

siff 

nal 

stre 

igtl 

\ 

i: 

12  > 

*19 

3 

1S 

13  J 

*19 



.4 



III 


>>     ?! 

5     2 


a     *?     > 


FIG.  13. — Variation  of  radio  transmission  occurring  with  seasonal  frequency. 

CURRENT  IN  THE  RECEIVING  ANTENNA  WHEN  THE  DISTANCE 
BETWEEN  THE  TUNED  TRANSMITTER  AND  RECEIVER  IS  VARIED. 
HEIGHT  OF  RECEIVING  ANTENNA,  56  FT.  HEIGHT  OF  TRANS- 
MITTING ANTENNA,  42  FT. 


Distance  in  Foot  botwoon 
Antennae. 

CURRENTS  IN  ANTENNA. 

Approximate  Wave 
Length. 

Transmitter 
Amperes  (eff). 

Receiver  Micro- 
Amperes  (eff). 

100 

0.501 

12320 

400ft. 

200 

0.507 

6435 

300 

0.558 

4548 

400    . 

0.541 

3108 

1260 

0.541 

715 

2420 

0.506 

283.5 

3700 

0.517 

105 

4600 

0.558 

96.5 

6220 

0.563 

69.5 

out  the  fact  that  it  is  uneconomical  to  attempt  radio  communication  over  2000  miles 
except  where  greater  distance  is  actually  required. 

1  "  Wireless  Telegraph  Measurements,"  by  W.  Duddell  and  J.  E.  Taylor,  Journal 
Inst.  Elec.  Eng.,  Lond.,  1905,  vol.  35,  p.  321.  The  receiving  antenna  had  an  effective 
resistance  of  about  60  ohms.  Later  tests  over  water  showed  that  for  distance  up  to  50 
miles  or  more  the  current  in  the  receiving  antenna  varied  inversely  as  the  distance. 


200  GENERAL  VIEW  OF  RADIO  COMMUNICATION         [CHAP.  Ill 

tests,  the  values  indicate  accurately  what  might  be  expected  over  water 


From  these  figures  it  is  readily  seen  how  small  the  received  power  is 
compared  to  the  power  input  to  the  transmitting  antenna  circuit. 

The  experiments  of  Austin,  previously  described,  resulted  in  the 
empiric  formula  given  on  page  196,  which  holds  approximately  for  dis- 
tances up  to  1000  miles.  For  the  smallest  distance  considered,  viz.,  22 
miles  between  the  stations,  using  a  1000-meter  wave,  the  following  values 
were  noted: 


Miles 
between 
Stations. 

Sending  Station. 

Receiving 
Station. 

Wave 
Length 
Meters. 

ANTENNA  CURRENT. 

Sending 
Station 
Amperes. 

Receiving 
Station 
Micro- 
Amperes. 

22 
22 

U.  S.  S.  Birmingham 
U.  S.  S.  Salem 

Brant  Rock 
Brant  Rock 

1000 
1000 

33 

27 

10,500 
11,000 

22 

22 

U.  S.  S.  Birmingham 
U.  S.  S.  Salem 

Brant  Rock 
Brant  Rock 

3750 
3750 

27 
24 

3,200 
4,100 

A  mathematical  analysis  of  the  Austin  formula  expressing  the  rela- 
tion between  the  transmitting  and  receiving  antennae  currents  shows  that 
in  so  far  as  transmission  alone  is  considered  under  given  conditions,  there 
exists  a  best  value  of  wave  length  to  be  used  for  any  given  distance  between 
the  stations.  This  best  wave  length  is: 

(.0015)2d2 


where  d  is  the  distance  between  the  stations  in  kilometers. 

The  following  table  gives  the  best  wave  lengths  for  various  values  of 
d  as  derived  from  the  above  formula: l 


dm  kilometers. 
X  in  meters . . 


700 
275 


1000 
562 


1500 
1260 


2000 
2250 


3000 
5070 


4000 
9000 


5000 
14,050 


For  a  distance  of  22  miles,  wave  lengths  of  1000  and  3750  meters  were 
far  greater  than  the  best  value  for  this  distance,  as  indicated  by  the  very 
much  diminished  antenna  currents  at  the  receiver  when  the  wave  length 
was  increased  from  1000  to  3750  meters.2 

"  Freak  "  Transmission. — The  ideas  presented  in  this  and  following 
chapter  regarding  the  power  used  in  radio  communication  represent 
average  conditions.  It  may  be  that  communication  between  two  stations 

1  It  is  to  be  noted,  however,  that  these  values  do  not  check  very  well  with  those 
given  on  page  187,  which  are  more  nearly  the  actual  values  used  in  practice. 

2  For  optimum  wave  length  see  note  by  Austin  in  Radio  Review,  February,  1922. 


IRREGULARITIES  IN  TRANSMISSIONS  201 

normally  perfect,  is  cut  off  completely  for  several  hours,  as  though  a 
screen  of  some  kind  had  been  put  between  the  two  stations.  It  often 
happens  that  a  station  on  an  island  cannot  communicate  with  a  ship  near 
the  opposite  shore,  but  that  if  the  ship  moves  away  perhaps  100  miles, 
the  intervening  land  of  the  island  offers  no  appreciable  obstruction.  This 
is  indicated  in  Fig.  14.  Illustrating  another  kind  of  freak  transmission 


XB 


Communication  from  station  to  ship  at  A 
impossible;  with  ship  at  B,  100  miles  from.  A, 
communication  is  good 


FIG   14. — A  peculiar  effect  often  observed  in  radio  communication,  giving  rise  to  the  idea 

of  radio  "shadows." 

there  is  apparently  substantial  evidence  that  a  low-power  station  (10  kw.) 
may  sometimes  give  perfectly  good  signals  to  a  ship  8000  miles  away. 
Such  freak  transmission  is  more  likely  to  occur  with  short  waves  than 
with  long  ones. 

Recent  transatlantic  tests  have  shown  that  with  modern  receiving 
apparatus,  including  carefully  designed  amplifiers,  in  the  hands  of  a  skilled 
operator,  as  little  as  five  watts  will  give  good  communication  between 
New  York  and  Scotland;  furthermore  instead  of  being  as  the  supposedly 
optimum  wave  length  of  several  thousand  meters  this  communication 
was  carried  out  with  a  wave  length  of  only  200  meters.  These  tests 
further  emphasize  our  lack  of  information  on  the  actual  transmission 
efficiency  of  radio  waves. 

It  is  to  be  noted,  when  discussing  the  amount  of  power  required  for 
radio  transmission,  that,  due  to  absorption,  reflection,  and  refraction  of 
the  electromagnetic  waves,  the  question  is  almost  as  indeterminate  as — 
how  far  can  a  man  shout? — over  a  quiet  lake  in  the  evening  a  man's  voice 
may  "  carry  "  two  or  three  miles;  the  same  voice  would  carry  about  500 
feet  on  a  city  street,  and  in  a  busy  shipyard  the  shout  would  be  heard 
probably  not  more  than  100  feet.  Atmospheric  disturbances  make  the 
range  of  a  radio  station  almost  as  indeterminate. 


CHAPTER  IV 
LAWS  OF  OSCILLATING  CIRCUITS 

Discharge  of  a  Condenser  through  an  Inductance  and  Resistance  in 
Series.  —  Practically  all  radio  sets  which  send  out  damped  (or  discon- 
tinuous) waves  generate  the  high-frequency  currents  required  by  charg- 
ing up  a  condenser  from  a  suitable  source  of  power,  then  letting  this  con- 
denser discharge  through  an  inductance  in  series  with  a  spark  gap.  In 
general  the  oscillatory  power  so  generated  is  transferred  by  coupling  of 
some  kind  to  another  circuit  from  which  it  is  radiated.  The  investigation 

of  the  form  of  oscillatory  current  in  these 
coupled  circuits  will  be  taken  up  later  in 
this  chapter,  we  shall  first  investigate  the 
discharge  of  a  condenser  in  the  single 
circuit. 

In  Fig.  1  is  shown  the  circuit;  the  con- 
FIG.  1.—  The  charged  condenser  C  denser  C  charged   to   voltage    E   is  to   be 
will  discharge  through  L  and  R  connected  to  the  circuit  consisting  of  L  and 
when  switch  S  is  closed.  R  [n  series  when   the   switch    S    is    closed. 

The  switch  is  not  used  in  the  actual  radio 

circuit,  a  spark  gap  performing  its  function,  but  the  resistance  of  the 
spark  gap  somewhat  complicates  the  analysis  so  that  its  action  is  de- 
ferred until  a  later  paragraph. 

It  will  be  supposed  at  first  that  the  condenser  has  no  leakage;  the 
equation  of  reactions  of  the  circuit  after  the  switch  is  closed  is, 


v  being  the  voltage  across  the  condenser  at  any  instant.    Then 

d2i        di    dv 


But  we  know  that  i  =  C 

at 

so  we  have  L  ^|+  Rji+^  =  0, 

or 

d?i    Rdi      i 
dt^Ld^LC^ 
202 


FORM  OF  CONDENSER  DISCHARGE  CURRENT  203 

The  solution  of  a  differential  equation  of  this  kind  is  obtained  by  an 
"  intelligent  guess."  It  is  evident  that  i  must  be  a  function  of  t  and 
furthermore  that  this  function  must  be  of  such  a  form  that  the  second 

r> 

derivative  of  the  function  plus  the  first  derivative  multiplied  by    :  plus 

LJ 

the  function  itself  multiplied  by  j-^  must  add  up  to  zero.     By  trial  we 

.L/C 

find  that  if  the  current  is  of  the  form 

i  =  Aemt 
Eq.  (1)  will  probably  be  satisfied.     Using  this  function  we  have 


and 

d2i 
W2 

Substituting  these  values  in  Eq.  (1),  we  get 

\  "^  -LJ\-S  f 

As  no  useful  solution  is  obtained  by  putting  A  =  0,  we  use  the  condition 


. 

There  are  two  roots  to  this  equation  either  of  which  will  satisfy  it.  As 
Eq.  (1)  involves  the  second  derivative  of  i  we  know  there  must  be  two 
independent  solutions  for  i  and  these  two  values  of  m  which  we  call  mi 
and  m,2,  permit  the  two  required  solutions  being  written.  The  complete 
solution  of  Eq.  (1)  is  the  sum  of  the  two  particular  solutions,  so  we  write 
as  the  complete  solution 

i  =  Aiem*t  +  A2em*,      ........     (2) 

where 

R       I'R2       T 
~±~       = 


So  we  have 

*)  ........     (3) 


As  initial  conditions  we  have,  at  the  instant  the  switch  is  closed  (2  =  0), 
r  =  0,  so  from  (3) 

ft  =  A\-\-A2 (4) 

Also  if 

_E 

=o         L' 


204  LAWS  OF  OSCILLATING  CIRCUITS  [CHAP.  IV 

which  when  substituted  in  Eq.  (3)  after  differentiation  gives 

-|=G8-«)Ai-G8+a)A2  .......     (5) 

Solving  (4)  and  (5)  for  AI  and  A2  we  get 


which  values  substituted  in  Eq.  (3)  give 


in  which 

R 


The  quantity  a  is  always  real,  which  means  that  the  amplitude  of  the 
current  continually  decreases  with  increase  of  time.  The  quantity 
(«#  —  e~#),  which  determines  the  form  of  the  current,  while  it  is  decaying, 
depends  for  its  value  on  the  quantity  |8;  this  may  be  either  real  or  imag- 

inary, according  as  a2  is  greater  or  less  than  -=r-^.     The  form  of  the  current 

.LC 

will  be  analyzed  for  the  three  conditions  — 


1  1  ,1 

a>LC>        a=LC>        a<LC' 


CASE  1.     a2>-r. 


In  this  case  /3  is  a  real  quantity  so  we  have 


The  negative  sign  indicates  that  the  effect  of  the  current  is  to  decrease 
E,  i.e.,  to  release  the  charge  on  the  condenser  —  as  to  whether  or  not  cur- 
rent is  actually  positive  or  negative  depends  upon  the  polarity  of  charge 
on  the  condenser  assumed  positive. 

The  form  of  current  in  this  case  is  shown  in  Fig.  2;  the  lines  properly 
marked  give  the  two  terms  e  ~  at  and  sinh  fit.  The  figure  is  drawn  to  scale 
for  #=100  volts,  C  =  10ju/,  L  =  .20  henry,  and  #  =  500  ohms.  By  cal- 
culation we  find  a  =  1250  and  /3  =  1030. 

The  maximum  current  is  reached  at  a  time  calculated  from  putting 
the  first  derivative  of  Eq.  7  equal  to  zero. 


NON-OSCILLATORY  CONDENSER  DISCHARGE 
This  results  in  the  equation 


205 


or 


'  =  3§lo8- 


(8) 


16 


14 


rrent 


2/3 


y\ 


sinh££ 


_ 
Time  in  10"   seconds 

FIG.  2. — Calculated  discharge  current  when  the  R  of  Fig.  1  is  too  high  for  oscillatory  dis- 
charge, 

Fig  3  shows  two  oscillograms  of  a  condenser  discharge  current  for  the 
case  just  analyzed. 


CASE  2.    a2  = 


J_ 
LC' 


In  this  case  we  have  0  =  0.     We  write  the  current  in  the  form, 


the  value  of  the  expression  in  the  parenthesis  being  indeterminate.    We 
evaluate  it  by  differentiation  and  get, 


2*. 


206  LAWS   OF   OSCILLATING    CIRCUITS  [CHAP.  IV 

Hence  in  this  case  the  equation  for  the  discharge  current  is, 

t'=-f«- (9) 

The  graph  of  such  a  discharge  current  is  shown  in  Fig.  4  for  E  =  100 
volts,  C=10  M/,  L  =  .20  henry,  and  R  =  282.3  ohms. 

The  time  at  which  maximum  current  occurs  is  obtained  as  outlined 
for  the  previous  case  and  yields  the  condition  that, 


a 


(10) 


For  the  conditions  given  this  time  is  .001410  second  after  closing  the  switch. 


FIG.  3. — Oscillograms  of  discharges  similar  to  Fig.  2. 

Fig.  5  shows  an  oscillogram  of  such  a  critically  damped  circuit;  the 
time  scale  on  the  lower  part  of  the  film  permits  the  validity  of  Eq.  (10) 
to  be  checked. 

CASE  3.     a2<  , 

In  this  case  /3  becomes  the  square  root  of  a  negative  quantity,  and  we 
write  it 


NON-OSCILLATORY  CONDENSER  DISCHARGE 


207 


Time  in  10     seconds 

FIG.  4. — Discharge  in  a  circuit  in  which  R  has  the  minimum  possible  value  without 
permitting  oscillatory  discharge. 


FIG.  5. — Oscillogram  of  current  for  conditions  assumed  in  Fig.  4. 


208  LAWS  OF  OSCILLATING   CIRCUITS 

Then  from  Eq.  (6) 
E 

t=  —  7^ *-<** 


[CHAP.  IV 


E 


--  •  ~  at 


sn 


(ii) 


The  current  in  this  case  is  oscillatory,  its  frequency  being  fixed  by 
the  value  of  o>;    the  term  e~at  represents  the  decay  of  the  current,  and 

Tjl 

the  theoretical  maximum  value  of  the  current  is  given  by  — r . 


1.0 


FIG.  6. — Value  of  R  of  Fig.  1  reduced  sufficiently  to  permit  the  ordinary  oscillatory  dis- 
charge, giving  a  "damped  sine  wave." 

In  Fig.  6  are  plotted,  in  dotted  lines,  each  of  the  terms  of  Eq.  (11)  for 
a  circuit  of  #=100  volts,  C=10  /*/,  L  =  .20  henry,  and  #  =  50  ohms. 


We  have 


___ 

OL  —  ,-».  -r   — 


50 


2L     2X.20 


But  co  =  27rf,  hence 


f=  7^— =110.5  cycles  per  second. 

^7T 

The  actual  equation  for  the  current  is  then, 


100 


695  X. 2 


sin  (27r  110.5  Q. 


OSCILLATORY  DISCHARGE  OF  A  CONDENSER 


209 


210 


LAWS   OF  OSCILLATING   CIRCUITS 


[CHAP.  IV 


This  curve  is  shown  in  the  full  lines  of  Fig.  6.  It  is  generally  called  a 
"  damped  sine  wave/'  the  term  e-at  giving  the  damping.  In  Fig.  7  is 
shown  the  oscillogram  of  a  damped  sine  wave  showing  how  the  actual 
current  is  of  the  form  indicated  by  Eq.  (11)  for  two  values  of  resistance. 
Effect  of  Condenser  Leakage. — In  case  the  condenser  has  appreciable 
leakage  the  solution  takes  a  slightly  different 
form.  The  circuit  is  now  as  shown  in  Fig.  8; 
the  energy  stored  in  the  condenser  when  the 
switch  is  closed  is  partially  consumed  in  the 
series  resistance  R,  partially  consumed  in  the 
leak  resistance  r,  and  the  rest  transformed 
into  magnetic  energy  in  the  coil;  then  the 
magnetic  energy  in  the  coil  is  transformed 
back  to  electrostatic  energy  in  the  recharged 
condenser,  but  during  the  transformation  more  of  the  energy  is  wasted 
in  R  and  r. 

The  differential  equation  of  the  circuit  becomes 


FIG.  8. — Oscillatory  circuit 
in  which  the  condenser  is 
"leaky." 


or 


d2i         di     dv 


We  have  ic  =  C-r,  and  ie  =  i-\-ig  where  ia  =  vg,  g  being  equal  to  -. 
cLt  r 

Now,  in  magnitude,  v  =  L-^-A-Rit  so  that  iff  =  gL-j-A-gRi. 
Substituting  then  -yf=fi  and  using  the  value  of  ig  just  obtained,  we  get 


/7V 


~Q,     ....    (12) 


which  may  be  written 


This  equation  is  similar  in  form  to  (1)  and  its  solution  is  of  exactly 
the  same  form.     For  this  case,  however,  we  have 


(13) 


and 


l/R     g\2      1 

!=A/7  IT -Til     —TTi (14) 


EFFECT  OF  CONDENSER  LEAKAGE  211 

The  three  cases  considered  in  the  previous  section  occur  also  for  this 
circuit;    the  conclusions  reached  are  the  same,  except  where  previously 

determined  the  damping,  we  now  have  the  quantity    o    +; 


The  conditions  for  oscillations  or  no  oscillations  is  affected  by  the  con- 
denser leakage  in  a  manner  not  to  be  expected;  with  no  leakage  the  non- 
oscillatory  condition  is  reached  when 


and  for  the  leaky  condenser  the  criterion  is 


_ 
2L     26 

That  is,  a  circuit  which  has  sufficient  series  resistance  to  be  critically 
damped  may  become  oscillatory  if  sufficient  leakage  is  introduced  across 
the  condenser. 

For  the  circuit  considered  in  the  previous  section  the  non-oscillatory 
condition  was  reached  when  R  was  adjusted  for  282.3  ohms;  we  then 
had  a  =  707.  If  we  now  shunt  the  condenser  by  a  leak  resistance  of  1000 
ohms  we  have 

282.3     105 


that  is,  greater  than  before,  but  we  now  have  an  oscillatory  circuit  because 

oT  ~o?0  ig  IGSS  ^nan     / Thus  we  have  the  unexpected  phenomenon 

AL    ZL/  V  LC 

of  increased  damping  changing  a  non-oscillatory  circuit  to  an  oscillatory 
one.  Fig.  9  shows  the  three  currents  for  the  circuit  with  leaky  condenser, 
as  in  Fig.  8. 

The  frequency  of  the  free  oscillation  is  lowered  by  the  series  resistance 
of  the  circuit,  but  it  is  raised  by  the  effect  of  shunt  resistance  until  this 

shunt  resistance  reaches  the  value  such  that  -r  =  ^.     If  the  shunt,  or  leak 

L     C 

resistance,  is  made  still  less  the  frequency  will  again  decrease;  from  this 
it  is  seen  that  the  effect  of  a  leak  resistance  (with  no  series  resistance) 
is  to  increase  the  damping  and  increase  the  period,  just  as  is  the  case  for 
a  series  resistance  above,  but  that  when  both  are  present  the  damping 
is  increased  by  an  amount  depending  on  the  sum  of  the  series  resistance 
and  leak  resistance,  but  that  the  effect  of  these  two  on  the  period  is  sub- 
tractive,  and  that  a  certain  relation  between  them  suffices  for  complete 
neutralization,  so  that  the  natural  period  is  the  same  as  it  would  be  if 
the  circuit  had  no  dissipative  reactions  at  all. 


212 


LAWS  OF  OSCILLATING  CIRCUITS 


[CHAP.  IV 


Frequency — Wave  Length. — In  the  previous  paragraph  the  frequency 
of  an  oscillatory  discharge  was  shown  to  be  fixed  by  the  damping,  induct- 
ance, and  capacity.  The  effect  of  the  damping  constants  in  the  fre- 
quency is,  in  ordinary  radio  circuits,  so  small  that  it  can  be  neglected  with- 
out appreciable  error,  so  that  this  formula  for  frequency  of  an  oscillatory 
circuit  becomes 


or 


VLC" 


i 


ZirVLC' 


(15) 


FIG.  9. — Calculated  currents  for  circuit  depicted  in  Fig.  8. 

In  the  formula  /  is  in  cycles  per  second,  L  in  henries,  and  C  in  farads. 
Now  in  radio  circuits  the  values  of  L  and  C  are  more  generally  measured 
in  micro-units  and  the  formula  becomes, 

i  f\fi 

(16) 


where  L  is  in  microhenries  and  C  in  microfarads. 

It  is  more  customary  to  use  the  term  wave  length  in  radio  literature, 
instead  of  frequency.  When  an  antenna  is  excited  by  an  oscillatory  cur- 
rent of  frequency  /  it  sends  out  over  the  earth's  surface  electromagnetic 
waves  which  travel  out  from  the  antenna  with  the  velocity  of  light,  i.e., 
3  X  IO8  meters  per  second.  In  any  wave  phenomenon  the  frequency  and 
wave  length  (always  designated  in  radio  by  the  symbol  A)  are  connected 
by  the  formula 

/X=F, (17) 


CURRENT   AND   VOLTAGES   IN   OSCILLATORY    DISCHARGE     213 

where  V  is  the  velocity  of  travel  of  the  waves.     We  therefore  find  for  the 
value  of  wave  length  of  these  electromagnetic  radiations 


In  this  formula  X  is  given  in  meters,  L  in  microhenries,  and  C  in  microfarads. 

Relation  of  Current  and  Voltage  in  Oscillatory  Circuits.  —  The  equa- 

tion for  the  discharge  of  condenser  for  the  ordinary  condition  (Case  3, 

p.  208,  Eq.  11)  is 

E 

i—  --  T*~at  sin  ut, 
uL 

R 

in  which  a  =  ^-T, 

2iLi 

and  we  have  said  that  in  the  ordinary  radio  circuit  co  is  approximately 

equal  to 

Equation  (11)  therefore  becomes, 


The  maximum  current  occurs  one-quarter  of  a  cycle  after  closing  the 

_m 

switch,  nearly;  the  effect  of  the  damping  term  e  2L  is  to  make  the  current 
a  maximum  shortly  before  the  quarter  cycle  interval.  The  value  of  this 
current,  neglecting  the  small  effect  of  the  damping  for  one  quarter  cycle, 

IS 

is  equal  to  E\l-f* 

Now  this  could  have  been  predicted  from  the  consideration  of  energy 
in  the  circuit  ;  before  the  switch  is  closed  all  the  energy  is  in  the  condenser 

CE2 

and  is  equal  to  —  ^—  .     One   quarter   cycle   after   closing  the   switch  the 
& 

voltage  across  the  condenser  is  zero,  so  that  all  the  energy  must  be  in 
the  coil,  hence  we  may  put 

CE2=LP 
2          2  ' 


or 

as  we  had  before. 

In  an  oscillatory  circuit  there  is  a  certain  amount  of  energy  oscillating 
back  and  forth  from  coil  to  condenser,  and  being  wasl  ed  during  the  trans- 


214  LAWS   OF   OSCILLATING    CIRCUITS  [CHAP.  IV 

for.  The  frequency  of  transfer  will  be  the  same  no  matter  what  the 
relative  value  of  L  and  C,  so  long  as  their  product  is  constant.  It  is 
sometimes  desired  to  establish  resonance  in  a  circuit  and  keep  the  voltage 
low;  in  such  a  case  a  low  value  of  L  and  correspondingly  high  value  of 
C  should  be  chosen.  In  radio-receiving  circuits,  however,  it  is  generally 
desired  to  obtain  as  high  a  voltage  as  possible;  this  is  done  by  using  as 
low  a  value  of  C  as  possible  (sometimes  as  low  as  100  micro-microfarads) 
and  a  correspondingly  high  value  of  L. 

_Rt_ 

Damping  and  Decrement. — In  Eq.  (19)  the  factor  e  2L    represents  a 

T> 

logarithmic  decrease  in  the  amplitude  of  the  current;  the  value  of  ^r 

is  called  the  damping  coefficient  of  the  circuit.  For  the  average  radio 
circuit  this  coefficient  is  of  the  order  of  1000  to  10,000,  being  greater  the 
shorter  the  wave  length  of  the  set.  The  damping  coefficient  multiplied 
by  the  time  of  one  cycle  is  called  the  logarithmic  decrement  or  merely  the 
decrement  of  the  circuit. 

If  we  write  the  values  of  successive  maxima  of  current  (maxima  in  the 
same  direction)  we  shall  have  from  Eq.  (19),  calling  T  the  period  of  oscil- 
lation, 

~2L4T_  7.    ~2Ll 


_  _ 

72=706     2L4  =  7l6      2L 

_*.(?!  ^  _Ay 

73  =  /oe   az,U+a  )=i.2€   -2L    jCtc. 

From  these  we  get 

Zi-.J  T      s 


where  5  is  the  decrement  of  the  circuit.     As  T  =  ^  it  is  evident  that 

R  (20) 


2/L' 

An  ordinary  radio  set  has  a  decrement  about  0.1;  the  large  stations  may 
have  a  decrement  as  low  as  .02,  while  the  upper  limit  for  a  transmitting 
station  is  0.2,  this  being  fixed  legally  as  the  maximum  decrement  a  spark 
station  is  allowed.  As  is  evident  from  Eq.  (20),  the  decrement  of  a  cir- 
cuit depends  directly  upon  the  resistance  of  the  circuit,  this  resistance 
being  interpreted  in  the  broadest  sense  as  suggested  on  page  112.  In 
transmitting  stations  the  ground  resistance  of  the  antenna  is  likely  to 
be  very  important  in  its  effect  on  the  decrement.  The  decrement  meas- 


DAMPING   AND   DECREMENT  215 

ured  from  the  upper  curve  of  the  film  of  Fig.  7  was  .150,  while  that  cal- 
culated from  the  constants  of  the  circuit  was  .152. 

In  a  continuous  wave  transmitting  station  the  source  of  high-frequency 
power  maintains  a  constant  amplitude  to  the  successive  cycles  and  the 
station  is  said  to  have  a  zero  decrement;  in  certain  receiving  circuits 
using  a  vacuum  tube  for  receiver,  the  effective  resistance  of  the  circuit 
made  to  approach  zero  as  nearly  as  desired,  thus  making  the  decrement 
of  the  receiving  set  approach  zero.  As  explained  in  Chapter  I,  pp.  62-65, 
the  decrement  is  the  important  factor  in  determining  the  selectivity  of 
a  receiving  circuit,  as  it  determines  the  sharpness  of  resonance. 

Decrement  Determined  by  Energy  Waste  per  Cycle.  —  The  decrement 
may  be  denned  as  the  ratio  of  the  energy  dissipation  per  cycle  to  the  energy 
transferred  during  the  same  interval  of  time.  Neglecting  the  small  change 
in  value  of  maximum  current  during  one  cycle  we  have: 

RI2 
Energy  dissipated  per  cycle  =  -^7-, 

47 

where  7  is  the  maximum  value  of  current. 

Suppose  we  consider  the  cycle  to  begin  when  I  has  maximum  positive 

LI2 

value  and  all  the  energy  is  in  the  coil,  this  energy  being  equal  to  —  ^-. 

2i 

Now  during  one  cycle  this  energy  flows  from  the  coil  to  the  condenser, 
back  to  the  coil  (when  7  goes  through  its  values  of  opposite  polarity) 
back  to  the  condenser  and  then  back  to  the  coil.  The  energy  makes 
two  complete  transfers  through  the  circuit  so  that  the  amount  of  energy 
transfer  during  one  cycle  is 


RP 

„  Energy  dissipated  _    2/  ..J^-* 

Energy  transferred  ~  ~2  ~  2/L  ~ 

If  the  above  analysis  were  carried  through  rigorously  (taking  account  of 
decrease  of  7  during  the  cycle),  it  would  be  found  that  the  above  relation 
for  d  is  correct. 

Current,  Voltage,  and  Energy  in  a  Damped  Wave.—  During  the  decay 
of  a  wave  train  the  corresponding  maximum  values  of  electrostatic  energy  of 
the  condenser  and  electro-magnetic  energy  of  the  coil  remain  practically 
equal;  the  voltage  across  the  condenser  goes  through  the  same  changes  as 
does  the  current  through  the  inductance.  Using  the  relation  between  the 
voltage  across  the  condenser  and  the  current  in  the  circuit 


-/" 


216 


LAWS  OF  OSCILLATING  CIRCUITS 


[CHAP.  IV 


we  get  from  Eq.  (11)  the  approximate  relation 

ec=E€~at  cos  ut. 

At  any  instant,  therefore,  the  energy  in  the  condenser  is 

CE2 


And  we  have  for  the  energy  in  the  coil, 

WL- 


(at. 


If  we  substitute  for  /o  its  value  determined  above 
we  get 


"" 


—  J  and  then  add 
(21) 


FIG.  10. — Conventional  energy  curve  representation  in  an  oscillatory  circuit. 

From  the  equation  we  see  that  the  original  energy  stored  in  the  con- 

C1  J?2 
denser,  — _— ,  undergoes  a  logarithmic   decay,   with  damping  coefficient 

twice  that  of  the  current. 

The  curves  of  current,  voltage,  and  energy  are  plotted  in  Fig.  10;  the 
total  energy  is  obtained  by  adding  the  corresponding  instantaneous  values 
of  the  magnetic  and  electric  energy.  In  reality  the  current  and  voltage 
are  not  exactly  90°  out  of  phase,  due  to  the  effect  of  the  resistance  of  the 
circuit  so  that  the  addition  of  the  two  components  of  energy  does  not  give 


ENERGY  DECAY  IN  AN  OSCILLATORY  CIRCUIT 


217 


the  smooth  exponential  curve  shown  in  Fig.  10,  but  a  wavy  exponential 

curve  as  indicated  in  Fig.  11.    Here  a  decrement  of  0.3  has  been  assumed, 

g 

giving  a  power  factor  of  —  =  .0955;  the  phase  difference  of  E  and  /  is  there- 
fore 84.5°.  The  energy  for  the  electric  and  magnetic  fields  no  longer  adds 
to  give  the  smooth  energy  curve  of  Fig.  10,  but  indicates  that  the  dissipa- 
tion of  energy  from  the  system  is  more  rapid  at  certain  parts  of  the  cycle 
than  at  others.  When  all  the  dissipated  energy  appears  in  the  form 
of  heat  in  the  series  resistance  (as  supposed  for  Fig.  11),  the  maximum 
rate  of  dissipation  corresponds  with  the  time  of  maximum  current  as  it 
should;  when  the  current  is  zero  there  is  no  energy  being  dissipated. 


FIG.  11. — Actual  energy  curve  for  an  ordinary  oscillatory  circuit. 

In  case  the  condenser  used  in  the  oscillatory  circuit  is  a  leaky  one, 
with  leak  conductance,  gr,  the  energy  dissipated  while  an  oscillatory  cur- 
rent is  flowing  is  used  up  partly  in  the  series  resistance  of  the  circuit 
and  partly  in  the  conductance  across  the  circuit.  The  rate  of  energy  dis- 
sipation in  the  series  resistance  is  i2R  and  the  rate  of  energy  dissipation 
in  the  leak  is  ec2g.  It  will  be  noticed  that  these  two  power  losses  do  not 
have  their  maxima  at  the  same  instant;  when  ec  is  a  maximum  i  is  prac- 
tically zero. 

If  the  series  resistance  and  shunt  resistance  are  properly  proportioned 
the  power  dissipated  in  each  will  be  the  same;  the  proper  ratio  is  obtained 
by  putting 

TJ12 


218  LAWS  Ol'1  OSCILLATING   CIRCUITS  [CHAP.  IV 

Now  we  have,  I2  =  u2C2E2, 

and  so, 


from  which 

The  relation  may  also  be  expressed 

R  =  ~rC' 
or  we  may  also  put  it  in  the  form, 

L  =  C' 

Such  a  proportionality  l  in  the  series  and  shunt  resistances  of  the  cir- 
cuit will  result  in  a  power  consumption  in  the  oscillating  circuit  which 
does  not  fluctuate  throughout  the  cycle  as  it  does  when  the  relation  is 
not  maintained.  Hence  the  energy  decay  in  the  circuit  is  not  a  wavy 
line  as  given  in  Fig.  11,  but  a  smooth  logarithmic  curve  as  given  in  Fig.  10. 

It  is  interesting  to  note  that  this  proportionality  of  series  and  shunt 
resistances  is  the  same  as  is  required  to  make  the  natural  period  of  oscil- 
lation the  same  as  if  no  dissipative  reactions  were  present  in  the  circuit. 
The  natural  period  of  such  a  circuit  was  given  in  Eq.  (14) ;  it  is  seen  that  if 


L    C' 
then 


Oscillatory  Discharge  through  a  Spark  Gap. — If  the  oscillating  cir- 
cuit contains  a  spark  gap  the  current  is  not  of  the  form  indicated  by  Eq. 
(11),  because  of  the  influence  of  the  gap;  as  pointed  out  on  page  139  the 
resistance  of  a  given  spark  gap  is  not  constant  but  depends  upon  the  cur- 
rent flowing  through  it.  The  resistance  of  the  gap  is  smaller  the  higher 
the  amplitude  of  current  through  it,  as  is  more  or  less  evident  from  the 
appearance  of  a  spark.  The  greater  the  current  through  the  gap  the 
larger  is  the  cross-section  of  the  hot,  ionized  gas  conducting  the  current, 
and  the  more  intensely  is  it  ionized,  both  of  these  effects  lowering  the 
gap  resistance. 

1  The  same  proportionality  has  a  peculiar  significance  when  applied  to  long  con- 
ductors, such  as  telephone  lines.  It  was  first  pointed  out  by  O.  Heaviside  that  such 
relation  between  the  various  constants  of  a  line  gives  so-called  "distortionless"  trans- 
mission of  speech  waves. 


OSCILLATORY    DISCI  I  A  R(  IK   TIIRorOH    A    SPARK    (JAP          219 

When  a  charged  condenser  discharges  through  the  circuit  represented 
in  Fig.  12,  the  equation  of  discharge  is 


(22) 


where  Rg  is  the  resistance  of  the  spark  gap.  If  Rg  can  be  written  as  a 
simple  function  of  the  current  this  equation  can  be  solved,  but  it  is  quite 
likely  that  tho  function  is  an  intricate  one,  depending  not  only  on  the 
magnitude  of  current,  but  on  the  frequency  of  the  oscillations. 

The  value  of  Rg  undoubtedly  varies  a  great  deal  throughout  the  cycle, 
but  these  variations  can  have  much  less  effect  on  the  magnitude  and  shape 
of  the  current  than  might  be  supposed.  The  resistance  reaction  is  the  only 
reaction  limiting  the  value  of  the  current  of  fundamental  frequency 

approximately  --  -7=  1  but  any  upper  harmonics  which  the  cyclically 
2?r  V  LC  / 

varying  resistance  might  tend  to  produce  in  the  circuit  would  be  opposed 
by  a  reactance  several  hundred  times  as  great  as  the  resistance,  because 
the  inductance  and  capacity  reactions  balance  only  for  the  fundamental 
frequency.  Hence  the  cyclical  change  in  resistance  may  be  neglected 
in  so  far  as  it  affects  the  solution  of  the  oscillatory  current  defined  by 
Eq.  (22). 

By  means  of  a  Braun  tube  oscillograph  photographs  have  been  taken 
of  the  oscillations  in   such  a   circuit 
as  that  of  Fig.  12,  and  the  commonly 
accepted  interpretation  of  these  pho- 
tographs is  that  the  decay  of  current    — 
is  linear  with  respect  to  time  instead 
of  exponential,  as  given  in  Eq.  (11). 


AAAAAAA/ — ' 


Spark  gap 


On    the    assumption    that   the  re-  FIG.  12.— Oscillatory  circuit  in  which  a 
sistance  of  the  circuit   did  not  affect  spark  gap  is  used, 

the   frequency  and   using  the   experi- 
mental data  given  by  Zenneck,  J.  S.  Stone  has  shown  that  if  the  gap 
resistance  is  written 

2BL 


A -Be 

A  and  B  being  constants,  and  the  other  resistance  in  the  circuit  is  negligible 
the  solution  of  Eq.  (22)  becomes, 


where  RQ  =  initial  resistance  of  spark  gap.     Although  not  so  stated  in 
Stone's  paper,  this  value  7?o  must  be  approximately  this  resistance  at  the 


220  LAWS  OF  OSCILLATING   CIRCUITS  [CHAP.  IV 

first  current  maximum.  The  other  symbols  have  their  ordinary  meanings. 
The  solution  is  really  of  little  importance  in  radio  work,  because  in  no 
case  is  the  spark  gap  the  controlling  factor  in  a  radiating  circuit.  Such 
a  circuit  would  use  up  practically  all  of  its  stored  energy  in  heating 
the  spark  gap,  so  it  is  practice  to  remove  the  high-frequency  power  from 
the  spark-gap  circuit  as  quickly  as  possible  and  let  it  radiate  from  a  cir- 
cuit which  has  no  gap.  Even  when  the  energy  is  in  the  spark-gap  circuit 
the  resistance  of  the  gap  is  small  compared  to  the  resistance  introduced 
into  this  circuit  by  the  coupled  antenna  circuit  as  indicated  by  Eq.  84,  p.  91. 

The  current  of  Eq.  (23)  is  different  from  that  of  Eq.  (11)  in  that  the 
successive  maxima  have  a  constant  difference,  whereas  those  of  Eq.  (11) 
have  a  constant  ratio.  Thus  the  linear  damping  gives  a  wave  train  (group 
of  oscillations)  which  has  a  definite  end,  whereas  the  logarithmic  decre- 
ment never  actually  reduces  the  current  to  zero. 

Number  of  Waves  in  a  Train.  —  When  an  oscillatory  current  is  expressi- 
ble by  Eq.  (11)  it  is  evident  that  there  must  be  an  infinite  number  of  cycles 
per  discharge  of  the  condenser  (or  per  wave  train);  the  damping  factor 

_Rt 

e  2L  makes  the  current  approach  zero  value,  but  theoretically  it  never 
reaches  the  zero  value.  It  is  customary  in  radio  practice  to  say  that  a 
wave  train  has  ended  when  the  current  amplitude  has  fallen  to  1  per  cent 
of  its  initial  amplitude;  this  means  of  course  that  the  energy  remaining 
in  the  circuit  is  only  (1  per  cent)2  =  .0001  of  its  initial  value. 
The  successive  maxima  of  current  are  related  by  the  equation 


and  if 


=100, 


we  have  log,  100  -=  (n  -  1)  5, 

or 

n=*«±*  .........     (24) 

Thus  if  the  decrement  of  an  antenna  is  .05  there  will  be  —    -^  —  =  93 

.  Uo 

complete  cycles  before  the  energy  has  been  sufficiently  dissipated  to  reduce 
the  current  to  1  per  cent  of  its  initial  value. 

In  the  case  of  a  linearly  damped  wave  train  the  number  of  waves  is 
very  few,  principally  because  if  the  gap  resistance  is  so  large  that  the  rest 
of  the  circuit  resistance  is  negligible  (a  necessary  assumption  for  linear 
decrement)  the  decrement  is  of  such  a  high  value  that  the  wave  train 
cannot  have  more  than  perhaps  five  to  ten  cycles  before  it  is  completely 
finished. 


EFFECTIVE  VALUE  OF  A  DAMPED  SINE  CURRENT  221 

It  is  interesting  to  note  that  at  the  end  of  a  logarithmically  decaying 
wave  train  the  condenser  in  the  circuit  is  completely  discharged,  while 
the  circuit  with  linear  decrement  may  leave  a  considerable  charge  in  the 
condenser  at  the  end  of  a  wave  train.  When  the  resistance  of  the  spark 
gap  becomes  too  high,  towards  the  end  of  the  train  when  the  current  is 
small,  the  gap  opens  (probably  at  a  time  when  the  current  is  zero),  leaving 
the  condenser  charged  to  some  appreciable  voltage. 

Effective  Value  of  Current  in  a  Damped  Wave  Train.  —  The  effective 
value  of  a  damped  sine  wave  may  be  obtained  by  integration  of  the  heat- 
ing effect  of  the  current 

T 


1   C 
=  JL 

1  Jo 


Evidently  the  value  of  this  integral  will  vary  with  the  length  of  time  over 
which  the  integration  is  extended,  and  is  to  this  extent  indeterminate  in 
value.  As  in  practice  one  wave  train  follows  another  in  rapid  succession 
we  are  really  interested  in  an  integral  of  the  form, 


\  ° 

JQ 


sin  ut)2dt  =  NI02        e~2at  sin2  ut  dt, 


where  N  is  the  number  of  discharges  per  second. 

This  may  be  integrated  by  standard  methods,  after  expressing  the 
sine  in  the  form  of  exponentials  and  these  yield  the  solution, 

72= 

Now  we  have  o>  = 

and 

«=A 
so 

CO2  (27T/) 


c^     C/5)2+(27r/)2     1+m* 


So 

p= 


Now,  ( ^- 


4/5  1- 

is,  for  the  most  radio  circuits,  negligible  compared  to 
unity.  If  "we  write  in  place  of  the  theoretical  .value  of  current  702,  its 
equal,  E2  j,  and  put 7y\2==  *>  we  8^ tne  expression, 


4/SL        2R   ' 


222 


LAWS  OF  OSCILLATING   CIRCUITS 


[CHAP.  IV 


or 


(25) 


We  could  have  obtained  the  same  result  by  noticing  that  all  the  energy 
stored  in  the  condenser  is  transformed  into  heat  or  radiation  by  the  oscil- 
latory current.  So  we  can  put 


or 


as  before. 

The  value  of  I  is  what  a  hot-wire  meter  in  the  circuit  would  indicate; 
the  maximum  instantaneous  value  of  the  current  directly  after  the  dis- 
charge starts  may  be  a  hundred  times  as  great  as  th'3  value  given  by 
Eq.  (25). 

Effect  of  Neighboring  Circuits  on  Frequency  and  Damping. — If  another 
closed  circuit  of  inductance  and  resistance  is  so  situated  that  currents 
are  induced  in  it  by  the  oscillatory  current  of  the  first  circuit,  the  damping 
of  the  first  circuit  is  increased  and  the  .frequency  is  increased  because  of 
the  decrease  in  inductance.  The  changes  in  L  and  R  due  to  the,  extra 
circuit  are  calculable  from  Eqs.  (73)  and  (74)  of  Chap.  I ;  the  effect  on  the 
decrement  is  increased  not  only  by  the  increase 
in  R,  but  also  by  the  decrease  in  L. 

In  spite  of  these  effects  it  is  sometimes  the 
practice  to  intentionally  short  circuit  part  of  the 
coils  in  a  transmitting  set.  Thus  in  Fig.  13  is 
shown  a  diagram  of  such  a  scheme;  the  induct- 
ance is  made  in  three  sections,  connected  elec- 
trically, and  also  magnetically.  When  being 
used  for  short  wave  lengths  (high  frequency) 
only  one  section  of  the  inductance,  L\  is  con- 
nected in  series  with  the  condenser,  the  others 
being  used  when  longer  wave  lengths  are  desired. 
Now  with  the  connection  as  shown,  the  inductance 
acts  like  an  autotransformer,  generating  very 
high  voltages  at  the  open  end  of  the  coil.  This 
high  voltage  may  cause  excessive  losses  due  to 
both  corona  and  dielectric  losses  in  the  insulating 
supports.  Also  the  voltage  generated  at  the  free 
end  may  be  high  enough  to  break  down  the 

coil  insulation.  To  obviate  these  difficulties  the  parts  Z/2  and  La  are 
short  circuited,  as  shown  by  the  dotted  line,  thus  increasing  the  decre- 
ment of  the  L\C  circuit,  as  noted  above.  The  decrement  may  in  certain 


FIG.  13. — In  many  radio 
sets  part  of  the  multi- 
sectional  transmitting 
inductance  Li-L2-L3  is 
short  circuited  when 
but  one  part  (e.g.,  LI)  is 
being  actually  used  for 
transmitting. 


OSCILLATIONS  OF   COUPLED  PENDULUMS 


223 


OB 


cases  be  even  less  with  Lz  and  L$  short  circuited,  than  it  would  be  if 
they  were  not  short  circuited. 

Effect  of  a  Neighboring  Tuned  Circuit  on  an  Oscillatory  Discharge. — 

When  an  oscillatory  discharge  takes  place  in  a  circuit  to  which  is  coupled, 
either  by  mutual  capacity  or  mutual  inductance,  another  circuit  consist- 
ing of  inductance  and  capacity,  the  form  of  the  current  is  no  longer  a 
simple  logarithmic  decay,  but  is  much  more  complicated,  the  exact  form 
depending  upon  the  coefficient  of  coupling  between  the  two  circuits,  the 
relation  between  the  natural  frequencies  of  the  two  circuits,  the  resistances 
of  each,  and  the  type  of  spark  gap  used  in  the  discharge  circuit. 

Before  anyone  takes  up  the  study  of  the  coupled  circuits  he  should 
make  himself  a  simple  piece  of  apparatus,  which  offers  the  same  peculiar- 
ities to  motion  as  coupled 
circuits  do  to  current.  This 
apparatus  is  shown  in  Fig. 
14;  it  consists  of  a  board 
about  10  cm.  by  30  cm.  with 
two  upright  posts  about  30 
cm.  high  fastened  at  the 
ends  of  the  board.  Across  the 
tops  of  the  two  posts  is  fast- 
ened a  string  and  from  this 
string  are  suspended  two  Fiq.  14— Coupled  pendulum  model, 

pendulums,   A   and   B,   the 

lengths  of  which  are  readily  adjustable  and  which  can  be  slid  along  the  sup- 
porting string  so  that  their  points  of  support,  a  and  b,  can  be  separated 
or  brought  together. 

This  simple  piece  of  apparatus  is  the  mechanical  analogue  of  two  reso- 
nant electrical  circuits;  each  of  the  pendulums  has  a  natural  period  of  its 
own  and  as  it  swings  it  tends  to  make  the  other  pendulum  oscillate  also. 

Suppose  that  bob  A  is  pulled  to  one  side,  bob  B  being  stationary; 
as  A  swings  sidewise  it,  of  course,  pulls  its  point  of  support,  a,  sidewise 
and  thus  pulls  point  6  sidewise  with  it.  This  motion  of  point  b  will  gradu- 
ally set  bob  B  into  motion,  as  the  amplitude  of  motion  of  B  increases 
that  of  A  decreases  and  after  perhaps  twenty  or  thirty  complete  vibra- 
tions of  A  its  motion  will  have  been  reduced  to  practically  zero  and  that 
of  B  will  have  increased  to  a  maximum,  practically  the  same  as  the  original 
amplitude  of  A.  This  remark  holds  good  only  if  the  lengths  and  weights 
of  the  two  pendulums  are  the  same. 

Qualitative  Analysis  of  the  Pendulum  Experiment.— The  natural  fre- 
quency of  a  pendulum  is  fixed  by  its  length  and  the  gravitational  force; 
hence  to  change  the  natural  period  of  a  pendulum  it  is  only  necessary 
to  change  its  length;  the  mass  of  the  bob  itself  has  no  appreciable  effect 


224  LAWS  OF  OSCILLATING  CIRCUITS  [CHAP.  IV 

on  the  natural  frequency.  It  must  be  noted,  however,  that  the  mass  of 
the  bob  does  have  a  considerable  effect  on  the  amplitude  of  vibration  for 
a  given  energy  in  the  oscillation,  hi  fact  for  a  given  energy  the  amplitude 
of  vibration  varies  inversely  as  the  square  root  of  the  mass  of  the  bob. 

The  damping,  therefore  the  decrement,  of  a  swinging  pendulum  is 
fixed  by  the  ratio  of  the  frictional  forces  (set  up  by  the  motion)  to  the 
mass  of  the  bob;  an  aluminum  bob  will  have  considerable  greater  decre- 
ment than  a  lead  bob,  the  two  being  the  same  diameter.  Of  two  bobs 
of  the  same  material  the  smaller  will  have  the  higher  damping  because 
the  mass  varies  as  the  cube  of  the  diameter  and  the  air  friction  in  the  bob 
approximately  as  the  square  of  the  diameter;  the  air  friction  on  the  string 
will  be  the  same  for  both.  Hence  a  small  bob,  or  one  of  less  dense  material, 
will  have  greater  damping  than  a  large  heavy  one. 

The  coupling  of  the  two  pendulums  depends,  for  a  given  length  of 
pendulum,  on  the  distance  apart  of  the  points  of  support,  a  and  6,  and 
on  the  tightness  of  the  supporting  string.  The  farther  apart  the  points 
of  attachment  a  and  6,  and  the  tighter  the  string  the  less  the  coupling 
of  the  two  pendulums.  For  a  given  tension  of  the  supporting  string,  and 
a  given  separation  of  the  points  of  attachment,  the  coupling  increases  as 
the  lengths  of  the  pendulums  are  decreased. 

The  decrement  of  these  pendulums  is  much  less  than  the  decrement 
of  a  radio  circuit;  if  it  is  desired  to  give  the  pendulums  a  greater  damping 
the  bobs  may  be  made  to  swing  in  a  pan  of  water,  or  other  liquid,  or  an 
air  damping  vane  may  be  fastened  to  the  pendulum  string;  the  closer 
the  vane  is  placed  to  the  bob  the  greater  will  be  its  damping  effect. 

By  watching  the  motion  of  the  bobs  under  various  conditions  the  fol- 
lowing approximate  deductions  may  be  drawn: 

1.  For  all  conditions  the  motion  of  either  bob  is  a  complex  harmonic 
motion,  the  amplitude  varying  periodically  from  a  maximum  to  a  miminum, 
the  average  value  of  the  amplitude  gradually  decreasing. 

2.  The  maximum  variation  in  amplitude  occurs  in  case  the  two  pendu- 
lums have  the  same  natural  frequency,  the  minimum  amplitude  of  each 
pendulum  for  this  case  being  practically  zero. 

3.  If  the  two  pendulums  have  the  same  mass  the  maximum  amplitude 
of  each  is  nearly  the  same,  if  not  of  the  same  mass,  the  lighter  bob  has 
the  greater  maximum  amplitude. 

4.  The  period  of  oscillation  for  each  pendulum  (time  between  succes- 
sive passages  through  zero  displacement,  in  the  same  direction)  is  prac- 
tically constant  with  similar  pendulums,  the  same  as  the  natural  period  of 
either  pendulum)  at  all  times  except  when  the  amplitude  is  going  through 
its  minimum  values;  at  this  time  a  sudden  reversal  of  phase  takes  place  in 
the  motion  so  that  the  motion  gains  (or  loses)  nearly  one  half  a  cycle  at 
this  time. 


MOTIONS  OF  COUPLED  PENDULUMS  225 

5.  During  the  time  a  pendulum  is  gaining  amplitude  its  motion  lags 
nearly  90°  behind  that  of  the  other  pendulum;    when  its  amplitude  is 
decreasing  its  motion  is  slightly  more  than  90°  ahead  of  that  of  the  other 
pendulum. 

6.  The  amplitude  of  the  first  pendulum  (the  one  originally  displaced 
to  start  oscillations)  varies  from  a  maximum  to  a  minimum,  the  value  of 
this  minimum  depending  upon  the  relative  lengths  of  the  pendulums; 
for  equal  lengths  the  minimum  is  practically  zero,  but  the  minimum 
increases  in  value  as  the  ratio  of  lengths  departs  from  unity  value.     For 
all  conditions,  however,  the  amplitude  of  the  second  pendulum  varies 
from  maximum  to  zero. 

7.  The  time  between  successive  maxima  and  minima  of  amplitude 
depends  entirely  on  the  coupling;    the  tighter  the  coupling  the  more 
rapidly  the  successsive  maxima  follow  one  another. 

8.  Beats  (periodic  variations  in  amplitude)  always  occur  unless  the 
coupling  is  weak  and  damping  is  high.     In  fact  practically  the  only  way 
to  prevent  beats  is  to  make  the  damping  so  high  that  for  the  coupling 
in  question  the  time  between  beats  (as  determined  for  low  value  of  damp- 
ing) is  sufficient  to  allow  nearly  complete  dissipation  of  the  energy  origi- 
nally put  into  the  first  pendulum. 

9.  If  after  the  first  pendulum  has  given  its  energy  to  the  second  pen- 
dulum (first  minimum  amplitude  of  the  first  pendulum)  it  is  in  some  way 
disconnected  from  the  second  by  cutting  its  string  (or  merely  by  holding 
the  first  bob  so  that  it  cannot  move),  the  second  pendulum  will  oscillate 
at  its  own  natural  frequency,  and  with  its  own  decrement,  until  all  the 
energy  originally  in  the  first  pendulum  has  been  dissipated  by  the  losses 
in  the  second.     This  condition  illustrates  the  operation  of  a  so-called 
"quenched  spark"  transmitting  set. 

Analysis  of  the  Motion  of  Coupled  Pendulums.  —  The  peculiar  motion 
of  each  of  the  oscillating  pendulums  discussed  in  the  previous  paragraph 
can  be  produced  synthetically,  more  easily  than  would  be  supposed.  If 
we  let  v\  and  V2  be  the  actual  velocities  of  the  two  bobs,  both  of  changing 
phase  and  amplitude  we  may  write, 


Vl  =  V  ie  -  ««  sin  2vf't+  V2e  ~  "*  sin  2ir/'%      ....     (26) 
V2  =  71€  -  «rf  sin  2*/  '«+  V2€  ~  <**  sin  (2,r/"*+ir),       .    .     (27) 


where  /'  and  /"  are  lower  and  higher  respectively  than  the  natural  period 
of  each  pendulum  and  V\  and  V2  are  maximum  velocities  of  these  two 
component  velocities,  and  a\  and  a2  are  the  damping  factors  of  the  coupled 
system  for  the  two  frequencies  /'  and  /".  In  Fig.  15  are  shown  the  graphs 
of  Eqs.  (26)  and  (27),  when  applied  to  pendulums  of  equal  length;  the 
resultant  v\  and  v2  will  be  recognized  at  once  as  the  form  of  the  velocity 


226 


LAWS   or   OSCILLATING    CIIUTITS 


[CHAP.  IV 


of  the  two  coupled  pendulums,  ^i  corresponding  to  the  pendulum  origi- 
nally displaced  to  start  vibrations;  the  reversal  of  phase  at  the  times  of 
minimum  amplitude  is  well  shown  in  the  curves.  In  these  curves  the 
damping  has  been  neglected;  for  the  ordinary  pendulum  the  damping 
is  very  small  for  so  short  a  time  as  shown  in  Fig.  15. 

After  having  clearly  in  mind  the  phenomena  which  occur  in  the  pair 
of  coupled  pendulums  we  will  analyze  mathematically  the  currents  in 
two  coupled  electrical  circuits  and  shall  find  solutions  exactly  similar 
to  Eqs.  (26)  and  (27). 


FIG.  15. — Full  line  curves  show  actual  motion  of  the  two  bobs  of  Fig.  14  for  tight  coup- 
ling; the  dashed  lines  represent  the  two  sinusoidal  components  of  the  actual  complex 
motion. 

Analysis  of  Oscillations  in  Coupled  Circuits. — When  the  switch  S, 
(Fig.  16),  is  closed  currents  flow  in  each  circuit  and  the  equation  of  reactions 
for  each  circuit  is  given  by 

=  V,  .     .     (28) 


(29) 


where  the  letters  have  the  meaning  shown  in  Fig.  16,  M  being  the  mutual 
induction  between  LI  and  Li  and  qi  and  52  being  the  charges  on  con- 


densers  Ci  and  €2  respectively. 


d  d2 

D  stands  for  —  and  D2  for  -p,  etc. 


CURRENTS   IN   COUPLED  CIRCUITS 
By  differentiating  (28)  twice 


Similarly  for  circuit  (2) 


Multiply  (31)  by  C2L2  and  (33)  by  C\M  and  subtract 
Cy1C2(LiL2  -M2)D*qi+ClC2L2R1D3ql 
+C2L2D2qi  -C\C 


227 

(30) 
(31) 

(32) 
(33) 

(34) 


FIG.  1G.  —  When  the  switch  is  closed  Ci  will  discharge  through  LI  and  /&;  current  will  also 
be  set  up  in  circuit  2,  the  actual  current  in  the  two  circuits  being  similar  to  the 
motion  of  the  pendulum  bobs  of  Fig.  14. 


Multiply  (30)  by  C2R2  and  add  to  (34). 


Add  (28)  to  (35)  and  get 


(35) 


ql  =  0.     .     (36) 

By  a  similar  procedure  an  identical  equation  can  be  obtained  for  52- 
The  exact  solution  of  Eq.  (36)  is  not  generally  attempted  in  texts  on 

Radio;    it  is  lengthy  and  the  exact  solution^1  differs  but  little  from  the 

approximate  solution  given  below. 

Determination  of  the  Two  Frequencies  of  Oscillation.  —  In  using  Eq. 

(36)  to  obtain  the  frequencies  of  oscillation  the  solution  is  much  simplified 

by  making  an  assumption  which  is  justified  in  all  ordinary  radio  circuits, 

1  For  the  exact  solution  the  student  is  referred  to  an  excellent  article  by  F.  E.  Pernot 
in  Vol.  1,  No.  8,  University  of  California  Publications  in  Engineering. 


228  LAWS  OF  OSCILLATING  CIRCUITS  [CHAP.  IV 

i.e.,  the  resistance  of  the  circuit  has  a  negligible  effect  on  the  frequency 
of  oscillation.  We  may  therefore  neglect  the  resistance  terms  in  Eq.  (36) 
in  solving  for  the  periods  of  oscillation;  by  doing  this  we  get  the  compara- 
tively simple  equation, 


(37) 


By  substituting 

this  becomes, 

A  similar  analysis  for  #2  would  yield 

)22<?2  =  0   .     .     .     (39) 


The  solutions  of  (38)  and  (39)   are,  by  inspection,  of  trigonometric 
form,  so  we  put 


=  Ai  cos  (co£+</>),      .......     (40) 

=  A2  cos  (wH-0')«     ........     (41) 


By  differentiating  these  equations  and  inserting  the  values  of  the 
proper  derivatives  in  Eqs.  (38)  and  (39)  we  obtain  the  two  values  of  co. 


~  •  • 

and 


2  -V((Qi2+  o>22)2  -4(t)i2o>22(l  -A;2)  ,.„. 


2(1  -k2) 

If  we  now  suppose  the  two  circuits  of  Fig.  16  to  be  tuned  alike,  i.e., 
LiCi  =  L2C2,  we  can  simplify  Eqs.  (42)  and  (43)  very  much.  By  intro- 
ducing the  condition  that  o>i  =  402  =  co  we  get, 


(44) 


and  co'  =  ^=- (45) 

From  (44)  and  (45)  we  can  get  the  value  of  the  coupling  coefficient  as 

if  — 


And  it  is  to  be  noticed  at  this  point  of  the  analysis  that  these  two 
frequencies  are  exactly  the  same  as  those  given  in  Eqs.  (103)  and  (104) 
of  Chapter  I  for  coupled  circuits  excited  by  an  alternating  e.m.f.  of  vari- 


CURRENTS  IN  COUPLED  CIRCUITS 


229 


able  frequency.  Indeed  from  the  similarity  of  procedure  we  may  conclude 
that  a  complex  circuit  having  sufficiently  low  resistance,  if  left  free  to 
oscillate  after  being  excited  in  some  way  or  other,  will  oscillate  at  those 
frequencies  for  which  the  system  has  zero  reactance  when  excited  by  an  alter- 
nating e.m.f. 

If,  therefore,  the  natural  periods  of  an  electric  circuit  are  desired  it  is 
only  necessary  to  excite  the  circuit  by  an  alternating  e.m.f.  of  variable 
frequency  and  note  those  frequencies  for  which  the  power  factor  of  the 
system  is  unity.  When  left  free  to  vibrate,  the  circuit  will,  in  general, 
oscillate  at  all  these  frequencies  simultaneously,  the  energy  dividing 
between  the  various  frequencies. 

This  general  theorem  in  resonance  is  a  very  useful  one.     Suppose  three 
circuits  as  pictured  in  Fig.  17  all  coupled  together  in  any  complex  way 
possible;    knowing  all  the  constants  of  the  circuits  it 
would  be  possible  to  set  up  the  differential  equations 
and,  after  some  laborious  transformations,    it  would 
be  possible  to  so  combine  them  as  to  eliminate  all  but 
one  variable.     The  resulting  equation  would,  however, 
be   difficult   to  solve,  because  schemes  have  not  yet 
been    evolved    for  solving  an   equation  of  the  sixth 
degree. 

But  if  an  alternating  e.m.f.  is  introduced  into  the 
complex  network,  and  the  frequency  of  this  e.m.f. 
be  varied  through  as  wide  a  range  as  necessary,  there 
will  be  found  three  frequencies  for  which  the  network 
shows  resistance  only,  the  reactance  being  zero. 
These  are  the  three  free  periods  at  which  network  will  oscillate  if  excited 
and  left  to  itself. 

The  point  where  the  power  is  introduced  when  determining  the  three 
resonant  frequencies  by  impressing  an  e.m.f.  is  of  no  importance;  it  will 
be  found  that  the  same  frequencies  will  result  in  unity  power  factor  if  the 
alternator  is  introduced  in  any  line  of  the  whole  network,  care  being 
taken  that  the  alternator  impedance  does  not  appreciably  alter  the  con- 
stants of  the  circuit. 

It  must  be  borne  in  mind  that  the  previous  remarks  hold  good  only 
for  circuits  having  low  damping  factors;  the  argument  depends  upon  the 
assumption  that  this  resistance  does  not  appreciably  affect  the  frequency 
of  oscillation.  The  assumption  is  always  warranted  because  the  radio 
engineer  is  seldom  interested  in  inefficient  circuits,  i.e.,  circuits  having  a 
low  ratio  of  reactance  to  resistance. 

We  therefore  write  the  solution  of  (38)  and  (39), 

.     .     .     (46) 

') (47) 


U 


FIG.  17.  —  General 
case  of  three 
coupled  circuits. 


230  LA\YS   OF   OSCILLATING    CIRCUITS  [CHAP.  IV 

By  differentiation  of  (46)  and  (47),  we  get  the  two  currents, 
ii  =  Aiu"  sin  (co"J+0")  +  #!<,>'  sin  (<,/£+<//) 

=  I"i  sin  (co"*+4>")-h/'i  sin  ((/£+</>'),  .....     (48) 
and 


=  7"2  sin  ((•>"/+  (/>")  +  7'2  sin  (eo'«+0')  .....     (49) 


The  constants  of  Eqs.  (48)  and  (49)  must  be  chosen  correctly  to  satisfy 
the  initial  conditions  of  the  problem. 

It  will  be  noticed  that  these  solutions  give  alternating  currents  of 
constant  amplitude,  evidently  an  impossible  condition  for  the  circuit  of 
Fig.  16.  The  currents  must  rapidly  die  away  as  the  energy  originally 
stored  in  the  condenser  C\  is  used  up  in  the  resistances  of  the  two  circuits. 
The  reason  no  damping  term  appears  in  the  expressions  for  i\  and  ii  is 
the  neglect  of  the  resistance  terms  of  Eq.  (36)  in  passing  to  Eq.  (37).  Of 
course,  a  circuit  having  no  resistance  has  no  damping. 

Before  proceeding  to  further  analysis  of  the  currents  in  the  two  cir- 
cuits it  is  well  to  summarize  the  results  so  far  obtained.  When  the  switch 
in  circuit  1  is  closed  complex  shaped  alternating  currents  begin  to  flow  in 
both  circuits  1  and  2;  these  complex  currents  are  exactly  represented  by  two 
currents  of  frequencies  fixed  by  co"  and  co',  in  each  circuit.  We  have  there- 
fore to  determine  the  relative  amplitude  and  phases  of  four  currents  I'i 
and  7'2  of  frequency  fixed  by  co'  (7'i  in  circuit  1  and  7'2  in  circuit  2), 
and  I"  \  and  l"<2.  of  frequency  fixed  by  co"  (I"\  in  circuit  1  and  I'r2  in 
circuit  2). 

Relative  Amplitude  and  Phases  of  Currents  in  the  Two  Circuits.  —  An 
analysis  of  the  phase  and  magnitude  relations  of  the  four  currents  I'\, 
I"i,  I'2,  7  "2  was  carried  out  by  ChafYee  and  the  deductions  verified  by 
an  ingenious  experiment;  the  results  given  below  are  taken  from  his 
paper.1 

By  using  Eqs.  (46)  and  (47)  in  combination  with  Eq.  (28)  (neglect- 
ing the  resistance  term  in  the  latter)  we  get, 


Ll 

^'Amplitude  Relations  in  Coupled  Circuits,"  E.  Leon  Chaffee,  Proc.  I.  R.  E.,  Vol. 
4,  No.  3,  June,  1916. 


CURRENTS   IN   COUPLED   CIRCUITS  231 

from  which 

A2  =  _w;/2--w12    III 
Ai  /cw"2   \LJ 

52^(01^-^/2      /IT 

B!~      ku"2     \L2' 


7/2     W1       w      ^.  .     (51) 

L2 

Eq.  (50)  gives  the  ratio  of  amplitudes  of  the  short  waves  in  the  two 
circuits  and  (51)  that  of  the  long  waves.  As  co"  is  greater  than  o>i  (see 
Eq.  (42)),  it  is  evident  that  7"2  and  l"\  are  in  opposite  phase;  when  one 
is  positive  the  other  is  negative.  The  long  waves  I'2  and  I'\  are  in  the 
same  phase,  however,  as  their  ratio  is  positive,  coi  being  greater  than  co' 
for  all  conditions  of  coupling. 

In  the  oscillation  transformer  of  a  transmitting  set,  therefore,  the 
effective  flux  for  the  short  waves  is  much  less  than  it  is  for  the  long  waves ; 
of  course,  this  might  be  surmised,  because  the  short  wave  in  each  circuit 
could  only  occur  if  the  effective  LI  and  L2  were  each  diminished  by  the 
action  of  the  other,  which  means  currents  in  the  two  coils  nearly  180° 
out  of  phase.  The  long  waves,  by  a  similar  argument,  must  occur  because 
the  mutual  action  of  LI  and  L2  increases  the  effective  inductance  of  each; 
this  could  only  occur  if  the  long  wave  currents  in  the  two  coils  LI  and  L2 
are  in  phase,  i.e.,  they  magnetize  their  mutual  field  in  the  same  direction. 

To  express  the  amplitude  relation  of  the  two  currents  in  each  circuit 
it  is  more  convenient  to  express  the  relations  of  Eqs.  (42)  and  (43)  in  terms 

2     T7 

of  wave  lengths.     Using  the  relation  X  =  —    -  for  each  frequency  involved 
( V  being  velocity  of  propagation  of  the  electromagnetic  waves) ,  we  get, 


2  -  V(Xl2  -  X22)2 


_ 


As  Eqs.  (42)  and  (43)  were  simplified  by  supposing  the  two  circuits 
tuned  alike,  i.e.,  Xi  =  X2=X  we  may  write,  for  this  condition,  Eqs.  (52)  and 
(53)  in  the  abbreviated  forms 


(54) 
(55) 


232  LAWS  OF  OSCILLATING  CIRCUITS  [CHAP.  IV 

Eqs.  (50)  and  (51)  may  also  be  written  in  terms  of  wave  length  and 
they  become, 

X"2 


(56) 


£-)   -1    n- 

/'t    *--v§ (5?) 

77  "I! 

To  determine  the  ratio  -yyf-  and  ~-  we  set  down  the  initial  conditions 
1   i          1  2 

of  the  circuit.     When  £  =  0  (time  of  closing  switch)  qi  =  Qo,  <?2  =  0,  z'i  =  0, 
and  i'2  =  0.     Using  these  values  in  Eqs.  (46),  (47),  (48)  and  (49),  we  get, 

Qo=  AI  cos  0"+#i  cos  0' (58) 

0=A2  cos  0"+#2  cos  0'. (59) 

0=Aico"  sin  0"+£ico'  sin  0/=7//i  sin  0"+7'i  sin  0'.      .  (60) 

0=A2co"  sin  0r/+B2co'  sin  0/=7//2  sin  0//+7/2  sin  0'.      .  (61) 

To  satisfy  these  conditions  we  must  have  0r  =  0"  =  0.     Then  we  find 
as  A2==  — -S2,  and  7"2  =  A2a//  and  7'2  =  7?2o/,  that 


'£K (62) 


^ 

_=_jl,   W 

T//      ~  // 

Dividing  (50)  by  (51) 


7"27'i          co"2-coi2        co'2  co//2-coi2co 


a/'2 


Multiplying  by  (62)  and  get, 

7'j          CO^-CO!2 


_ 


(63) 


For  convenience  in  using  the  relations  of  Eqs.  (62)  and  (63),  the  values 
\ff          ^/ 

Of  —  an(j  —  have  been  calculated  by  Chaffee  and  are  reproduced  in  Fig. 
Xi  AI 

•v//  \r          -\ 

18      In  this  figure  are  shown  the  variations  in  —  and  T—  as  — ,  is  varied. 

AI  AI        AI 

this  ratio  being  varied  by  varying  X2  by  a  variation  in  condenser  C2. 

This  keeps  k  constant  as  the  ratio  -^  is  varied. 

AI 


J'i  =  B^'  and  7"i  = 


CURRENTS  IN   COUPLED  CIRCUITS 

To  get  the  magnitudes  of  the  four  currents,,  we  solve  for  AI,  B\t  and 
A2,  B2.    From  (58) 


From  (60) 
from  which 

2.0 

1.5 


"   r 


X 


X 


.5  1.0 

Value  of  * 


k= 


•y 


k+l.Q 


/ 


1.5 


2.0 


FIG.  18.— Variation  in  ratios  of  X"/X,  and  777,  as  the  ratio  of  Xi  /X2  is  varied,  foi 

different  values  of  coupling. 

From  this  equation,  by  using  (63), 


or 


Substituting  this  value  of  B\  in  above  equations  for  Q0  gives 
And  as  Bi  =  Q0  —  A\.  we  have 


o;i2-a/2  co"2 
co"2-a/2^' 


co'/2-co'2 


(64) 
(65) 


From  (61) 


234  LAWS  OF  OSCILLATING  CIRCUITS  [CHAP.  IV 

and  by  using  (50)  then  substituting  for  I\'  its  equal  w"Ait  we  get 

- 

then  using  (64) 

.  (»i»  -»*)(«"«  -»!*)    /ET 

-Q°-  *«!*(«"»  -«"—\z;;  •  •  (G6) 

then  from  (59), 

fc 

.     -     -     .     (07) 


Substituting  the  values  of  Eqs.  (64-67)  in  (48)  and  (49),  we  get, 

ii  =  uiQo(F"i  sin  co"£+F'i  sin  «'0       .....     (68) 
and 

~(Fff2  sin  w'^+F'2  sin  co'O,   .     .  (69) 


in  which  the  F  coefficients  are  factors  depending  on  the  condition  of  tun- 
ing, must  conveniently  expressed  in  terms  of  X",  X'  and  Xi.     They  are 


» 

2    " 


"2 


The  values  of  these  F  factors  are  plotted  in  Figs.  19-22,  which  serve  to 
show  how  the  four  different  currents  vary  as  €2,  the  condenser  in  circuit 
2,  is  varied,  other  things  remaining  constant.  An  examination  of  these 
curves  shows  that  with  weak  coupling  and  tuned  circuits  the  variation 
in  amplitude  (due  to  beats)  is  from  maximum  to  zero  as  the  values  of  F"\ 
and  F'\  are  equal  in  magnitude  as  are  those  of  F"2  and  F'2.  For  tighter 

couplings  the  ratio  of  ^-  must  be  different  than  unity  to  make  F"i=F'i 


CURRENTS   IN   COUPLED   CIRCUITS 


235 


or  F"z  =  F'z.     Furthermore  with  other  coupling  than  very  loose  no  ratio  of 

^  can  be  found  which  will  make  both  F"i  =  F\  and  F"2  =  Ff2  so  that, 
AI 


-.5 


FIG.  19. — Values  of  the  F  coefficients  for  10%  coupling. 
1.0 


1 
Ratio 


FIG.  20. — Values  of  the  F  coefficients  for  30%  coupling. 

except  for  very  weak  coupling  the  beats  are  not  complete  in  both  circuits, 
i.e.;  the  minimum  amplitude  is  not  zero.    It  may  be  made  zero  in  circuit  1 


236 


LAWS  OF  OSCILLATING  CIRCUITS 


[CHAP.  IV 


for  any  value  of  coupling  by  the  proper  amount  of  de-tuning,  but  the  values 
of  F'f2  and  F'2  are  such  as  to  preclude  the  possibility  of  zero  amplitude  beats 


1.0 


\ 


Rdtio 


0.5 


FIG.  21. — Values  of  the  F  coefficients  for  50%  coupling. 


l.o 


i 

Ratio 


,fc=:1.0 


15 


FIG.  22. — Values  of  the  F  coefficients  for  100%  coupling. 

for  any  except  the  weakest  coupling,  no  matter  how  much  X2  and  Xi  are 
made  to  differ. 

A  critical  examination  of  the  foregoing  analysis  shows  that  maximum 


DECREMENTS  IN  COUPLED  CIRCUITS  237 

current  occurs  in  the  second  circuit  when  the  ratio  of  -^  is  slightly  greater 

AI 

than  unity.  This  might  have  an  important  bearing  on  the  use  of  a  wave 
meter;  this  instrument  is  a  coil  and  variable  condenser  which  has  an 
ammeter  (or  other  device)  for  indicating  resonance  with  the  circuit,  being 
tested.  A  precise  analysis  shows  that  maximum  current  will  occur  in 
this  wave  meter  when  its  natural  period  is  somewhat  longer  than  that 
of  the  circuit  being  tested;  as  maximum  current  in  the  wave  meter  is 
ordinarily  taken  to  signify  resonance  with  the  circuit  tested  it  is  evident 
that  an  appreciable  error  might  be  incurred. 

It  appears,  however,  that  with  a  coupling  between  wave  meter  and 
the  circuit  tested  as  high  as  10  per  cent  the  error  in  wave  meter  reading 
is  less  than  1  per  cent  and  as  the  wave  meter  coupling  is,  in  practice, 
seldom  more  than  1  per  cent  or  2  per  cent,  the  error  is  probably  well  within 
the  precision  of  measurement. 

The  previous  analysis  of  amplitudes,  resulting  in  Eqs.  (68)  and  (69) 
for  the  currents  in  the  two  circuits,  was  carried  out  without  considering 
the  resistance  terms  in  the  original  equations,  (28)  and  (29).  The  consid- 
eration of  damping  would  have  greatly  complicated  the  derivations,  and 
the  damping  factors  can  be  introduced  now  without  invalidating  the  pre- 
vious work. 

The  damping  factor  of  the  high-frequency  wave  is  the  same  for  the 
high-frequency  current  in  both  circuits  and  similarly  for  the  low-frequency 
wave.  If  we  call  the  damping  factors  a"  and  a',  it  is  possible  to  derive 
the  relations 1 


a'  —  0/1  _i_  7,\(oT     f~oT/> (71) 


a"  being  for  the  high-frequency  currents  and  a    for  the  low-frequency 
currents. 

It  is  to  be  noticed  that  if  Eqs.  (70)  and  (71)  are  changed  to  give  decre- 
ments (the  two  circuits  being  tuned),  they  assume  the  forms 

„_      1 
VT 
and 

.,  _ 

- 


1  A.  Oberbeck,  Wied.  Ann.  der  Physik,  1895,  Vol.  55,  p.  623. 


238 


LAWS  OF  OSCILLATING  CIRCUITS 


[CHAP.  IV 


where  5i  and  62  are  the  decrements  of  the  primary  and  secondary  circuits, 
respectively.  These  solutions  are  approximate  and  good  only  when  the 
decrements  are  low. 

The  complete  solutions  then  become, 

i 

(72) 
.     .     (73) 


12  =  ca 


sn 


Actual  Shapes  of  Currents  in  Coupled  Circuits. — In  Figs.  23-26  are 
shown  oscillograms  of  currents  in  each  of  two  coupled  circuits,  the  cir- 


FIG.  23. — Currents  in  coupled  tuned  circuits  with  42.4%  coupling. 

cuits  being  practically  identical.  For  each  L  =  .0395  henry  and  C  =  39.5 
microfarads.  The  coefficients  of  coupling  were  .424,  .282,  .114,  and 
.0707,  respectively,  for  the  several  curves.  The  films  do  not  quite  bear 
out  the  preceding  theory  on  amplitudes,  as  the  values  of  F\  and  F\" 
are  evidently  not  near  enough  in  amplitude  to  neutralize  each  other  for 
even  the  minimum  coupling,  7.07  per  cent.  It  is  quite  likely  that  the 
rather  high  decrement  of  the  circuit  had  an  appreciable  effect  on  the 
various  amplitude  factors,  not  accounted  for  in  the  previous  analysis. 

Frequency  of  the  Actual  Complex  Current. — By  inspection  of  the  films 
shown  in  Figs.  23-26  it  is  seen  that  the  time  between  successive  zero  points 
in  the  current  wave  is  practically  constant  (indicating  constant  frequency) ; 
in  fact,  careful  measurement  shows  the  frequency  constant  (for  Fig.  26), 
within  about  1  per  cent,  except  at  the  points  of  minimum  amplitude,  where 


CURRENTS   IN   COUPLED  CIRCUITS 


239 


the  time  between  successive  zero  points  changes  very  much.  Just  what 
changes  take  place  in  the  magnitude  and  phase  of  the  current  at  this 
time  depends  altogether  upon  the  relative  amplitudes  of  the  two  component 
currents. 


FIG.  24. — Currents  in  coupled  tuned  circuits  with  28.2%  coupling 


FIG.  25. — Currents  in  coupled  tuned  circuit?  with  11.4%  coupling 

In  Figs.  27,  28,  and  29  are  shown  three  possible  conditions  at  this 
time  of  minimum  amplitude  of  the  actual  current.  In  Fig.  27  we  have 
shown  the  condition  for  Fi"  =  .5  F'i,  in  Fig.  28  for  F"i  =  .9  F'\  and  in 


240 


LAWS  OF  OSCILLATING  CIRCUITS 


[CHAP.  IV 


Fig.  29  for  7<"'i  =  1.25  F'i.  For  all  three  figures  we  have  «"=1.20«', 
which  means  a  value  of  coupling  of  the  two  circuits  of  about  20  per  cent. 

It  might  seem  that  as  the  frequency  (time  between  successive  zero 
points)  of  this  "  beating  "  current  is  constant,  that  a  third  circuit,  coupled 
to  the  circuit  carrying  this  complex  current,  would  respond  most  strongly 
if  tuned  to  this  frequency.  As  a  matter  of  fact  but  little  response  will 
be  had  in  this  third  circuit  if  tuned  to  this  actual  frequency;  if  tuned  to 
either  of  the  component  currents  of  this  actual  complex  current,  however, 
a  strong  response  will  be  obtained. 

Thus  suppose  the  two  circuits  of  Fig.  16  are  each  adjusted  for  a  natural 
period  of  100  cycles,  and  they  are  coupled  20  per  cent.  Then  the  two 


FIG.  26. — Currents  in  coupled  tuned  circuits  with  7.07%  coupling. 

frequencies  generated,  when  the  condenser  in  circuit  1  discharges,  will  be 
(by  Eqs.  (44)  and  (45)) 


r= 

f  = 


100 


Vl-0.2 

100 

Vl+0.2 


=  111.7  cycles; 
=  91.2  cycles. 


The  oscillatory  current  in  each  of  the  circuits  will  have  a  period  of 
.01  second  (except  at  the  minimum  amplitude  points)  but  if  a  third  cir- 
cuit loosely  coupled  to  either  of  the  others  is  tuned  to  a  natural  period 
of  .01  second  the  current  induced  in  it  will  be  much  smaller  than  if  it 
(the  third  circuit)  is  tuned  to  a  natural  frequency  of  either  111.7  or  91.2. 


CURRENTS  IN  COUPLED  CIRCUITS 


241 


i 

x" 

5 

\ 

/ 

\ 

/ 

\ 

/ 

/ 

/ 

\ 

/ 

/ 

/ 

\ 

/ 

/  J 

•— 

"^ 

\ 

/ 

/ 

/ 

^ 

\ 

/} 

s^ 

\ 

\ 

/ 

\ 

, 

i 

J 

1 

\ 

/ 

V, 

V 

/ 
1 

1 

/ 
^ 

f\ 

t 

\ 

\ 

\ 

/ 

\ 

y 

1 

/ 

/ 

1 

\ 

\ 

a 

/ 

\ 

/ 

/ 

/ 

1 

\ 

S 

> 

• 

\ 

/ 

3( 

.0 

3 

15 

2r 

°/ 

22 

i 

1 

to 

1[ 

5 

9 

0 

4 

5 

/ 

K 

4 

5 

9 

0 

i: 

5 

18 

\ 

I2 

*/ 

2? 

0 

3 

5 

¥ 

0 

.. 

/ 

( 

\ 

i 

v 

\ 

\ 

/ 

J 

1 

/ 

\ 

/ 

\ 

*s 

s 

I 

V 

/ 

/ 

/ 
/ 

V 

i 

\ 

/  > 

S 

/ 

( 

' 

1 

\ 

s 

'l 

1 

\ 

\ 

{/ 

\ 

. 

/ 

/ 

1 

\ 

s>^. 

_^- 

X/' 

/ 

/A 

Ctl 

n\ 

cu 

rei 

it 

V 

/ 

/ 

/ 
/ 

\ 

t 

</ 

/ 

F! 

"= 

0.5 

FI 

1 

/ 

I'l 

V 

/ 

0) 

,,_ 

1.2 

co' 

\ 

-s 

FIG.  27. — Form  of  current  and  minimum  amplitude,  high-frequency  current   much 

smaller  than  low-frequency. 


\ 


360 


180 


90 


NDO 


„ 


27 


3  0 


\ 


5 


X 


jl 


I 


z1 


-Actu 


Current 


f0.9F 


1.2  w' 


FIG.  28. — Form  of  current  at  minimum  amplitude,  high-frequency  current  of  nearly 
the  same  amplitude  as  low-frequency. 


242 


LAWS  OF  OSCILLATING  CIRCUITS 


[CHAP.  IV 


The  magnitude  of  current  in  this  third  circuit,  as  its  natural  frequency 
is  changed  by  changing  the  value  of  its  condenser,  will  be  about  as  indi- 
cated in  Fig.  30.  The  reason  for  this  weak  response  to  the  100-cycle 
tuning  is  the  reversal  of  the  phase  in  the  exciting  current  at  the  minimum 
amplitude  points;  what  current  is  built  up  in  circuit  3  during  time  t—ti, 
Fig.  31,  is  destroyed,  or  neutralized  by  the  action  during  time  t\  —  fe,  because 
of  the  phase  reversal  in  the  inducing  current  at  time  t\. 


: 


V 


360 


no 


<>0 


i  .0 


3  0 


tu 


1  current 


1.25  FI 


1.2  w' 


W 


FIG.  29. — Form  of  current  at  minimum  amplitude,  high-frequency  current  greater  than 

low-frequency. 


Vector  Representation  of  Current  in  Coupled  Circuits. — Such  a  func- 
tion as  that  given  in  Eq.  (72)  can  be  represented  vectorially  but,  of  course, 
the  vector  diagram  is  not  of  the  ordinary  type.  If  we  let  the  instantane- 
ous value  of  the  current  be  represented  by  the  projection  on  the  y  axis 
of  the  resultant  vector  obtained  by  adding  F"ie~a"'  and  F\e~at  the 
construction  will  be  as  shown  in  Fig.  32.  When  t  =  0  the  two  vectors  co- 
incide in  position ;  with  increase  in  time  the  F"\  vector  advances  its  phase 
over  that  of  F'\,  so  after  F'\  has  advanced  90°,  as  shown  at  OA  the  vector 
F"\y  has  moved  to  position  OB.  The  resultant  of  these  two  vectors  OR, 
gives,  by  its  projection  in  the  OY  axis,  OD,  the  instantaneous  value  of 


CURRENTS  IN  COUPLED   CIRCUITS 


243 


the  actual  current  i\.  As  the  two  vectors  OA  and  OB  rotate  their  mag- 
nitudes must  continually  diminish  to  keep  them  equal  to  F"\Ca>t  and 
F'\Ca>i.  The  loci  of  the  terminals  of  the  vectors  are  logarithmic  spirals 
about  the  point  0.  The  logarithm  of  the  ratio  of  the-  values  of  a  vector, 
in  two  successive  passages  through  the  same  phase  gives  the  decrement 


\ 


90  100  110 

Natural  frequency  of  third  circuit 


120 


FIG.  30.  —  Amplitude  of  current  in  a  third  circuit  coupled  very  loosely  to  either  of  the 
two  coupled  oscillating  circuits. 


of  the  current  represented  by  that  vector;  thus  we  have  log£  77^7 


5"  the 


logarithmic  decrement  of  the  current  I"\. 

The  unusual  motion  of  this  resultant  vector  as  the  two  component  vec- 
tors pass  through  phase  opposition  is  indicated  in  Fig.  33.     Vector  OA,  the 


FIG.  31. — At  minimum  amplitude  points  the  actual  current  in  either  of  the  two  oscil- 
lating circuits  reverses  its  phase. 

one  with  less  angular  velocity,  is  shown  stationary  and  the  vector  OB 
is  shown  in  several  successive  positions  around  its  phase  opposition  posi- 
tion; OB  is  slightly  greater  in  magnitude  than  OA.  With  OB  in  the 
position  indicated  by  OB\,  the  resultant  of  OA  and  OBi  is  shown  by  ORi, 
etc.  It  may  be  seen  that  this  resultant  vector  moves  through  the  angle 
RiORr>,  which  is  more  than  180°,  while  the  vector  OB  has  moved  about 
45°. 

The  case  of  OB  being  smaller  than  OA  is  given  in  Fig.  34;    in  this 
case  when  OB  goes  through  its  opposition  phase  the  resultant  vector, 


244 


LAWS  OF  OSCILLATING  CIRCUITS 
Y 


[CHAP.  IV 


FIG.  32. — For  damped  sine  waves  the  terminals  of  the  e.m.f.  vectors  must  lie  on  log- 
arithmic spirals. 


FIG.  33. — Resultant  vector  when  high-frequency  current  has  the  greater  amplitude. 


CURRENTS  IN  COUPLED  CIRCUITS 


245 


instead  of  speeding  up  as  it  did  in  Fig.  33,  slows  down  and  goes  through 
the  successive  values  OR\,  OR2,  OR3,  etc.,  for  the  correspondingly  marked 


FIG.  34. — Resultant  vector  when  low-frequency  current  has  the  greater  amplitude* 


FIG.  35. — Resultant  vector  when  both  currents  have  the  same  amplitude. 

positions  of  OB.  If  the  two  vectors  OB  and  OA  happen  to  have  equal 
magnitudes  as  they  go  through  phase  opposition  the  successive  positions 
and  values  of  the  resultant  vector  are  as  shown  in  Fig.  35;  for  this  con- 


246  LAWS   OF   OSCILLATIXC,    CIRCUITS  {CHAP.  IV 

dition  when  the  two  vectors  are  180°  out  of  phase  the  resultant  vector 
is  zero. 

It  is  quite  possible  so  to  adjust  the  tuning  of  the  two  circuits  that 
the  vector  OB  is  greater  than  OA  at  the  start  of  the  oscillations;  then 
as  the  oscillations  continue,  OB,  having  greater  damping  than  OA,  will 
become  equal  to  OA  and  then  smaller.  Hence  in  three  successive  beats 
it  is  possible  to  have  the  resultant  vector  OR  go  through  phase  changes  as 
depicted  in  Figs.  33,  34  and  35,  respectively,  as  the  amplitudes  of  the  actual 
current  goes  through  its  minimum  values.  The  effects  of  these  peculiar 
angular  velocities  of  the  resultant  vector,  in  combination  with  its  changes 
in  magnitude,  account  for  the  peculiar  form  of  the  actual  current  during 
the  one  or  two  cycles  of  minimum  amplitude.  It  is  seen  in  Figs.  27  and 
29  that  the  180°  phase  shift  which  occurs  at  the  point  of  minimum  ampli- 
tude may  be  produced  by  either  a  gain  of  180°  or  a  loss  of  180°  at  this 
time.  Fig.  27  shows  a  loss  and  Fig.  29  a  gain  of  nearly  180°  during  the 
time  shown  in  those  curves. 

Frequency  of  Beats. — The  beats  are  not  well  pronounced  unless  the 
two  circuits  are  tuned  to  the  same  natural  frequency;  in  this  case  all  of 
the  energy  surges  back  and  forth  from  one  circuit  to  the  other.  With 
untuned  circuits  only  a  part  of  the  energy  is  exchanged  between  the  two, 
most  of  it  remaining  in  the  primary  circuit;  in  this  case  the  beats  are  not 
so  pronounced  as  for  the  tuned  circuits,  because  it  is  really  the  to-and-fro 
flow  of  the  energy  which  gives  the  beats 

In  the  case  of  tuned  circuits  the  two  frequencies  are  given  by  Eqs. 
(44)  and  (45), 

u/'  =  o/-         J]  and  «'  =  «(-         A 
Wl-fc/  \Vl+kJ 

Hence 

w"-V  =  a/  -JL, — 7±=}~<*k.      .  .     (74) 

Wl-.f*     Vl+fc/~ 

This  holds,  of  course,  for  low  values  of  k  only. 

As  the  number  of  beats  per  second  is  equal  to  the  difference  in  frequency 
per  second  of  the  two  component  frequencies,  we  must  have  the  number 
of  beats  per  second  which  are  given  by  the  relation  N=fk. 

We  have  shown  previously  that  the  frequency  of  the  complex  current 
for  tuned  circuits  (except  at  the  minimum  amplitude  point)  is  /.  The 
number  of  cycles  of  current  per  beat  is  therefore  obtained  from  Eq.'  (74) 
by  writing, 

N=f"-f'=fk, 
where  N=  beats  per  second.    From  this,  we  get 

(75) 


ACTION  OF  QUENCHING  SPARK  GAP  247 

This  equation  is  useful  in  determining  the  coupling  of  a  pair  of  circuits 
from  the  shape  of  the  complex  wave  of  current.  Thus  if  there  is  one  beat 
for  five  cycles  of  current  the  coupling  must  be  20  per  cent. 

Form  of  Secondary  Current  if  Primary  Circuit  is  Opened  at  the  Right 
Time. — The  two  circuits  of  Fig.  16  are  used  in  practically  every  radio 
spark  transmitting  set;  the  condenser  €2  is,  in  the  actual  sets,  the  capacity 
of  the  antenna  and  part  of  the  resistance,  Rv  is  the  radiation  resistance  of 
the  antenna.  From  the  foregoing  analysis  of  the  current  in  circuit  2  it 
is  evident  that  two  wave  lengths,  X"  and  X',  would  be  radiated  from  the 
antenna;  this  is  undesirable  both  from  the  standpoint  of  efficiency  and 
interference,  this  latter  factor  being  so  important  that  government  license 
will  be  granted  only  to  those  stations  in  which  such  precautions  have  been 
taken  that  practically  all  their  power  is  radiated  in  one  wave. 

As  previously  stated,  all  the  energy  (to  be  transformed  into  oscillatory 
power)  is  originally  stored  in  condenser  Ci;  when  the  switch  S  is  closed 
this  electric  energy  starts  surging  back  and  forth  from  L\  to  Ci  and  also 
starts  to  flow  over  to  circuit  2.  If  the  two  circuits  are  properly  tuned 

all  of  the  energy  will  have  been  transferred  to  circuit  2  in  -^j-  cycles; 

2  K 

unless  prevented  from  doing  so  the  energy  then  starts  to  flow  back  to 
circuit  1.  Suppose,  however,  that  circuit  1  is  opened  by  some  device  or 
other,  at  that  instant  when  all  of  its  energy  has  been  transferred  to  cir- 
cuit 2;  the  retransfer  of  the  energy  to  circuit  1  is  made  impossible  Because 
no  current  can  flow  in  circuit  1  if  it  is  open. 

Such  an  action  is  accomplished  by  a  "  quenched  "  spark  gap  to  be 
described  in  detail  in  Chapter  V.  The  forms  of  current  in  the  primary 
and  secondary  circuit  for  this  case  are  as  indicated  in  Fig.  36;  the  curves 
are  drawn  for  a  coupling  of  20  per  cent.  The  number  of  cycles  per  beat 
for  such  a  coupling  is  five;  hence  the  time  A—B  during  which  energy  is 
being  transferred  to  the  secondary  (being  one-half  the  time  of  a  beat) 
will  be  2J  cycles.  At  time  B  the  primary  circuit  is  opened  and  from  this 
time  on  the  secondary  circuit  oscillates  just  as  if  the  primary  circuit  was 
not  present;  in  fact,  electrically,  circuit  1  is  not  present,  it  being  open  at 
the  spark  gap  after  time  A-B. 

The  form  of  the  current  in  the  secondary  circuit  during  time  A-B 
will  approximate  that  given  by  Eq.  (73);  this  equation  is  not  strictly 
applicable  because  of  the  variable  resistance  (spark  gap)  in  circuit  1. 
However,  the  resistance  of  the  spark  gap  is  probably  negligible  compared 
to  the  resistance  due  to  the  coupling  of  circuit  2  to  circuit  1,  so  that  Eq. 
(73)  closely  represents  the  form  of  current  during  time  A-B.  After  time 
B  circuit  1  is  disconnected  (by  the  opening  of  the  spark  gap)  and  the 
equation  of  secondary  current  is  fixed  by  Eq.  (11),  the  frequency  and 
damping  of  the  current  being  fixed  by  the  secondary  constants  only. 


248  LAWS  OF  OSCILLATING  CIRCUITS  [CHAP.  IV 

The  proper  value  of  E  to  put  in  Eq.  (11)  is  very  nearly  equal  to 


where  E  is  the  voltage  of  condenser  C\  when  discharge  began, 

7?  7? 

'  A—  B. 


With  the  conditions  as  represented  -in  Fig.  36  the  current  in  circuit 
2  (except  for  the  first  one  or  two  alternations)  is  of  frequency  /,  the  nat- 
ural frequency  of  circuit  2,  and  the  power  is  practically  all  radiated  at 
this  one  frequency. 


FIG.  36. — Forms  of  primary  and  secondary  currents  if  primary  circuit  is  opened  at  the 

first  minimum. 

Possibility  of  No  Beats  without  a  Quenching  Gap. — If  the  damping 
of  the  circuits  is  high  and  coupling  is  loose  the  beating  phenomena  will 
be  absent,  even  if  the  spark  gap  in  the  primary  does  not  offer  any  quench- 
ing action.  This  is  illustrated  by  Fig.  37,  in  which  oscillograms  of  pri- 
mary and  secondary  current  are  shown  for  the  circuit  of  Fig.  16,  there 
being  no  spark  gap  at  all  in  the  primary  circuit.  The  two  circuits  were 
tuned  alike,  the  coupling  was  weak,  ft  =  .07,  and  the  decrement  of  each 
circuit  was  high,  5i  =  62  =  .30. 

This  method  of  getting  a  current  in  the  secondary  of  essentially  single 
frequency  is  of  no  use  to  the  radio  engineer,  because  it  really  means  that 
most  of  the  energy  originally  stored  in  C\  is  dissipated  as  heat  in  the 
primary  circuit;  but  little  power  is  supplied  to  the  secondary  circuit 
where  it  is  needed  to  carry  out  the  useful  function  of  radiation. 


IMPULSE  EXCITATION 


249 


Oscillatory  Discharge  in  One  Circuit  and  Non-Oscillatory  Discharge 
in  the  Other.  —  Under  exceptional  conditions  it  is  possible  with  coupled 
circuits  to  have  a  non-oscillatory  discharge  in  one  circuit  and  an  oscilla- 
tory discharge  in  the  other.  If  the  primary  circuit  has  a  high  decrement 
and  the  secondary  circuit  a  comparatively  low  decrement  then  when  the 
primary  condenser  discharges  there  may  be  a  single,  unidirectional  pulse 
in  the  primary  during  which  some  of  the  primary  energy  is  transferred 
to  the  secondary  and  some  of  it  used  as  heat  in  the  primary.  Such  a 
scheme  is  frequently  used  in  small  radio  sets,  and  goes  by  the  name  of 
"  impulse  excitation."  The  primary  circuit  has  generally  a  high  decre- 


/vv 


^^^^^^^•^•M«i^^^««M«MMH^^^MMHaMM^^HMMMHHl^MHH^B^HHHHH^^^HH^HMHHM^I^HH^HHOT^^^B 

FIG.  37.  —  Forms  of  currents  in  coupled  tuned  circuits  when  the  coupling  is  weak  and 

damping  is  high. 

ment,  having  a  large  condenser  and  only  one  or  two  turns  in  its  induct- 

r> 

ance.     This  gives  a  high  value  to  —^r,  especially  when  the  resistance  of  the 

ZJL 

spark  gap  is  taken  into  account.  In  addition  to  the  high  primary  decre- 
ment, the  gaps  used  in  this  method  of  generating  oscillations  are  of  the 
quenching  type  so  that  when  they  are  functioning  properly  but  one  pulse 
exists  in  the  primary  and  the  secondary  is  left  free  to  oscillate  at  its  own 
period  and  its  own  decrement. 

Oscillatory  Circuit  Excited  by  Continuous  Voltage.  —  In  case  a  circuit 
of  L,  C,  and  R,  in  series  is  connected  to  a  source  of  continuous  voltage 
E,  Fig.  38,  the  equation  of  reactions  is 


(76) 


By  differentiating  once  this  equation  becomes  the  same  as  Eq.  (1),  and 
so  its  solution  must  be  the  same.    The  same  three  cases  are  to  be  con- 


250  LAWS   OF  OSCILLATING   CIRCUITS  [CHAP.  IV 

sidered  here  as  they  were  for  Eq.  (1) ;  the  more  important  one  of  the  solu- 
tions being  that  of  Eq.  (11).  The  initial  and  final  conditions  of  the  problems 
are  different  than  those  considered  previously.  Evidently  at  t  =  Q,  vc  =  Q 
and  at  t  =  <x>,  vc  =  E;  these  conditions  affect  the  equation  of  voltage  across 
the  condenser  terminals,  which  becomes  approximately, 

-—             /     \ 
e  2^cofi-~ j (77) 

This  equation  brings  out  the  interesting  fact  that  the  maximum  volt- 
age across  the  condenser  in  such  a  circuit  as  that  given  in  Fig.  38  is  nearly 

double  that  of  the  source  of  e.m.f.  to 
which  the  circuit  is  connected.  This 
is  illustrated  by  the  film  shown  in 
Fig.  39;  the  voltage  of  the  c.c.  line  to 

fpnoQQQQ I  which      the      circuit      was      connected 

1  was    105  volts,  whereas    the    maximum 

FIG.   38.— Oscillatory  circuit  con-      potential  difference   across   the    conden- 
nected  to  a  source  of  continuous-      ser  was   190    voltg>      It  ig    evident    from 

this  oscillogram  that  if  the  dielectric 
strength  of  a  condenser  is  to  be  tested 

by  connecting  it  to  a  source  of  continuous  e.m.f.,  a  resistance  should  be 
used  in  series  with  the  condenser  of  sufficient  magnitude  to  make  the 
circuit  aperiodic.  If  this  is  not  done  the  maximum  voltage  across  the 
condenser  is  not  E,  the  voltage  of  the  line  used  for  testing,  but  is  equal 

5 

to  E(l  +  e  2"),  where  <5  is  the  decrement  of  the  circuit. 

Oscillatory  Circuit  Excited  by  Energy  Stored  in  Inductance. — In 
certain  radio-testing  circuits  oscillations  are  produced  not  by  the  energy 
stored  in  a  condenser  but  by  the  energy  in  the  magnetic  field  of  the  induct- 
ance. The  circuit  is  indicated  in  Fig.  40;  in  the  actual  testing  set  the 
battery  circuit  is  made  and  broken  many  times  a  second,  perhaps  1000, 
the  function  of  the  switch  being  performed  by  the  contact  points  of  a 
small  buzzer.  When  the  switch  $  is  closed  the  condenser  C  charges  at 
once  to  battery  voltage  and  the  current  through  L  and  R  rises  on  a  log- 
arithmic curve — Eq.  (10),  p.  32,  to  a  value  E/R,  the  magnetic  energy  in  the 

T  J?2 
coil  being  -^^.     When   the   switch   is  opened    this   magnetic  energy   is 

ZH 

emptied  into  the  condenser  C,  and  then  the  energy  surges  back  into  L 
as  described  in  the  first  paragraph  of  this  chapter. 

At  the  end  of  the  first  quarter  of  a  cycle  of  the  oscillation  all  the  energy 
from  the  coil  is  in  the  condenser;  it  is  then  charged  to  such  a  potential 


CIRCUIT  EXCITED  BY  CONTINUOUS  VOLTAGE 


251 


252 


LAWS  OF  OSCILLATING  CIRCUITS 


[CHAP.  IV' 


difference  Ee  that  we  have  (if  the  decrement  of  the  circuit  is  so  low  that 
the  damping  for  one-quarter  of  a  cycle  may  be  neglected), 

CTP     LP         /C      L 


=    2C 

' 


or 


(78) 


The  cycle  of  events  in  such  a  circuit  as  shown  in  Fig.  40  is  shown  in 
the  film  of  Fig.  41  ;  of  course,  all  the  constants  of  the  circuit  used  in  getting 
this  film  are  much  greater  than  those  used  in  the  so-called  "  buzzer  wave- 
generator  "  used  in  radio,  but  the  form  of  voltages  and  currents  are  nearly 
the  same  as  those  occurring  in  the  radio  circuit. 

Oscillating  Circuits  Excited  by  being  Connected  to  a  Line  of  Alter- 
nating e.m.f.  —  If  a  circuit  of  L,  R,  and  C,  in  series,  Fig.  42,  is  suddenly 

switched  to  an  alternating  current 
line,  the  current  must  be  zero,  no 
matter  at  what  point  the  e.m.f.  wave 
the  switch  is  closed;  in  general, 
the  condenser  of  the  circuit  will  not 
be  charged.  Now  in  the  steady 
state  the  current  must  have  a  certain 
value  for  any  given  value  of  e.m.f. 
as  fixed  by  Eqs.  (35)  and  (36)  of 
Chapter  I.  Also  the  condenser  must 
have  a  definite  charge  for  this  value 
of  impressed  e.m.f.  It  is  evident, 

therefore,  that  in  general  the  initial  conditions,  when  the  switch  is  closed, 
will  not  satisfy  the  conditions  required  by  the  steady  state. 

For  this  reason  the  current  for  the  first  few  cycles  after  switching  the 
circuit  to  the  line  will  be  of  irregular  form;  the  circuit  requires  time  to 
"  settle  down  "  to  the  steady  state.  Mathematically  this  is  accomplished 
by  adding  to  the  equation  for  the  steady  current  a  suitable  damped 
oscillation,  the  magnitude  of  which  depends  upon  the  time  the  switch  is 
closed  and  the  frequency  of  which  is  fixed  by  the  L  and  C  of  the  circuit. 

The  actual  current  after  closing  the  switch  is  therefore  the  sum  of 
the  steady  value  of  current  and  a  damped  oscillation  at  the  natural  period 
of  the  circuit,  the  two  sufficing  to  satisfy  the  required  initial  conditions 
on  closing  the  switch. 

If  the  impressed  voltage  is  e  =  E  sin  pt,  the  circuit  having  constants, 

L,  C  and  R  and    «T 


-0),    .     .     (79) 


FIG.  40. — Oscillatory  circuit  to  be  ex- 
cited by  stored  magnetic  energy. 
This  circuit  is  the  same  as  used  for 
"  buzzer  excitation  "  of  radio  circuits. 


__LV 

pC) 


CIRCUIT  CONNECTED  TO  ALTERNATING  VOLTAGE  253 


254  LAWS  OF  OSCILLATING    CIRCUITS  [CHAP.  IV 

in  which  tan  </>  =  (  pL  —  -^  j  /R, 

a  =  7>T  anc^  w  =  V  77^'  approximately, 

and  t'  is  the  time  counted  from  the  start  of  the  supposititious  transient 
oscillatory  current;  it  is  sometimes  written  (t+At)  where  At  is  the  time 
between  the  start  of  the  supposititious  transient  term  and  the  closing  of 
the  switch—  this  increment  of  time  is  indicated  in  Fig.  44. 

A  and  tf  are  to  be  suitably  determined  to  satisfy  the  initial  condition 
that  i  =  Q  and  vc=Q.     This  condition,  vc  =  Q,  supposes  the  condenser  to  be 

uncharged  at  the  time  of  switching  the 
circuit  to  the  line;  if  it  is  charged  to  a 
certain  potential  difference  V,  then  the 
initial  conditions  are  i  =  Q,  vc=V. 

Let  us  suppose  the  steady  state  of  the 
circuit   is   as   represented   in  Fig.  43,  and 

„  further  let  us  suppose  that  the  'switch  is 

FIG.  42.—  Oscillatory  circuit  to  .  .    .. 

be    connected    to    source   of      closed  at  the  Phase  indicated  by  fl.     In  the 
alternating-current  power.          steady  state  the  current  should  be  /'  and 

the  voltage  across  the  condenser  should  be 

V.  Actually  the  current  at  the  time  of  closing  the  switch  is  zero,  and 
we  also  suppose  an  uncharged  condenser,  so  that  vc  =  Q.  We  must  then 
determine  t'  and  A  of  Eq.  '(79)  that  these  initial  conditions  are  satisfied. 
The  equation  for  voltage  across  the  condenser,  due  to  the  transient 
term  only,  we  write, 

vc=E0e-at'  cosut',       .......     (80) 

and  hence,  the  current  due  to  the  transient  term  is, 

1  =  C  ~JT  =  -uCEoe-at'  sin  w/  —  aCEoe-al'  cos  ut'. 
at  v 

We  here  make  the  same  assumption  we  have  previously  made  for 
similar  circuits,  that  a  is  negligible  compared  to  w,  and  so  we  get, 

i=  -wCEoe-at'sm  co/'  .....    -.     .     .     (81) 

Using  the  condition  that  the  voltage  across  the  condenser  must  be 
zero  at  the  time  of  closing  (lie  switch,  we  have 


in  which  t'o  is  the  value  of  t'  when  the  switch  is  closed. 
Then 


.#„=  -  (82) 

e   at  °  cos  tot  o 


CIRCUIT  CONNECTED  TO  ALTERNATING  VOLTAGE 


255 


Also, 


'  =  0,  so  from  (81)  using  also  (82) 


/'=_"^ 


sn 


or 


tan  «C0=  - 


(83) 


Time  of  closing  switch 


FIG.  43. — Proper  "steady  state"  values  of  voltages  and  current  of  circuit  of  Fig.  42, 

at  time  of  closing  switch. 

In  case  the  damping  of  the  circuit  is  small  this  equation  may  be  written 

tan  0/0=  -y-'\c° 

From  this  equation  we  get  tan  o/o  and  so  may  find  the  value  of  cos  ut'o. 
Knowing  co£'o  and  w  we  get  £'o  and  so  can  calculate  €~at'°  and  then  substi- 
tuting in  (82),  we  get  EQ]  evidently  A=  -<*>CEo,  which  can  now  be 
substituted  in  Eq.  (79). 


256 


LAWS  OF  OSCILLATING  CIRCUITS 


[CHAP.  IV 


In  Fig.  44  are  reproduced  in  dotted  lines  the  current  and  voltage 
curves  of  Fig.  43  and  in  dashed  lines  the  transient  current  and  condenser 
voltage  determined  from  Eqs.  (83)  and  (82)  and  (81).  The  addition  of 


the  steady  value  of  current  and  the  transient  current  gives  the  full  line 
curve  which  is  the  actual  current  in  the  circuit  after  closing  the  switch. 
In  Fig.  45  is  shown  an  oscillogram  of  the  transient  current  after  switch- 
ing such  a  circuit  as  the  one  used  in  plotting  the  curves  of  Fig.  44.     From 


PERIODIC  DISTURBANCES  IN  OSCILLATORY  CIRCUIT         257 


Figs.  44  and  45  it  may  be  seen  that  on  switching  a  circuit,  of  L,  R,  and  C, 
in  series,  to  an  alternating  current  line  the  condenser  might  be  subjected 
to  much  higher  voltages  than  occur  in  the  steady  state,  nearly  twice  as 
much  if  the  damping  is  low. 


FIG.  45. — Oscillogram  of  transient  current  corresponding  to  condition  shown  in  Fig.  44. 

Periodic  Disturbances  in  a  Resonant  Circuit. — In  every  radio  spark 
set  there  is  a  circuit  the  equivalent  of  that  shown  in  Fig.  46;  in  place  of 
the  switch  shown  there  is  a  spark  gap  which  performs  the  same  function. 
An  alternator  supplies  power  to  a  condenser  C,  through  a  transformer  T't 

_  once  every  cycle  (or  alterna- 

tion) the  condenser  is  short 
circuited  for  a  very  short  time, 
in  an  actual  set  by  the  spark 
gap  breaking  down,  in  the  set 
from  which  the  following  os- 

Transformer  i  cillograms  were  taken,   by  a 

FIG.  46. — Elementary  circuit  illustrating  the  action  suitable  revolving  switch.  The 
occurring  in  every  spark  set  when  the  spark  time  of  switch  closure  was 
gap  breaks  down.  adjusted  for  maximum  volt- 

age  in  the  secondary  circuit 

and  took  place  at  the  same  phase  of  each  cycle.  The  voltage  across 
the  condenser  and  current  in  the  secondary  of  the  transformer  for 
this  case  have  been  worked  out  theoretically,  but  they  are  rather 


Alternator 


258  LAWS  or  OSCILLATING    CIRCUITS  [CHAP.  IV 

unwieldy,  as  one  might  suppose  after  an  elementary  consideration  of  the 
problem.1 

For  each  closure  of  the  switch  S,  a  transient  term  is  introduced  into 
the  circuit,  and  as  the  damping  is  not  sufficient  to  eliminate  one  transient 
before  another  is  introduced,  the  actual  current  and  voltage  consist  of  the 
steady  values  with  a  whole  series  of  transients  superimposed.  The  form 
of  voltage  and  current  depend  largely  upon  the  ratio  of  the  frequency  of 
the  impressed  e.m.f.  to  the  natural  frequency  of  the  circuit. 

In  Figs.  47,  48,  and  49  are  shown  the  forms  of  voltage  across  the  con- 
denser arid  current  in  the  secondary  of  the  transformer  for  three  values 


FIG.  47. — Voltage  and  current  in  such  a  circuit  as  that  shown  in  Fig.  46,  the  switch  S 
being  closed  synchronously.  Natural  frequency  of  secondary  circuit  greater  than 
alternative  frequency. 

of  this  ratio.  In  Fig.  47  the  natural  period  was  less  than  that  of  the 
alternator,  in  Fig.  48,  the  two  were  equal,  and  in  Fig.  49,  the  natural 
period  was  greater  than  that  of  the  alternator.  As  the  films  were  taken 
at  high  speed  they  are  not  very  distinct,  so  two  cycles  have  been  dotted 
in  with  ink. 

It  will  be  seen  at  once  that  any  mathematical  expression  to  represent 
these  curves  must  be  a  complex  one.  With  the  switch  adjusted  to  mtiko 
one  closure  per  cycle  the  circuit  is  a  rectifying  one;  if  the  voltage  across 
the  condenser  at  the  time  of  short  circuit  is  E  it  is  evident  that  each  cycle 

1  Fulton  Cutting,  "The  theory  and  design  of  Radio  Telegraphic  Transformers," 
Proc.  I.  R.  E.,  Vol.  4,  No.  2,  April,  1916.  This  article  serves  to  show  how  complicated 
an  exact  treatment  may  become;  in  Chapter  V,  p.  307-8,  are  shown  some  curves  which 
are  calculated  from  simpler  formulae,  which  curves  represent  quite  accurately  the  form  of 
disturbance  in  the  ordinary  spark  transmitting  set. 


PERIODIC   DISTURBANCES   IN    OSCILLATORY   CIRCUITS         259 

the  secondary  of  the  transformer  carries  more  in  one  direction  than  it 
does  in  the  other  a  quantity  of  electricity  equal  to  CE. 

Oscillating  Circuit  Excited  by  Pulse. — It  often  occurs  in  radio  work 
that  an  oscillatory  circuit   is  excited  by  a  unidirectional  pulse  of  some 


FIG.  48. — Similar  to  Fig.  47  but  with  secondary  circuit  having  a  natural  frequency  equal 

to  that  of  the  alternator. 


FIG  49. — Similar  to  Fig.  47  but  with  secondary  circuit  having  a  natural  frequency  less 

than  that  of  the  alternator. 

shape  or  other;  thus  it  is  quite  likely  that  atmospheric  disturbances  in 
radio  receiving  circuits  are  due  to  some  sort  of  highly  damped  oscillation 
or  a  series  of  short  pulses.  The  effect  of  a  pulse  on  a  resonant  circuit 


260  LAWS  OF  OSCILLATING  CIRCUITS  [CHAP.  IV 

will  depend  upon  two  factors,  the  ratio  of  the  duration  of  the  pulse  to 
the  natural  period  of  the  circuit,  and  the  intensity  or  amplitude  of  the 
pulse.  Also  to  a  minor  extent  the  exact  form  of  the  pulse  will  determine 
the  amount  of  disturbance  produced. 

The  simplest  kind  of  a  pulse  to  consider  mathematically  is  a  "square  " 
pulse,  one  in  which  the  voltage  rises  suddenly  from  zero  to  a  certain  value, 
holds  this  value  for  a  short  time  and  then  again  drops  suddenly  to  zero. 
If  such  a  pulse  of  voltage  is  introduced  into  a  circuit  consistent  of  L,  C, 
and  R,  in  series  the  shape  of  the  current  can  be  obtained  by  properly  com- 
bining the  solutions  of  Eqs.  (76)  and  (1).  Eq.  (76)  gives  the  conditions 
when  the  voltage  is  applied  to  the  circuit  and  Eq.  (77)  gives  the  voltage 
on  the  condensar  at  any  time  t  after  the  voltage  has  been  applied.  When 
the  pulse  of  voltage  ends,  Eq.  (1)  applies,  the  voltage  on  the  discharging 
condenser  being  that  determined  from  Eq.  (77). 

Thus  in  Fig.  50  is  shown  at  a  the  pulse  of  e.m.f.  introduced  into  the 
oscillating  circuit,  in  b  is  shown  in  full  lines  the  condenser  voltage  curve, 
determined  from  Eq.  (77)  and  in  the  dotted  line  the  current  produced 
in  the  circuit  by  the  introduction  of  voltage  E. 

Counting  t  =  0  at  the  beginning  of  the  pulse,  we  have 

^^U-*'  sin  co*,  (84) 

O>L/ 

and 

e-<cos«0,  (85) 


1  7? 

in  which  oo  =     .  _  and  a  =  pry-,  the  solution  being  approximate  as  a  has 
VLC  ^ 

been  considered  small  compared  to  co. 

If  the  pulse  has  a  duration,  T,  at  the  end  of  the  pulse  the  voltage  in 
the  condenser  is 

e-aTcosuT)  .......     (86) 


Now  at  the  end  of  the  pulse  the  solution  of  Eq.  (1)  is  available  if  we 
substitute  the  proper  initial  conditions.  The  circuit  solved  in  Eq.  (1) 
was  one  in  which  the  initial  conditions  were  a  charged  condenser  and  the 
zero  current.  By  inspection  of  Eqs.  (86)  and  (84)  it  is  evident  that  if 

we  make  T  =  -  the  current  at  the  end  of  the  pulse  is  zero  (sin  co  T  =  0) 

CO 


and  the  voltage  in  the  condenser  is  vc  =  E(l  +  e~aT),  as  cos  uT=  —1. 

The  equation  for  current  from  the  end  of  the  pulse  (for  length  of  pulse 
=TT/CO)  is  therefore, 

E 

i=  --  f 

CO.L/ 


EFFECT  OF  PULSE  OF  E.M.F.   ON   OSCILLATORY   CIRCUIT     261 

where  t'  is  reckoned  after  the  end  of  the  pulse.     This  current  is  shown  in 
curve  c,  Fig.  50.     At  time  t'  =  ^— ,  sin  co£'  =  1  and  the  value  of  current  is 

7^  S  35 


(87) 


<              T                "> 

E 

Length  of  pulse  =  ^  where    w^'ytt 
(a) 

| 

1'ir 

ne 

> 

^ 

^^ 

T 

/ 

1 

^ 

..^ 

> 

1 

\ 

/ 

\ 

/ 

s 

/ 

vr 

J. 

\ 

(b 

) 

/ 

\ 

. 

\ 

/ 

3 

/ 

\ 

y 

\ 

-s 

V 

/ 

\ 

/ 

\ 

/ 

'1 

X^ 

Sj 

\ 

/. 

\ 

/ 

\ 

1 

\! 

1 

\ 

/ 

\ 

s 

/ 

s- 

•*> 

\ 

( 

/      / 

\ 

UJ 

^ 

*/ 

s 

\ 

f     / 

\ 

I 

f 

^ 
\ 

/ 

^ 

O 

•> 

t 

\ 

/ 

' 

\ 

/ 

\ 

/i 

.. 

£ 

sin 

0) 

\ 

/ 

N 

/ 

\ 
\ 

/ 
f 

•^ 

/ 

x^ 

.s 

f 

\ 

\ 

^ 

/ 

' 

f 

"> 

/ 

\ 

/ 

\ 

^ 

f 

\ 

1 

y 

/( 

/ 

\ 

(Z 

o 

>- 

t' 

/ 

\ 

\ 

i 

\ 

/ 

\ 

\ 

I 

\ 

7 

\ 

7 

\ 

1 

11 

T 

- 

77T 

\ 

/ 

\ 

/ 

i 

f 

s, 

fY/' 

V 

/ 

\ 

/ 

\ 

/ 

i 

h- 

k 

-i-fi 

u/ 

)£ 

S 

n\ 

wt 

/ 

^ 

/ 

\ 

I 

\ 

/ 

\ 

f 

V. 

J 

FIG.  50. — Effect  of  introducing  a  rectangular  pulse  of  e.m.f.  into  an  oscillatory  circuit. 

This  is  the  maximum  current  obtainable  from  a  rectangular  pulse,  of 
amplitude  E,  no  matter  what  its  duration  may  be.  Any  duration  either 
more  or  less  than  TT/OJ  will  give  less  value  to  /max. 

A  more  fundamental  way  of  looking  at  the  problem  is  to  consider  a 
voltage  of  +  E  impressed  on  the  circuit  at  the  beginning  of  the  pulse,  and 
that  this  voltage  is  maintained;  at  the  end  of  the  pulse  a  voltage  of  —E 
is  impressed  on  the  circuit  and  maintained.  Each  of  the  impressed  volt- 
ages will  produce  a  current,  and  the  actual  current  at  any  time  is  the  sum 
of  the  two. 


262 


LAWS  OF  OSCILLATING   CIRCUITS 


[CHAP.  IV 


The  current  after  the  second  voltage  (  -  E)  is  impressed 


i=  + 


E 


snl  ">t 


— 

coL 


sn 


in  which  i  is  the  time  after  the  (+E)  voltage  is  impressed  and  i'  is  the 
time  after  the  second  voltage  (-E)  is  impressed.  If  the  interval  between 
the  application  of  these  two  voltages  is  TO,  then  the  current  after  time 
To  has  passed  is 


sn  w*  - 


sn 


FIG.  51. — Oscillogram  of  oscillatory  current  produced  by  short  pulse  of  e.m.f. 


If  the  damping  is  comparatively  small,  the  maximum  current  will 
occur  when  sin  co£',  and  sin  w(t'-\-To)  are  simultaneously  equal  to  unity 
and  of  opposite  sign.  Moreover,  it  is  evident  that,  because  of  the  damp- 
ing factors,  this  maximum  current  will  have  its  greatest  value  when  the 
above  conditions  occur  for  the  smallest  possible  value  of  at'.  Inspection 
shows  this  to  be  when  co£'=7r/2  and  wTo  =  ir;  this  means  that  the  length 
of  the  pulse  (time  between  applying  +  E  and  -E)  should  be  equal  to 
one-half  the  natural  period  of  the  circuit  and  the  maximum  current  occurs 
one-quarter  of  a  period  after  the  end  of  the  pulse.  Putting  To=T/2 


EFFECT   OF   PULSE   OF   E.M.F.   ON   OSCILLATORY   CIRCUIT      263 
(T  being  the  natural  period  of  the  circuit),  the  equation  for  current  becomes 

{=    -  -—(€-<*<'+ 6~a  V    +  2)  )  gin  ^ 

u>L 

and  if  we  now  suppose  ut'  =  ir/2  and  write  the  damping  in  terms  of  decre- 
ment, we  get 

E     _!      _?* 
7  (maximum)  = j-(e  4+c   4). 

COJL/ 


FIG.  52. — Similar  to  Fig.  51  but  with  longer  pulse. 

An  oscillographic  investigation  of  impulse  excitation  was  carried  out 
by  the  author  J  and  some  of  the  films  obtained  are  shown  in  Figs.  51,  52, 
and  53.  The  upper  record  of  the  films  shows  the  shape  and  length  of 
pulse  of  e.m.f.  introduced  into  the  oscillatory  circuit  and  the  lower  curve 
shows  the  current  set  up  in  the  circuit  by  the  pulse.  A  complete  set  of 
films  was  taken  varying  the  length  of  pulse  from  less  than  0.2  of  the  natural 
period  of  the  circuit  to  several  times  the  period.  The  amplitude  of  the 
first  and  second  alternations  were  measured  and  their  values  plotted  in 
terms  of  the  ratio  of  pulse  length  to  natural  period  of  the  circuit;  the 

1  Proc.  I.  R.  E.,  Vol.  8,  No.  1,  February,  1920. 


264 


LAWS  OF  OSCILLATING  CIRCUITS 


[CHAP.  IV 


results  are  given  in  Fig.  54  and  it  is  seen  that  the  results  are  in  accord 
with  the  prediction  of  Eq.  (87). 


FIG.  53. — Similar  to  Fig.  52  but  with  longer  pulse. 

In  case  a  series  of  irregularly  timed  pulses  are  impressed  on  an  oscil- 
latory circuit  the  resulting  current  will  be  of  rather  complex  form;  Figs. 
55  an.d  56  show  how  such  irregular  pulses  excite  an  oscillatory  circuit. 


40 
35 
30 
25 
20 

10 
5 

^ 

~-v 

X 

\ 

'^ 

\ 

Se 

2on 

d  t 

dte 

rnt 

itid 

n 

f 

\ 

/ 

\ 

~7_ 

" 

\ 

, 

\ 

Ki 

st 

Ait 

ern 

ati 

on 

^ 

s 

> 

•^ 

/ 

' 

.1 


.2 


L.3       1.4       1.5 


.3        .4         .5         .6          .7         .8         .9        1.0        1.1       1.2 
Ratio  of  pulse  length  to  natural  period  of  circuit 

FIG.  54. — Variation  in  amplitude  of  oscillatory  current  with  length  of  pulse. 

It  is  evident  (Fig.  55)  that  pulses  properly  timed  may  practically  neu- 
tralize one  another  as  in  this  case  the  circuit  was  nearly  dead  after  the 
last  pulse. 


EFFECT  OF  PULSE  OF   E.M.F.   ON  OSCILLATORY   CIRCUIT     265 


FIG.  55. — Irregular  current  produced  by  series  of  pulses. 


FIG.  56. — Irregular  current  produced  by  series  of  pulses. 


20(3 


LAWS  OF  OSCILLATING   CIRCUITS 


[CHAP.  IV 


Antenna 


Infinite  Impedance 
circuit 


To  detecting 
circuit 


Ground 

FIG.  57. — Showing  the  use  of  a  parallel  resonant 
circuit  for  weeding  out  undesired  signals  from  an 
antenna.  Such  a  parallel  circuit  is  often  called 
an  "infinite  impedance." 


and  so  predicts  nothing  re- 
garding the  behavior  of  the 
circuit  for  other  than  steady 
alternating  voltages ;  even  in 
this  case  the  equations  are 
goodonlyifthee.m.f.has  been 
applied  sufficient  time  for  the 
transient  terms  to  disappear. 
Because  of  the  "  infinite 
impedance "  characteristic 
the  circuit  is  often  used  to 
eliminate  from  a  circuit  some 
undesired  frequency;  thus 
in  Fig.  57  the  L-C  parallel 
circuit  is  so  adjusted  that 
its  natural  period  is  the  same 
as  that  of  some  undesired 
frequency  which  is  impressed 
on  the  antenna.  Now  it  is  to 
be  remembered  that  the  L-C 
circuit  offers  "infinite  imped- 
ance "  only  for  the  steady 
state  and  it  is  interesting  to 
note  the  impedance  offered 
by  it  to  a  pulse  of  e.m.f. 


Impulse    Excitation    of    a 
Parallel  Resonant  Circuit. — A 

condenser  and  coil  in  parallel 
act  like  a  circuit  of  very  high 
resistance  for  an  e.m.f.  of  the 
same  frequency  as  that  nat- 
ural to  the  circuit.  The  value 
of  the  resistance  is  predicted 
by  Eq.  (48),  Chapter  I,  and 
curves  are  shown  in  Chapter 
I,  Figs.  70  and  71;  because 
of  this  characteristic  the  cir- 
cuit is  often  called  an  "  infinite 
impedance  "  circuit.  The  Eq. 
(48)  was  derived  from  the 
steady  state  of  the  circuit. 


FIG.  58. — Action  of  an  approximately  rectangular 
pulse  of  e.m.f.  (a)  impressed  across  parallel  circuit. 
Curves  in  (6)  show  the  separate  currents,  the  total 
current  being  that  shown  at  (c) . 


PULSE  EXCITATION  OF  PARALLEL  RESONANCE 


267 


If  the  pulse  is  a  square  one,  such  as  used  in  Figs.  50-53,  the  current 
flowing  in  the  supply  line  (the  impedance  of  the  circuit  other  than  that 
of  the  "  infinite  impedance  "  being  neglected)  will  be  about  as  shown  in 
Fig.  58.  The  e.m.f.  pulse  form 
is  shown  in  curve  a;  the  full 
line  curve  of  6  shows  the 
current  flowing  through  the 
condenser  and  the  dotted  line 
that  through  the  coil;  in  c  is 
shown  the  actual  current  in 
the  line,  that  is,  the  current 
which  the  "  infinite  imped- 
ance "  circuit  lets  through. 
These  curves,  as  mentioned 
before,  are  drawn  on  the  as- 
sumption that  the  impedance 
of  the  rest  of  the  circuit  is 
negligible. 

It  would  seem  likely  that 
if  the  circuit  does  have  such 
a  very  high  impedance  for  a 
certain  frequency  then  it  will 
offer  a  high  impedance  to  a 
pulse,  if  this  pulse  is  in  the 
form  of  one  alternation  of  a 
sine  wave  of  the  same  fre- 
quency as  that  natural  to  the 
circuit.  Fig.  59  shows  the 
analysis  of  this  case;  a  shows 
the  form  of  pulse  e  =  E  sin  ut 
(holding  only  between  oit  =  0 
and  CO£=TT);  the  curves  of  b 

indicate  the  currents  through  each  branch,  and  curve  c  shows  the  current 
passed  by  the  combined  circuit.  As  the  resistance  in  the  parallel  path 
is  made  to  approach  zero  this  line  current  approaches  a  true  rectangular 
form,  i.e.,  current  of  constant  magnitude  and  equal  to  2irfCE,  where  /  is 
the  frequency  of  the  e.m.f.  of  which  the  pulse  is  the  alternation. 

Analyzed  mathematically,  we  have 


FIG.  59. — Effect  of  impressing  a  sinusoidal  pulse 
of  e.m.f.  across  a  parallel  circuit. 


ic  —  uCE  COS  ut 


and 


sm  "l  - 


cos 


268  LAWS  OF  OSCILLATING  CIRCUITS  [CHAP.  IV 

this  being  derived  as  a  special  case  of  Eq.  (79). 

For  a  good  coil,  i.e.,  one  having  a  high  value  for-^-,    we  have  as  an 
approximate  value, 


R  1  1    -**t 

7  —  ^T^  sin  co£  --  T  cos  coH  —  re  L 
(coL)2  coL  coL 


Adding  to  this  the  condenser  current  we  get  for  the  current  passed  by 
this  parallel  combination, 


R 


sn 


/  1  \ 

1  coC  --  r) 
\  COL// 


coscoH 


If  now  the  constants  of  the  circuit  are  such  that  coC  =  — j ,  then 
E  /  R 


(88) 


Oscillatory  Circuit  Excited  by  a  Damped  Sine  Wave. — Let  us  con- 
sider a  circuit  made  of  L,  R}  and  C  in  series  as  e.g.,  the  ordinary  antenna, 
to  be  excited  by  a  damped  sine  wave  of  voltage  such  as  is  induced  many 


FIG.  60. — Form  of  voltage  induced  in  a  receiving  antenna  by  the  passage  of  one  wave 
train  as  emitted  from  the  ordinary  spark  transmitter. 

times  each  second  in  an  antenna  by  a  signal  from  a  distant  spark  station. 
The  voltage  caused  in  an  antenna  by  every  discharge  in  the  transmitting 
circuit  is  not  exactly  representable  by  a  damped  sine  wave,  because  for 
the  first  few  cycles  its  amplitude  is  increasing  instead  of  decreasing;  this 
is  indicated  in  Fig.  60,  which  shows  about  the  form  of  voltage  actually 
induced  in  an  antenna.  The  part  A-B  is  relatively  short  (2J  cycles  for 
20  per  cent  coupling  in  the  transmitting  station)  and  the  part  B-C  is 
really  a  damped  sine  wave  represented  by  Ee~ki  sin  pt. 

The  form  of  current  induced  in  the  antenna  is  determined  in  the  usual 
way  by  putting  the  sum  of  its  reactions  equal  to  the  impressed  force. 


at 
v  being  the  voltage  across  the  condenser. 


(89) 


OSCILLATORY  CIRCUIT  EXCITED  BY  DAMPED  SINE  WAVE      269 

Writing  the  impressed  force  as  a  cosine  function  indicates  that  we  are 
going  to  consider  the  case  of  maximum  voltage  at  £  =  0;  such  is  the  case 
when  the  circuit  we  are  considering  is  acted  upon  by  the  oscillatory  cur- 
rent set  up  in  a  neighboring  circuit  by  the  discharge  of  a  condenser.  Eq. 
(89)  may  be  written  in  the  form, 


....     (90) 

tM/~  Utf  AW 

by  using  the  relations 

dv          R 

Differentiating  (89)  twice  with  respect  to  time  and  eliminating  the 
right-hand  number  by  multiplying  (90)  by  (p2  -k2),  its  first  derived  equa- 
tion by  2k,  and  adding  both  the  resulting  equations  to  the  second  derived 
equation,  we  obtain 


0.     .  (91) 

This  equation  is  in  standard  form  for  integration,  the  value  of  v  being 
of  the  form 

v  =  Vie~kt  sin  (pt+0)  +  V2e-at  sin  M+0).     .     .     .  (92) 

From  this  equation  we  get 

z  =  /ie-*<  sin  (pt+e')  +  I2e-atsm(ut+<t>').    .     .     .  (93) 


This  solution  shows  that  the  current  flowing  in  the  circuit  is  made  up 
of  two  components,  one  of  the  same  frequency  as  the  impressed  force  and 
one  of  the  natural  frequency  of  the  circuit. 

This  might  have  been  surmised  from  an  elementary  analysis  of  the 
problem.  Suppose  the  damping  of  the  impressed  force  is  zero,  then 
Eq.  (79)  page  252,  would  give  the  correct  solution  and  this  has  two  terms, 
one  of  the  frequency  of  the  impressed  force  (which  is  the  solution  for  the 
steady  state)  and  the  transient  term  which  dies  away  at  a  rate  fixed  by  the 
decrement  of  the  circuit. 

The  relative  amplitudes  of  the  two  currents,  I\  and  /2,  will  evidently 
depend  in  some  way  upon  the  relative  values  of  the  damping  factors,  k 
and  a,  also  upon  the  relative  values  of  the  frequencies  fixed  by  p  and  o>. 

By  getting  the  values  of  v,  -3-,  and  -r-2  from  (92)  and  substituting  them  in 
(90),  we  find  the  value  of  V\  to  be 


_ 
V[co2  -p2  +  (a  -/c)2]2+4p2(a  -k)2' 


270  LAWS  OF  OSCILLATING   CIRCUITS  [CHAP.  IV 

and 


. 

2p(a  -k) 

Now  by  substituting  in  Eq.  (92)  the  initial  conditions  that  when  £  =  0 
i>  =  0,  then  differentiating  (92)  and  in  this  equation  putting  -77  =  0  when 

£  =  0  we  get  the  value  of  ¥2  in  terms  of  V\.     Substituting  the  value  of 
Vi  from  (94),  we  get, 


V2  =  E— — -v      2       ^^22        2         ~'     ...     95) 
and 


co 
Q~ 


From  the  values  of  V\  and  F2  we  find  at  once  7i  and  72  by  using  the 
relations  Ii  =  pCVi  and  72  =  coCF2: 

7i  =  #-  -^-  (90) 

LV[co2  -p2+(«  -fc)2]2+4p2(a  -jfe)2 

-*>>  .     .     .     (97) 

a  -k)2]2+4p2(a  -k)2 

The  values  of  0'  and  0' — Eq.  (93) — are  determined  from  the  values 
of  0  and  (/>  given  above,  by  increasing  each  of  them  by  7r/2. 

The  exact  form  of  current  in  the  circuit  is  now  fixed  by  the  values  of 
7i,  72,  fc,  a,  p  and  co.  It  will  be  evident  that  if  both  damping  factors  arc 
low  and  nearly  equal,  and  the  two  frequencies,  fixed  by  p  and  co,  are  nearly 
equal,  the  conditions  are  the  same  as  those  for  the  secondary  current  in 
coupled  circuits  as  illustrated  in  Fig.  26  of  this  Chapter.  If  p  =  co  there 

can  be  no  beats;  for  all  values  of  damping,  the  current,  with  frequency  — 

Zir 

increases  in  value  from  zero  to  a  certain  maximum  and  then  decreases 
again. 

An  analysis  due  to  Bjerknes  1  shows  that  this  current  can  be  repre- 
sented by  the  equation 

i  =  mCM  cos(mt+tf, (98) 

in  which  m  =  ~~--  and  ^  is  the  phase  of  the  impressed  e.m.f.  at  time 
*  =  0. 

1  V.  Bjerknes,  ''Electrical  Resonance,"  Wied.  Ann.,  1895,  Vol.  55. 


OSCILLATORY  CIRCUIT  EXCITED  BY  DAMPED  SINE  WAVE      271 

o          k-\-ot    1      k  —a 


If  we  let  n  = 


2    '"        2    ' 


,  then 


in  which 


m 

i 

Pl  =  e-2a<(e-26<_|_  C26<  _2  CQS  n£)  . 

P2  =  e~2at(ne2bt  —n  cos  r^  —6  sin 

PS  =  c-2a/(5€2w  _^  cos  2n^+n  sin 

In  certain  cases  the  form  of  M  is  simpler  than  indicated  in  Eq.  (99). 


,    -     (99) 


If  p  =  u  and  k=a 
If  p  =  co  and  kj^a 
If  7>^w  and  &=« 


J?f 

M=-J ^L_,-a« 


TTJ 


(101) 


E 


2mnLC 


•-^smnt (102) 


Equation  100 


•V 


Equation 


FIG.  Gl. — Two  possible  forms  of  current  in  the  antenna  excited  by  the  wave  trains  from 

a  spark  transmitter. 

In  case  neither  the  damping  factors  nor  frequencies  are  the  same  the 
general  form  given  in  Eq.  (99)  must  be  used. 

In  Fig.  61  are  shown  the  forms  of  current  in  the  oscillatory  circuit 
for  the  cases  given  in  Eqs.  (100)  and  (102) 


272  LAWS  OF  OSCILLATING  CIRCUITS  [CHAP.  IV 

Resonance  Curve  of  an  Oscillatory  Circuit  Excited  by  Damped  Sine 
Waves.  —  In  Chapter  I  we  analyzed  the  action  of  an  oscillatory  circuit 
(L,  C,  and  R  in  series)  when  excited  by  an  alternating  e.m.f.  of  constant 
amplitude  and  showed  that  the  form  of  the  curve  obtained  when  either 
C,  L,  or  /  was  varied  (E  being  held  constant  in  amplitude),  enables  us 
to  determine  the  decrement  of  the  circuit.  The  form  of  the  resonance 
curve  for  the  steady  state  depends  only  upon  the  relation  between  the 
impedance  of  the  circuit  and  the  frequency  of  the  impressed  force. 
When  such  a  circuit  is  excited  by  a  damped  sine  wave  the  reading 
of  the  indicating  device  for  showing  resonance  will  depend  on  both  of 
the  terms  in  Eq.  (93)  .  If  a  hot-wire  ammeter  is  used  to  show  resonance 
it  is  evident  that  its  reading  will  depend  upon  the  average  integral  of  the 
square  of  each  of  the  currents  I\  and  /2.  Bjerknes  and  others  have 
analyzed  the  value  of  this  integral  and  by  somewhat  lengthy  deductions 
have  obtained  the  relation, 

E*    k+a  1 

16L2    ka         -co22 


this  holding  good  only  for  a  much  less  than  w,  k  much  less  than  p,  and 
for  frequencies  close  to  the  resonance  point. 
At  resonance  (w  =  p)  this  reduces  to 

& 


From  (103)  and  (104) 

I2  (k+a)2 

I2~(p-u)2+(k+a)2' 


= 

I2  (k+a)2' 

From  this  we  get 


If  we  now  introduce  the  decrements,  instead  of  damping  factors,  we 
have,  putting  k  =  nd\  and  a=fd2 


If  now  n  is  nearly  equal  to  /,  so  we  may  put  without  much  error  -  =  1 
we  get,  

(105) 


RESONANCE  WITH  DAMPED  SINE  EXCITATION 


273 


If  then  we  have  plotted  a  curve  showing  the  variation  of  'the  current 
in  the  oscillatory  circuit  as  its  natural  frequency  is  varied  we  can  calculate 
the  sum  of  the  decrements  of  the  circuit  and  exciting  voltage;  if  one  of 
them  is  known  the  other  may  then  be  obtained.  The  curve  between 
(current)2  and/  will  have  the  shape  indicated  in  Fig.  62;  when/=n,  I  has 
its  maximum  value  I,,  and  it  decreases  as /  departs  from  n.  The  amount 
of  decrease  in  /  for  a  given  difference  between  n  and  /  is  the  same  whether 

71 

f  is  greater  or  less  than  n,  provided  the  value  of  v  does  not  differ  materially 
from  unity. 


fr 
Frequency 

FIG.  62. — Resonance  curve  of  a  circuit  excited  by  damped  sine  wave. 

If  we  then  read  the  two  values  of/  (call  them/2  and/i,  /2  being  greater 
than  n  and  f\  being  less  than  n),  so  chosen  that  the  current  is  reduced  to 

—7=  of  its  resonance  value  we  shall  have 

V2 


Q.5/,2 


2  _ 


o 

=2, 


and  also 


—n 


Adding  these  two  values,  we  get 


-/i  =  rf2-/it 

W  /r 


(106) 


274  LAWS  OP  OSCILLATING   CIRCUITS  [CHAP.  IV 

In  this  equation  /r  is  that  frequency  of  the  circuit  which  gives  greatest 
current;  this  frequency  we  know  to  be  practically  the  same  as  the  fre- 
quency of  the  impressed  force  which  we  have  been  calling  n. 

As  the  frequency  of  a  circuit  varies  with  the  square  root  of  the  capacity 
in  the  circuit,  we  may  write  Eq.  (106)  in  terms  of  the  amount  of  capacity 
used  in  getting  the  resonance  curve.  If  Cr  is  the  value  used  to  get  the 
maximum  current  and  €2  and  C\  correspond  to/2  and/i  of  Eq.  (106)  then 
we  have,  very  nearly, 


(107) 


This  is  the  equation  generally  used  when  using  a  wave  meter  for  getting 
the  decrement  of  a  transmitting  set;  although  approximations  have  been 
made  in  deducing  it,  the  errors  incurred  are  small  if  the  sum  of  the  two 
decrements  is  small  (say  less  than  0.25),  which  is  always  the  case  in  prac- 
tical radio  sets. 


CHAPTER  V 


SPARK  TELEGRAPHY 

Spark  Transmission  and  Equipment. — The  transmission  of  intelli- 
gence by  means  of  electromagnetic  and  electrostatic  energy  radiation  from 
an  open  oscillator,  produced  by  the  high-frequency  oscillatory  discharge 
of  a  condenser  in  an  associated  circuit,  is  called  spark  telegraphy.  The 
fundamental  circuits  of  such  a  transmitter  have  already  been  discussed 
(Chapter  III),  and  the  action  and  inherent  necessity  of  the  spark  to  this 
form  of  transmission  indicated.  Thus  the  reason  for  the  term  "  spark  " 
telegraphy. 

In  the  diagram  of  connections  (Fig.  1)  and  description  of  the  trans- 
mitter, a  certain  conventional  and  more  or  less  standard  arrangement 


Antenna 


FIG.  1. — Circuit  diagram  of  the  ordinary  spark  transmitter. 

of  equipment  has  been  assumed.  Commercial  transmitters  may  differ 
from  this  arrangement  in  several  details,  for  instance,  in  the  method 
of  energy  supply,  form  of  spark  gap  used,  and  the  kind  of  coupling  employed 
between  the  closed  and  open  (radiating)  oscillatory  circuits. 

An  examination  of  the  set  shows  it  to  consist  of  three  main  circuits: 
(1)  a  low-voltage,  low-frequency  circuit  which  includes  the  alternator 
(A),  the  key  (K),  the  low-tension  winding  of  the  step-up  power  trans- 
former (P),  and  a  variable  reactance  (V.R.),  which  is  also  called  a  reac- 
tance regulator  or  choke  coil;  (2)  a  high  voltage,  high-  and  low-frequency 
circuit,  including  the  high-tension  winding  of  the  step-up  power  trans- 
former (S),  the  capacity  (Ci);  the  inductances  (Li)  and  (Z/i)  and  the 
radio-frequency  choke  coils  (H),  the  spark  gap  G  being  shunted  across 
the  circuit  as  shown  in  the  diagram;  that  part  of  this  circuit  comprising 

275 


276  SPARK  TELEGRAPHY  [CHAP.  V 

LI,  L'i,  Ci,  and  the  gap,  in  series  is  called  the  closed  oscillating  circuit; 
(3)  a  third  circuit,  known  as  the  open  (radiating)  oscillatory  circuit,  of 
high  frequency  only,  containing  the  following  equipment:  Inductance  Lz, 
coupled  inductively  with  LI,  and  forming  with  LI  the  oscillation  trans- 
former; a  tuning  inductance  Ls,  the  antenna  or  aerial  (represented  in 
the  diagram  by  a  fictitious  lumped  capacity  €2)  the  hot-wire  ammeter 
Aij  and  the  short  wave  condenser  €3  equipped  with  short-circuiting  switch. 

The  detailed  action  and  function  of  the  above  equipment,  represent- 
ing all  the  essential  elements  of  a  spark  transmitter,  will  now  be  discussed. 

The  Alternator. — The  function  of  the  alternator  is  to  supply  electrical 
energy  to  the  set,  it  itself  usually  being  driven  by  a  direct-current  motor. 

Where  a  supply  of  electrical  energy  is  not  available  it  may  be  driven 
by  a  gas,  steam,  or  oil  engine.  When  motor  driven,  a  storage  battery 
is  sometimes  connected  across  the  supply  mains,  to  steady  the  voltage 
impressed  on  the  motor  and  to  act  as  a  reserve  in  case  of  interruption 
to  the  source  of  supply. 

The  construction  and  characteristics  of  the  alternator  are  discussed 
below  (page  287). 

The  Switch  K,  called  the  key,  is  used  to  control  manually  the  energy 
supply  to  the  step-up  transformer.  If  this  energy  is  interrupted  in  accord- 
ance with  a  prearranged  or  conventional  plan  (i.e.,  the  International  Morse 
Code),  then  the  radiated  energy  will  vary  in  the  same  manner,  and  thus 
signals  may  be  transmitted.  (See  Chapter  III.)  The  diagram  indicates 
the  key  as  making  and  breaking  the  main  circuit  current.  On  the  higher 
powered  sets  it  becomes  impracticable  manually  to  open  the  main  circuit 
directly,  due  to  the  large  currents  involved  requiring  a  long  break  and 
heavy  set  of  contacts.  The  key,  therefore,  is  usually  arranged  to  operate 
in  an  auxiliary  circuit,  connected  to  actuate  one  or  more  relays,  whose 
contacts,  in  turn,  make  and  break  the  main  circuit. 

The  Step-up  Transformer. — Consisting  of  high  and  low-tension  wind- 
ings S  and  P,  raises  the  potential  of  the  energy  supply  from  perhaps 
120  to  10,000-20,000  volts.  This  increase  in  the  voltage  is  required  for  the 
proper  operation  of  the  spark  gap. 

For  the  lower  powered  sets,  i.e.,  sets  having  less  than  1  kw.  rating, 
the  alternator  and  step-up  transformer  may  be  replaced  by  a  storage 
battery  and  high-tension  induction  coil.  The  limitation  and  operation 
of  the  induction  coil  is  considered  in  detail  below  (see  page  282) . 

The  capacity  Ci  forms  the  reservoir  for  energy  storage  as  the  voltage 
impressed  across  the  inductance  (Li+L'i)  and  C\  approaches  its  maximum 
value.  That  the  impressed  voltage  is  practically  all  consumed  across  the 
condenser,  and  the  condenser  thus  charged  to  this  voltage,  can  be  seen  at 
once  if  the  reactance  of  (Li-j-L'i)  and  C\  are  considered  at  the  frequency 


ESSENTIAL  PARTS  OF  A  SPARK  TRANSMITTER  277 


of  the  supply.     Thus,  assuming  Li+L'i  =  50M,  Ci  =  .002/z/,  frequency 
=  500  cycles,  we  have, 


=  .157  ohm, 
106 


ohms' 

Since  the  same  current  flows  through  both  (Li+L'i)  and  Ci  on  charge, 
it  is  apparent  that  the  drop  across  the  inductance  is  negligible,  and  that 
the  charging  voltage  is  practically  impressed  directly  across  Ci.  Forms 
of  high  potential  condensers  and  their  construction  are  described  below 
(page  297). 

The  inductance  LI  is  essential  to  the  closed  circuit,  since  high  fre- 
quency oscillations  are  to  be  produced  when  the  condenser  C\  discharges. 
In  addition  to  its  function  of  energy  storage,  LI  forms  the  means  of  coup- 
ling the  closed  and  open  (radiative)  circuits;  in  conjunction  with  Z/2  it 
is  known  as  an  oscillation,  or  Tesla  high-frequency,  transformer.  The 
variable  inductance  L'i  is  not  essential  to  the  operation  of  the  set,  and 
is  seldom  used  in  practice. 

The  function  of  the  spark  gap  G  has  already  been  briefly  considered 
(Chapter  III).  Essentially,  its  action  is  that  of  a  trigger  which  permits 
the  stored-up  energy  of  the  charged  condenser  C\  to  be  discharged  in 
the  form  of  high-frequency  oscillations,  when  the  potential  between  its 
electrodes  has  reached  a  certain  critical  value.  The  several  forms  of 
spark  gaps  used  on  modern  transmitters,  and  their  action,  are  considered 
later. 

The  secondary  winding  L2  of  the  oscillation  transformer  forms  the 
seat  of  induced  high-frequency  electromotive  force  and  is  the  means 
of  energy  transfer  from  the  closed  oscillating  circuit.  To  control  this 
energy  transfer  and  to  secure  proper  operating  conditions  the  position 
of  this  coil  is  varied  with  respect  to  LI,  i.e.,  the  coupling  between  the 
two  circuits  is  adjusted  to  give  the  best  results. 

When  adjusting  for  the  transmission  of  long  wave  lengths,  it  becomes 
undesirable  to  tune  the  open  oscillating  (radiating)  circuit  by  increasing 
L2,  as  this  may  increase  the  coupling  to  greater  than  the  desired  value; 
excessive  coupling  possesses  several  disadvantages  as  outlined  below. 

Function  of  the  Tuning  Inductance  L3.  —  To  tune  the  circuit,  without 
increasing  the  coupling  the  tuning  inductance  L3  is  inserted;  note  that 
coefficient  of  coupling  between  the  two  circuits  is  decreased  if  La  is  increased 
and  L2  is  unchanged.  This  inductance  has  no  inductive  relationship 
with  either  LI,  or  L2,  and  is  cut  into  the  circuit  only  when  adjusting  the 
set  to  transmit  at  the  longer  wave  lengths.  The  insertion  of  a  capacity 
in  multiple  with  €2,  or  across  L2,  would  produce  a  similar  effect. 


278  SPARK   TELEGRAPHY  [CHAP.  V 

Antenna. — The  aerial  or  antenna  represents  primarily  a  condenser 
of  large  physical  dimensions,  and  forms  the  radiating  element  of  the  set 
(see  Chapter  IX).  A  capacity  of  small  dimensions,  such  as  is  used  in 
the  closed  oscillating  circuit,  possesses  no  appreciable  ability  to  throw 
off  or  radiate  electromagnetic  energy  even  though  the  frequency  of  oscil- 
lation be  extremely  high.  For  this  reason  the  radiating  capacity  is  made 
of  large  physical  dimensions,  and  as  such  is  called  the  aerial  or  antenna. 

Function  of  the  Short-wave  Condenser  €3. — The  functions  of  €3  is 
to  permit  tuning  the  open  circuit  with  the  closed  circuit,  when  the  wave 
length  to  be  transmitted  is  very  short.  It  is  therefore  called  the  short- 
wave condenser  and  is  connected  in  series  with  the  antenna,  the  total 
capacity  of  the  circuit,  and  the  wave-length,  being  thus  decreased.  In 
I  he  absence  of  this  condenser  it  would  be  necessary  to  tune  by  decreasing 
L2  (Ls  being  cut  out  of  circuit  at  some  intermediate  wave-length),  in 
which  case  the  energy  transferred  from  the  closed  to  the  open  circuit 
may  be  too  small  for  satisfactory  transmission,  the  coupling  having  been 
made  too  weak. 

Protective  Equipment. — In  addition  to  the  above  apparatus,  the  set 
is  equipped  with  certain  protective  devices.  High  resistances  or  con- 
densers are  connected  across  the  field  and  armature  terminals  of  the 
alternator  and  its  driving  motor,  to  prevent  the  flow  of  high-frequency 
currents  in  these  highly  inductive  circuits.  These  high-frequency  cur- 
rents may  be  caused  to  flow  by  direct  inductive  effects  from  the  closed 
and  open  oscillating  circuits,  particularly  if  the  space  is  restricted,  as 
on  shipboard,  and  the  several  circuits  are  close  together.  High-frequency 
current  flowing  or  tending  to  flow  through  a  high  inductance  means  a 
high-potential  drop  across  the  winding,  this  potential  usually  being  con- 
centrated ("  piled  up  ")  at  the  end  turns  of  the  winding.  This  potential 
may  be  sufficient  to  puncture  the  winding  insulation,  and  to  prevent  this 
the  coil  is  shunted  by  resistance  or  capacity,  through  which  the  high- 
frequency  current  can  easily  flow,  without  any  abnormal  potentials  being 
produced.  Also  this  resistance  or  capacity  usually  has  its  neutral  point 
connected  to  ground,  to  prevent  excessive  potential  stresses  with  respect 
to  ground.  The  connection  of  a  protective  resistance  (R')  and  condenser 
(C")  is  indicated  in  the  diagram  (Fig.  1). 

Since  the  breakdown  of  the  gap  virtually  short  circuits  the  high  tension 
side  of  the  step-up  transformer,  some  means  must  be  introduced  to  pro- 
vent  the  abnormal  current  flow  which  would  otherwise  occur  under  this 
condition.  If  this  is  not  done,  the  transformer  and  alternator  may  be 
damaged,  and  the  arc  across  the  gap  become  a  sustained  condition,  pre- 
venting the  recharging  of  the  capacity  Ci,  with  resultant  decrease  of  the 
high-frequency  energy.  Three  means  may  be  used,  all  three  involving 
the  insertion  of  reactance  in  the  low  voltage  supply  circuit:  (a)  High 


ESSENTIAL  PARTS  OF  A  SPARK  TRANSMITTER  279 

reactance  (high  impedance)  in  the  alternator;  (6)  an  iron-cored  induct- 
ance in  the  supply  leads  to  the  transformer;  (c)  high  leakage  reactance 
in  the  step-up  transformer. 

The  action  of  this  added  reactance  is  to  rapidly  decrease  the-veltage 
as  the  current  flow  increases,  as  the  gap  breaks  down.  In  addition  to 
the  above,  a  more  or  less  resonant  adjustment  of  the  circuit  constants 
may  be  used  to  secure  an  equivalent  result.  The  action  of  this  arrange- 
ment is  discussed  in  detail  on  pages  310  et  seq. 

To  prevent  any  appreciable  high-frequency  current  from  flowing 
through  the  high-tension  winding  of  the  transformer,  thus  setting  up 
high  potentials  with  liability  of  puncture  to  the  winding,  high-frequency 
reactance  coils  H  are  inserted  between  the  gap  and  the  transformer. 
These  coils  have  a  very  low  impedance  to  the  flow  of  current  of  alter- 
nator frequency,  but  present  a  very  high  impedance  to  the  high-frequency 
discharge  current,  which  is  thus  forced  to  follow  the  gap  circuit.  These 
coils  may  be  simply  a  helix  of  copper  wire  wound  on  a  porcelain  or  bake- 
lite  spool,  and  are  designed  to  possess  a  high  "  turn  insulation."  They 
can  thus  safely  withstand  potential  strains  which  would  cause  puncture 
to  the  transformer  winding  if  permitted  to  occur  at  this  point.  Another 
advantage  is  that  the  high-frequency  current  is  forced  to  flow  in  the  low- 
resistance  gap  circuit,  instead  of  through  the  higher-resistance  by-path 
presented  by  the  transformer  winding.  The  damping  is  thus  decreased, 
and  the  operating  efficiency  of  the  set  increased.  (The  damping  is 
decreased  by  the  decrease  of  closed  circuit  PR  losses.)  With  modern 
transmitters,  where  the  end  turns  of  the  high-tension  winding  have  been 
specially  insulated  to  withstand  the  high  potentials,  these  high-frequency 
choke  coils  are  usually  omitted. 

Conductive  and  Capacitive  Coupling. — The  above  description  of  the 
spark  transmitter  has  considered  an  oscillation  transformer,  with  two 
windings,  conductively  independent,  but  coupled  electro-magnetically,  as 
the  means  of  transferring  energy  from  the  closed  to  the  open  oscillating 
circuit.  This  is  the  form  in  common  use  to-day,  and  is  known  as  inductive 
coupling.  Under  certain  conditions,  where  space  is  at  a  premium,  such 
as  military  field  sets  and  aeroplane  equipment,  it  becomes  desirable  to 
concentrate  the  oscillation  transformer  into  one  winding,  the  connections 
then  being  made  as  shown  in  Fig.  2  (A). 

Such  coupling,  which  is  known  as  direct  or  conductive  coupling,  is 
equivalent  as  a  means  of  energy  transfer,  to  the  inductive  type.  It,  how- 
ever, is  not  so  flexible  in  its  coupling  adjustment  as  the  latter,  and  requires 
two  movable  contacts  for  the  open  circuit  terminals,  if  very  loose  coupling 
is  desired  (Fig.  2  (B)).  In  any  case  the  adjustment  is  more  difficult  than 
with  the  two-coil  transformer,  wherein  the  coupling  is  easily  adjusted 
by  movement  of  the  one  coil  (open  circuit.)  relative  to  the  other  (closed 


280 


SPARK   TELEGRAPHY 


[CHAP.  V 


circuit  coil).  Direct  coupling  has  the  advantages  of  reduced  space  require- 
ments, simplicity  and  increased  efficiency;  it  avoids  also  the  necessity 
of  insulating  the  two  windings  from  each  other.  This  latter  point  is 
important  only  when  very  tight  coupling  is  desired,  as  under  normal 
coupling  conditions  the  space  between  the  two  coils  is  such  that  the 
insulation  is  ample,  unless  very  high  voltages  are  involved. 


A 
FIG.  2. — Two  schemes  for  using  conductive  coupling  in  a  i  park  transmitter. 

Capacitive  coupling,  instead  of  the  inductive  form,  could  also  be  used, 
but  is  very  rarely  adopted  in  practice,  due  to  the  greater  adjustment 
facility  and  simplicity  of  the  latter  form.  Capacitive  coupling  is  shown 
in  Fig.  3. 


FIG.  3. — A  capacitively  coupled  transmitter. 

Forms  of  Excitation. — All  of  the  above  methods  involve  what  is  known 
as  indirect  excitation,  that  is,  energy  is  stored  in  the  closed-circuit  con- 
denser, and  a  portion  then  transferred  from  this  circuit  to  the  open  or 
radiating  circuit,  when  the  high-frequency  oscillatory  discharge  occurs. 
The  antenna,  however,  possesses  distributed  capacity  and  inductance  and 
the  earlier  forms  of  transmitters  stored  the  energy  in  this  antenna  capacity 
directly,  the  antennae  circuit  being  thus  synonymous  with  the  closed  cir- 
cuit of  the  modern  transmitter.  This  method  is  known  as  direct  excita- 
tion, and  possesses  advantages  as  regards  economy  in  first  cost,  less  space 
requirements,  and  greater  simplicity.  The  connections  are  shown  in 
Fig.  4. 


ESSENTIAL  PARTS  OF  A  SPARK  TRANSMITTER 


281 


This  arrangement  may  be  used  particularly  for  very  small  power  sets, 
using  a  storage  battery  and  induction  coil  as  the  source  of  high  potential 
energy.  It  will  be  noted  that  the  capacity  of  the  aerial  is  charged  by 
the  induction  coil,  and  when  the  gap  breaks  down,  a  high-frequency  dis- 
charge is  produced  exactly  as  in  the  case  of  the  closed  circuit.  A  portion 
of  the  high-frequency  energy  will  be  radiated,  and  by  its  proper  control 
signals  may  be  transmitted  as  with  the  indirectly  excited  transmitters. 

The  circuit  possesses  the  fundamental  disadvantage  that  the  gap 
resistance  is  in  the  radiating  circuit.  The  radiated  energy  will  thus  have 
a  high  decrement  and  cause  interference  to  any  station  which  may  be 
within  its  sending  radius, 
unless  the  station  be  tuned 
to  a  wave  length,  remote 
from  that  of  the  transmitter 
considered.  The  efficiency 
of  such  a  radiator  is  low, 
most  of  the  energy  being 
dissipated  as  heat  in  the 
spark  resistance  and  as 
other  circuit  losses.  Also 
the  capacity  of  the  antenna 
is  small  compared  to  the 
capacity  which  may  be 
placed  in  the  closed  cir- 
cuit when  indirect  excitation  is  used  thus  the  current  through  the  spark 
gap  is  much  smaller  than  it  would  be  if  the  gap  were  in  a  high  capacity 
circuit.  The  resistance  of  the  gap  is  higher  the  smaller  the  current  through 
it,  hence  the  high  damping  effect  of  the  gap  when  placed  in  the  antenna 
circuit.  The  decrement  of  the  radiated  energy  is  still  further  increased 
by  the  increased  length  of  gap  required  as  well  as  by  excessive  leakage 
losses,  corona,  etc.,  which  may  occur  at  these  increased  voltages.  The 
decrement  may  be  reduced  by  inserting  a  low  resistance  inductance  L 
in  the  aerial  circuit  as  shown  in  Fig.  4,  and  as  shown  by  the  formula  for 
decrement  given  on  page  214.  The  oscillations  will  thus  decay  more 
slowly,  giving  a  more  sustained  effect  to  the  radiated  energy;  but  the 
amount  of  energy  radiated  is  less. 

It  may  not  be  possible,  however,  to  insert  this  inductance,  if  it  is 
desired  to  transmit  at  certain  short  wave  lengths.  For  these  reasons  the 
direct  excitation  method  is  not  used  on  medium-  or  high-powered  trans- 
mitters, and  is  found  only  on  very  small  or  emergency  sets,  when  low 
first  cost  or  space  restriction  may  be  the  primary  consideration. 

Means  of  Energy  Supply. — Modern  spark  transmitters  may  be  equipped 
with  one  of  two  forms  of  energy  supply  to  the  closed  circuit : 


FIG.  4. — The  earliest  type  of  radio  transmitter,  using 
direct  excitation,  the  spark  gap  being  in  the 
antenna  circuit. 


282  SPARK  TELKGKAPHY  [CHAP.  V 

(a)  The  storage  battery  and  induction  coil. 

(6)  The  alternator  and  step-up  power  transformer. 

The  Storage  Battery  and  Induction  Coil. — Sets  utilizing  the  storage 
battery  and  induction  coil  are  usually  of  an  emergency  or  portable  nature, 
and  of  relatively  low  power.  (Not  over  1  kw.)  The  connections  of 
such  a  set  have  already  been  indicated  in  Fig.  4.  The  direct  excitation 
used  in  the  figure,  however,  is  rarely  employed,  conductive  coupling 
between  the  closed  and  radiating  circuit  usually  being  employed. 

The  induction  coil  is  simply  an  "  open-core  "  transformer,  possessing 
a  primary  winding  wound  with  a  few  turns  of  heavy  wire,  and  a  secondary 
winding  consisting  of  a  large  number  of  turns  of  fine  wire.  Closing  the 
key  completes  the  primary  circuit  and  connects  the  primary  winding 
directly  across  the  battery.  Current  will  thus  flow  through  the  winding, 
magnetizing  the  iron  core.  When  the  magnetization  has  reached  a  certain 
critical  value,  the  armature  A,  Fig.  4,  is  drawn  toward  the  core,  opening 
the  circuit  at  the  contact  C.  This  sudden  opening  of  the  primary  causes 
the  flux  set  up  in  the  core,  which  links  both  secondary  and  primary  wind- 
ings, to  collapse  or  decrease  at  a  very  high  speed.  In  collapsing  the  flux 
cuts  the  secondary  winding  and  a  very  high  electromotive  force  is  thus 
induced  in  this  winding.  This  e.m.f.,  impressed  on  the  antenna  circuit, 
charges  the  antenna  up  to  that  potential,  at  which  the  gap  breaks  down, 
whereupon  a  high  frequency  oscillatory  discharge  occurs,  as  already 
described  in  the  first  pages  of  Chapter  IV. 

The  decrease  of  flux  in  the  core  reduces  the  attraction  on  the  armature 
A,  which  is  drawn  back  to  its  initial  position  by  the  spring  S,  thus  closing 
the  primary  circuit  again,  whereupon  the  cycle  of  events  just  described 
is  repeated.  The  frequency  with  which  the  armature  makes  and  breaks 
the  primary  circuit  determines  the  frequency  of  the  high  voltage  pulses 
impressed  on  the  closed  circuit,  and  thus  also  determines  the  group  or 
spark  frequency  of  the  set.  This  frequency  may  range  from  30  to  100 
"  makes  "  and  "  breaks  "  per  second  on  modern  interrupters  of  this  type, 
known  as  the  "  hammer  break  "  type.  The  constants  of  the  armature 
system  (the  inertia  of  the  armature  and  the  spring  tension)  determine 
this  frequency,  which  may  therefore  be  adjusted  within  the  limits  indi- 
cated above  to  give  a  required  group  frequency.  This  is  usually  accom- 
plished by  adjustment  of  the  spring  tension  and  initial  position  of  the 
armature. 

Requirements  of  Interrupter  Action. — Since  the  function  of  the  induc- 
tion coil  is  to  charge  a  capacity  to  certain  high  potential  in  a  very  short 
interval  of  time  (the  duration  of  the  high  e.m.f.  in  the  secondary  is  very 
short),  the  following  requirements  must  be  fulfilled. 

(a)  The  primary  must  be  broken  cleanly  and  quickly,  so  that  the  pri- 
mary current  and  thus  the  flux  surrounding  both  windings,  decreases 


ACTION   OF  INDUCTION   COIL 


283 


very  rapidly,  and  (6)  the  time  constant  of  the  secondary  or  high-tension 
circuit  must  be  sufficiently  low.  In  considering  the  above  requirements, 
it  is  desirable  to  analyze  somewhat  carefully  the  actions  which  occur  in 
the  induction  coil  at  "  make  "  and  "  break." 

Action  of  Shunting  Condenser. — If  we  assume  the  operating  key 
closed,  we  have  the  condition  of  a  constant  e.m.f .  impressed  on  an  inductive 
circuit.  Therefore  the  current  in  the  primary  increases,  as  already 
described  (page  32),  and  as  indicated  in  curve  a,  Fig.  5.  The  flux  through 


vOl  sec- 


FIG.  5. — Currents  and  voltages  in  the  circuits  of  a  spark  coil  having  a  vibrating  contact. 

the  core  and  linking  both  windings  follows  a  nearly  similar  variation,  as 
shown  in  curve  b.  We  therefore  have  voltages  induced  in  both  windings 
of  the  coil;  in  the  case  of  the  primary  this  voltage  represents  the  c. e.m.f. 
of  self-induction;  in  the  case  of  the  secondary,  it  is  simply  an  induced 

e.m.f.  and  is  equal  to  Ns  -£-,  Ns  being  the  number  of  secondary  turns. 

ut 

The  secondary  induced  e.m.f.  is  indicated  by  curve  c. 

At  the  instant  the  contact  closes  the  primary  circuit  the  changing  flux 
in  the  core  must  be  just  sufficient  to  balance  the  impressed,  or  battery, 

voltage.     We  may  therefore  write  for  this  instant,  -r-  =  — ^ — ,  E  being 

dt         J\  p 

the  impressed  voltage  and  Np  being  the  number  of  turns  in  the  primary 


284  SPARK  TELEGRAPHY  [CHAP.  V 

winding.  If  there  were  no  magnetic  leakage  between  the  primary  and 
secondary  coils  the  induced  secondary  voltage  would  be  equal  to  ^  -p 

N 
which  may  evidently  be  written  E  ~.     Hence  at  the  instant  of  "  make  " 

J\p 

the  induced  secondary  voltage  is  comparatively  low,  practically  negligible 
compared  to  the  voltage  obtained  at  the  break. 

When  the  primary  circuit  is  interrupted  at  the  contacts  of  the  vibrator, 
a  high  e.m.f.  will  be  induced  in  each  winding,  the  relative  value  of  the 
primary  and  secondary  e.m.f.  being  determined  by  the  turn  ratio.  The 
counter  e.m.f.  of  self-induction  will  tend  to  maintain  a  current  in  the  pri- 
mary across  the  gap  between  the  vibrator  contacts,  and  if  permitted  to 
do  so,  this  current  will  flow  as  an  arc  across  this  gap,  injuring  the  contacts 
and  preventing  the  very  rapid  decrease  of  flux  desirable.  To  prevent 
this  action,  a  large  capacity  is  shunted  across  the  vibrator  contacts  as 
shown  in  Fig.  4.  The  counter  e.m.f.  of  the  primary  now  charges  this 
condenser,  which,  since  its  capacity  is  relatively  large,1  does  not  rise  to 
very  high  potentials,  and  thus  limits  the  potential  across  the  contacts, 
which  cannot  exceed  that  of  the  condenser.  Sparking  or  arcing  at  the 
contacts  is  thus  avoided. 

As  the  condenser  becomes  charged,  and  the  energy  of  the  magnetic 
field  is  discharged,  a  point  will  be  reached  where  the  potential  of  the  con- 
denser is  greater  than  that  of  the  coil.  The  condenser  will  then  discharge 
into  the  coil,  but  the  current  will  oppose  the  original  flow  of  current 
and  therefore  increase  the  rate  of  decay  of  current  in  the  circuit.  In 
effect  the  primary  circuit  is  an  oscillating  circuit,  although  the  first  oscil- 
lation only  is  of  importance,  due  to  the  very  high  damping.  The  effect 
of  the  shunting  condenser  is  thus  (a)  to  prevent  arcing  and  sparking 
at  the  contacts  of  the  vibrator,  resulting  in  a  cleaner  break,  higher  induced 
e.m.f.'s  in  the  secondary  winding,  and  decreased  injury  to  contacts;  (b)  an 
opposing  discharge  current  flows  into  the  primary  winding,  which  increases 
the  rate  of  decay  of  flux,  thus  also  increasing  the  e.m.f.  induced  in  the 
secondary.  For  these  reasons  a  shunting  condenser  is  always  used  in 
connection  with  the  induction  coil,  being  usually  assembled  in  the  base 
of  the  induction  coil  case. 

Duration  of  High  Potential  Induced  in  Secondary  Circuit. — The  period 
of  time  during  which  the  high  voltage  is  available  at  the  secondary  ter- 
minals is  extremely  small.  This  may  be  seen  from  the  following:  if 
the  primary  circuit  has  no  condenser,  the  decay  depends  primarily  on  the 
quickness  and  cleanness  with  which  the  vibrator  opens  its  contacts.  The 

1  The  condenser  should  be  only  just  large  enough  to  suppress  arcing  at  the  contacts; 
if  the  value  of  the  capacity  is  greater  than  this  required  amount  the  secondary  induced 
voltage  will  be  lower  than  if  a  proper  condenser  is  used. 


ACTION  OF  INDUCTION  COIL  285 

resistance  then  inserted  in  the  circuit  is  very  high  and  the  time  constant 

(  =  _  )  is  therefore  very  small.     The  collapse  of  the  flux  is  then  correspond- 
\    w 

ing]y  rapid  if  we  neglect  the  effect  on  this  flux  of  whatever  current  may  be 
present  in  the  secondary  circuit  during  this  time. 

If  a  condenser  shunts  the  contacts,  the  time  is  fixed  by  the  natural 
period  of  this  circuit;  thus  if  we  assume  Cp=  1/if,  Lp  =  .01  henry,  the  time 
of  the  first  alternation  of  secondary  voltage  is  given  by  the  equation 

27rXlO-3X.l 


If  a  spark  does  not  take  place,  other  alternations  of  voltage  will  follow 
this  one,  but  will  be  successively  smaller  in  amplitude  and  hence  would 
evidently  not  produce  a  spark  if  the  first  alternation  did  not. 

Action  in  the  Secondary  Circuit*  —  In  the  secondary  circuit,  the  e.m.f. 
induced  must  overcome  the  reactions  of  the  winding  resistance  and  the 
condenser,  or 

Ns      =  IsRs+vc  .........     (1) 


This  circuit  is  equivalent  to  the  circuit  considered  on  page  37,  where 
the  charging  of  condenser  through  resistance  was  discussed.  The 
induced  voltage  may  be  considered  as  acting  on  the  capacity  through  Rs. 

The  time  constant  of  this  circuit  is   CSRS  and  since  Ns-~  has  such  a 

at 

short  duration,  it  is  essential  that  CSRS  be  small,  if  the  capacity  is  to  be 
charged  to  the  maximum  possible  potential.  Since  Cs  is  fixed  by  the  wave 
length  and  energy  requirement  of  the  set,  Rs  must  be  made  as  low  as  pos- 
sible. For  this  reason  induction  coils  intended  for  radio  service  have  their 
secondaries  wound  with  wire  several  sizes  larger  than  would  ordinarily 
be  used,  as  for  instance,  in  a  coil  intended  for  gas-engine  ignition.  It 
must  be  borne  in  mind  that  the  actual  electrical  efficiency  of  the  coil 
intended  for  radio  work  may  be  of  importance,  and  when  this  is  so,  it  is 
evident  that  the  PR  loss  in  the  secondary  winding  must  be  kept  as  low  as 
possible.  This  is  another  reason  for  keeping  the  resistance  of  the  second- 
ary winding  low. 

The  action  which  occurs  in  the  secondary  circuit  at  the  instant  of 

1  This  elementary  analysis  is  based  on  the  assumption  that  the  secondary  circuit 
has  no  effect  on  the  time  constant  of  the  primary  circuit;  if  a  condenser  is  connected 
across  the  secondary  terminals  (or  the  internal  capacity  of  the  secondary  winding  has 
an  appreciable  effect)  this  assumption  is  hardly  warranted. 


286 


SPARK  TELEGRAPHY 


[CHAP.  V 


primary  "  break  "  is  indicated  to  a  larger  time  scale  in  Fig.  6  l  where  (a) 
indicates  the  conditions  with  the  spark  gap  disconnected  from  the  second- 
ary circuit  while  (6)  shows  the  operation  when  both  the  condenser  and 
gap  are  across  the  high-tension  winding  as  in  normal  operation. 

The  duration  of  the  train  of  high-frequency  oscillations,  assuming  a 
decrement  of  0.2  (which  is  not  excessive  for  this  type  of  circuit),  and  a 
frequency  of  1,000,000,  is  calculated  as  follows: 


4.6+6     4.6+0.2 


0.2 


=      waves 


and  the  duration  is, 


1 


x  1,600,000 

=  24X10~6  seconds. 


Instant  of  Gap  Breakdown 


(Decrement  of  Oscillations  =  0.2) 
(6) 


0  .0005  .001  0 

Conditions  when  gap  does 

not  break  do.wn 


.00001 


Conditions  when  gap 
breaks  down 


FIG.  6. — Action  of  a  spark  coil  connected  to  an  oscillatory  circuit. 

This  time  would  be  indicated  by  practically  a  straight  vertical  line 
on  the  scale  of  Fig.  5.  Conditions  as  indicated  in  Fig.  6  (a)  would  also 
apply  to  the  primary  circuit  if  a  suitable  condenser  is  used  across  the 
contacts. 

Types  of  Interrupters. — As  has  been  mentioned,  the  induction  coil  is 
used  chiefly  on  sets  of  low  power,  usually  representing  emergency  equip- 
ment. On  these  the  principal  type  of  interrupter  used  is  the  "  hammer 

lln  calculating  the  time  scale  for  diagram  6  (a),  it  has  been  assumed  that  the 
secondary  winding  has  an  inductance  of  25  henries,  and  that  the  condenser  used  in 
the  secondary  circuit  has  a  capacity  of  .002  microfarad. 


ALTERNATING  CURRENT  GENERATOR          287 

break  "  interrupter  as  mentioned  previously.  This  type  of  break,  however, 
is  limited  in  its  ability  to  interrupt  large  currents,  and  in  the  frequency  of 
interruption  to  which  it  can  be  adjusted.  The  turbine  break,  which  opens 
the  primary  circuit  by  periodically  interrupting  a  jet  of  mercury  which 
completes  the  circuit,  may  be  used  when  larger  currents  and  power  are 
involved.  The  frequency  of  interruption  is  also  under  ready  control,  and 
can  be  varied  from  30  to  1200  breaks  per  second,  by  adjusting  the  speed 
of  the  rotating  member,  which  is  usually  driven  by  a  small  motor. 

The  electrolytic  type,  and  various  types  of  motor  (commutator)  inter- 
rupters have  also  been  used.  The  student  is  referred  to  Fleming's  "  Prin- 
ciples of  Electric  Wave  Telegraphy  and  Telephony  "  for  more  detailed 
information  on  these  types,  which  are  relatively  little  used  on  modern 
spark  transmitters. 

The  foregoing  interrupters  are  not  capable  of  properly  "  making  " 
and  "  breaking  "  large  currents  many  times  per  second  (500  or  1000)  and 
for  this  reason  the  induction  coil  is  at  present  limited  in  application  to 
small  power  sets. 

Alternator  and  Step-up  Transformer. — The  use  of  an  alternator  and 
step-up  transformer  is  practically  universal,  with  the  exception  of  very 
small  sets,  which  may  economically  and  conveniently  be  supplied  by  a 
storage  battery  and  induction  coil  as  described  above.  Alternators  for 
radio  service  are  usually  motor  driven,  where  electrical  power  is  available. 
If  no  electrical  source  of  power  is  provided,  a  gas,  oil  engine,  or  small 
steam  turbine  may  be  used  as  the  prime  mover. 

Alternator  Construction. — The  general  construction  of  such  an  alter- 
nator does  not  differ  radically  from  that  of  the  ordinary  machine  of  power 
engineering,  and  will  be  in  accordance  with  one  of  the  following  construc- 
tional arrangements: 

(a)  Fixed  Field  and  Rotating  Armature; 
(6)  Rotating  Field  and  Fixed  Armature; 
(c)  Inductor  Type. 

The  first  two  arrangements  have  been  widely  used  in  the  past,  while 
the  third  type  is  more  recent.  It  possesses  the  advantage  that  all  windings 
are  fixed  in  position  and  thus  liability  of  damage  to  insulation  is  reduced 
and  greater  mechanical  strength  and  ruggedness  is  obtained. 

Alternator  Action. — The  action  of  all  three  arrangements  is  to  induce 
in  the  armature  winding  an  alternating  e.m.f.  Types  a  and  b  secure 
this  result  by  varying  the  position  of  the  field  windings  relative  to  the 
armature  winding,  thus  causing  a  periodic  change  in  the  flux  linking  a 
given  coil  and  inducing  therein  an  alternating  e.m.f.  This  action  is 
indicated  in  Fig.  7. 

In  the  inductor  type  the  relative  position  of  the  armature  and  field 


288 


SPARK  TELEGRAPHY 


[CHAP.  V 


windings  is  fixed,  but  a  revolving  rotor  periodically  varies  the  reluctance 
of  the  flux  path,  and  thus  the  flux  linking  a  given  winding  in  the  armature, 
periodically  increases  and  decreases  as  indicated  in  Fig.  8.  The  rotor 
carries  no  windings,  the  projections  (pole  teeth)  on  its  periphery  acting 
to  cause  the  required  periodic  variation  of  flux. 


Position  of  conductor 
FIG.  7. — Induction  of  e.m.f.  in  the  conductor  of  a  revolving  armature  alternator. 

Frequency  of  Generated  E.M.F.— In  the  case  of  the  first  two  types  the 
flux  of  adjacent  poles  is  always  in  the  opposite  directions:  Thus  a  con- 
ductor passing  through  the  flux  emanating  from  the  N  pole  will  have 
induced  in  it  an  e.m.f.  of  one  direction  or  polarity,  and  in  passing  through 
the  S  pole  flux,  will  have  the  direction  of  e.m.f.  reversed,  i.e.,  a  complete 
cycle  of  alternating  e.m.f.  is  induced  in  the  conductor  as  it  passes  a  pair 
of  poles. 


Armature  Winding 


Field  Winding 


FIG.  8. — Action  of  an  inductor  alternator. 

In  the  case  of  the  inductor  type,  the  direction  of  the  flux  relative  to 
the  armature  winding  is  always  the  same,  but  this  flux  varies  periodically 
with  time  as  the  reluctance  of  its  path  increases  and  decreases.  When 

the  flux  is  increasing  the  induced  e.m.f .  ( e  =  N  -5-  j  will  have  a  certain 

polarity.  When  the  rate  of  change  of  flux  reverses,  that  is,  becomes  a 
decrease,  the  induced  e.m.f.  reverses  and  an  alternating  e.m.f.  is  thus 
developed. 


ALTERNATING-CURRENT  GENERATOR  289V 

For  classes  (a)  and  (b)  the  frequency,  i.e.,  the  number  of  complete 
cycles  per  second,  is  equal  to  the  number  of  pairs  of  poles  (in  passing  one 
pair  of  poles  the  induced  e.m.f.  passes  from  0  to  +  maximum  to  0  to 
-maximum  and  back  to  0)  times  the  revolutions  per  second,  or^ 

/=pXr.p.s (2) 

Thus  a  4-pole  machine,  when  driven  at  1800  r.p.m.,  will  give  a  fre- 
quency of  60  cycles  per  second. 

In  the  inductor  type,  a  complete  cycle  is  obtained  when  the  rotor 
moves  through  the  angle  of  the  pole  pitch  (pole  pitch  =  distance  from  a 
point  on  one  field  projection  on  rotor  to  the  corresponding  point  on  the 
adjacent  projection). 

Thus,  if  the  rotor  makes  one  complete  revolution,  the  cycles  generated 
are  equal  to  the  number  of  teeth  or  projections  on  the  rotor.  The  cycles 
per  second  are  thus  equal  to 

/=nX(r.p.s.),   .  ' (2a) 

where  n  =  the  number  of  pole  teeth,  or  slots  on  the  rotor 

Radio  alternators  differ  from  alternators  used  for  power  engineering, 
in  two  important  characteristics:  (a)  frequency,  (6)  internal  reactance. 
The  frequency  of  the  alternator  determines  the  spark  or  group  frequency 
of  the  set  (neglecting  the  application  of  the  non-synchronous  gap  discussed 
below),  which  in  turn  determines  the  number  of  times  the  receiver  dia- 
phragm is  impulsed  per  second  at  the  receiver  station,  or  the  pitch  of  the 
note,  heard  in  the  phones  by  the  receiving  operator.  Modern  receiver 
diaphragms  normally  have  a  natural  frequency  of  about  1000  cycles  per 
second,  and  the  human  ear  is  most  sensitive  at  about  this  frequency;  it 
is  therefore  desirable  to  use  this  frequency  of  wave  trains,  if  the  maximum 
audibility  of  the  received  signal  is  to  be  obtained.  (When  the  signal 
frequency  corresponds  to  the  natural  frequency  of  the  telephone  diaphragm 
maximum  signal  strength  for  a  given  impressed  e.m.f.  results.)  Thus 
modern  radio  alternators  are  constructed  to  give  very  much  higher  fre- 
quencies than  are  used  in  power  engineering  practice,  a  usual  value  being 
500  cycles,  giving  a  group  frequency  of  1000,  when  the  gap  is  adjusted 
to  break  down  once  every  half  cycle. 

This  high  frequency  requires  a  large  number  of  poles,  or  excessively 
high  speeds,  for  its  generation.  Thus  a  four-pole  machine  would  have  to 
be  run  at  250  r.p.s.  or  15,000  r.p.m.,  to  give  500  cycles  per  second.  This 
high  speed  would  involve  difficult  and  expensive  construction  and  there- 
fore the  number  of  field  poles  is  increased  to  obtain  the  desired  frequency 
at  a  lower  speed.  To  secure  the  required  number  of  poles  around  the 
periphery  of  the  armature,  without  making  the  latter  excessively  large, 


290  SPARK  TELEGRAPHY  [CHAP.  V 

requires  special  construction.     Thus,  assuming  an  alternator  driven  at 
1500  r.p.m.,  or  25  r.p.s.,  we  have, 


y=500  =  nX25,  where  n  =  No.  of  pairs  of  poles 
n  =  20 

Thus,  20  pairs,  or  40  poles,  would  be  required  for  the  field.     To  mini- 

mize the  space  required,  field  coils  are  placed  only  on  alternate  poles  (A7"), 

p}eld  the  remaining  poles  (S) 

thus  being   consequent 
I         poles.     This    construc- 


tion  is    illustrated    in 


Armature  Fig-  9; 

FIG.  9.— The  ordinary  small  radio  alternator  has  a  field  Witn  tne  inductor 
coil  on  every  other  pole  only,  half  the  poles  being  con-  type,  very  much  higher 
sequent  poles.  speeds  are  permissible, 

as     all     windings    are 

fixed  in  position,  and  the  rotor  can  be  specially  designed  and  constructed 
for  high-speed  operation.  Such  construction  is  illustrated  by  the 
Alexanderson  high-frequency  alternator  described  in  Chapter  VII.  With 
the  inductor  type  it  is  not  difficult  to  secure  the  necessary  frequency 
by  increasing  the  number  of  pole  teeth,  keeping  the  speed  within  reason- 
able values.  Thus  for  the  case  considered  above,  20  teeth,  each  tooth 
and  its  associated  slot  being  equivalent  to  a  pair  of  poles,  would  be 
formed  on  the  rim  of  the  rotor. 

Driving  Motor. — The  driving  motor  for  any  type  of  radio  alternator 
should  have  a  practically  constant  speed-load  characteristic  over  the  load 
range  in  which  it  is  to  operate.  This  requirement  is  fulfilled  sufficiently 
well  by  the  modern  shunt  motor,  although  differential  compound  wound 
motors  are  also  used  to  secure  the  desired  constancy  in  speed.  Poly- 
phase synchronous  or  induction  motors  may  also  be  used  where  a.c.  power 
only  is  available. 

Internal  Impedance  of  Radio  Alternators. — The  second  characteristic 
which  differentiates  the  alternator  used  for  commercial  power  purposes 
and  the  radio  alternator,  is  the  internal  or  armature  impedance.  The 
radio  alternator  operates  always  for  a  small  part  of  its  cycle,  under  short- 
circuit  conditions.  It  has  already  been  indicated  (page  278)  that  the  exces- 
sive current  which  would  flow  in  the  alternator  and  transformer  windings 
throughout  the  interval  during  which  the  gap  is  carrying  current  and 
hence  has  very  low  resistance,  may  be  minimized  by  high  reactance  in 
the  transformer,  artificial  inductance  in  the  transformer  supply  leads 
(choke  coils),  or  high  impedance  in  the  armature  of  the  alternator.  The 
last  named  method  is  that  usually  employed,  and  modern  practice  indi- 
cates that  the  high  impedance  alternator  is  the  best  solution  of  the  problem. 


INTERNAL  IMPEDANCE  OF  ALTERNATORS 


291 


the   main  field  flux.     It  is 
local   flux,  as  indicated  in 


Choke  coils  or  reactance  regulators  represent  additional  equipment  and 
complication,  and  are  therefore  relatively  little  used. 

A  high  armature  impedance  means  essentially  a  high  armature  reac- 
ance,  the  resistance  usually  being  quite  small  compared  to  the  reactance. 
The  reactance  of  the  armature  is  made  _  _  i 

up  of  two  components: 

(a)  leakage  reactance; 
(6)  armature  reaction. 

The  leakage  reactance  is  caused   by 
the   flux   surrounding   the  winding   con- 
ductors, this  so-called  leakage  flux  having 
no  effect   on 
essentially  a 
Fig.  10. 

This  flux  induces  a  c.e.m.f.  of  self- 
induction  in  the  armature  winding,  and 
represents  the  inherent  reactance  of  the 

armature  circuit.     The  voltage  required    to    send    a    current  /  through 
the  armature  at  standstill  is  therefore, 


FIG.  10. — Conventional  diagram  of 
leakage  flux  around  an  armature 
conductor. 


E  =  IZ,  where  Z  = 


X2 


leakage, 


the  measurements  being  made  as  for  any  inductive  circuit.  They  must 
be  repeated  with  the  armature  slots  in  several  different  positions  with 
respect  to  the  field  poles,  and  the  results  averaged,  since  the  reluctance 
of  the  leakage  flux  path  is  affected  by  the  position  of  the  field  poles. 

Armature  reaction  is  the  name  given  to  the  distorting  and  demagnet- 
izing effect  of  the  armature  magnetomotive  force  on  the  main  field.  (It 
is  evident  that  since  the  armature  is  made  up  of  turns  of  wire  carrying 
current  wound  on  an  iron  core,  that  the  armature  represents  a  certain 
number  of  ampere  turns,  and  thus  also  a  m.m.f.)  This  effect  is  separate 
from  the  leakage  flux  (which  does  not  necessarily  react  on  the  main  field); 
and  is  indicated  in  Fig.  II.1 

The  first  reactance  causes  a  real  reactive  voltage  which  must  be  over- 
come by  the  generated  e.m.f.  in  the  circuit.  The  second  reaction  may 
be  considered  as  an  apparent  reactance  inserted  into  the  circuit,  the 
induced  e.m.f.  being  assumed  constant.  Actually  the  induced  e.m.f.  does 
not  remain  constant,  but  increases  on  leading  load  and  decreases  on  lagging 
load.  The  relation  between  terminal  voltage,  armature  current,  armature 

1  In  Fig.  11  the  vectors  showing  armature  m.m.f  .  are  merely  indications  of  the  aver- 
age effect  of  the  armature  m.m.f.;  actually  the  armature  reaction  of  a  single-phase 
alternator  (all  radio  alternators  are  single  phase)  is  variable  in  magnitude  and  direc- 
tion. For  an  elementary  analysis  see  Morecroft,  "  Continuous  and  Alternating  Current 
Machinery,"  p.  244  et  seq. 


292 


SPARK  TELEGRAPHY 


[CHAP.  V 


constants,  and  armature  reaction  is  indicated  in  Figs.  12  and  13,  which 
have  been  drawn  for  a  commercial  alternator  and  a  machine  intended 
for  radio  service  under  normal  load  and  sustained  short-circuit  conditions.1 
On  the  former  machine  the  short-circuit  current  (sustained  value)  may  be 
2.5  to  3  times  the  normal  value,  while  with  the  radio  alternator,  the  short- 
circuit  current  is  only  slightly  larger  than  the  normal  value.  Thus  the  cur- 
rent carried  in  the  low-tension  circuit  does  not  increase  to  excessive  value 
when  the  gap  break-down  short-circuits  the  transformer,  and  thus  abnormal 
strains  and  resultant  damage  of  equipment  are  prevented.  In  other  words 


FIG.  11. — Various  directions  of  the  armature  magneto  motive  force,  for  loads  of  different 

characteristics. 


on  modern  alternators  designed  for  radio  service  it  does  not  require  an 
excessive  current  in  the  armature  to  make  the  armature  ampere  turns 
practically  equal  to  those  of  the  main  field.  This  means  that  the  effective 
or  net  ampere  turns  are  small,  and  the  net  flux  is  small;  thus  only  a  small 
e.m.f.  is  induced  in  the  alternator  winding,  and  the  short-circuit  current 
is  correspondingly  small. 

The  Power  Transformer. — The  function  of  the  power  transformer  in 
a  transmitting  set  has  already  been  outlined  on  page  276.  The  choice 
and  design  of  such  a  transformer  are  of  great  importance,  in  so  far  as  the 
set  may  work  very  poorly  or  fail  altogether  unless  the  transformer  has  the 
proper  characteristics. 

1  It  must  be  noted  that  the  short-circuit  condition,  i.e.,  broken  down  spark  gap, 
on  the  radio  alternator  exists  for  such  a  small  fraction  of  the  cycle,  that  conclusions 
reached  from  the  short-circuit  diagram  in  Fig.  13  are  not  directly  applicable.  An 
exact  treatment  would  require  the  analysis  of  successive  short-circuit  transients. 


REGULATION   DIAGRAMS  OF  ALTERNATORS 


293 


Total  field  \   \       Effective 
mmf.~-\\    y<"  mmf. 


Open  circuit  voltage 

at  full  load 


Voltage  Effect  of  - 
Armature  Reaction 


Leakage 


(6) 


Armature 
\rnmf. 
V       ^       Effective 


Total  field 
mmf. 


COMMERCIAL  ALTERNATOR 
(a)  Normal  Load  Conditions 
(6)  Short  circuit  " 


FIG.  12. — Regulation  diagram  for  ordinary  alternator. 


Armature 
mmf. 


(a) 


IX  Leakage 


RADIO  ALTERNATOR 
(a)  Normal  Load  Conditions 
£  (6)  Short  circuit 


(fr)  Armature 

^°'  -mmf. 


Total  flel 
mmf. 


,  IX  Leakage 


Effective 
mmf. 


IR 


=  1.51, 


FIG.  13. — Regulation  diagram  for  radio  alternator  showing  greater  effect  of  armature 
leakage  and  magnetomotive  force. 


294 


SPARK  TELEGRAPHY 


[CHAP.  V 


In  order  that  the  following  discussion  be  more  fully  understood  Fig. 
1  of  page  275  is  here  reprinted,  as  Fig.  14. 

The  main  requisites  of  a  power  transformer  are: 

1st.  That  it  shall  charge  the  condenser  C\  to  the  voltage  necessary 
to  store  therein  an  amount  of  energy  such  that,  when  the  gap  G  breaks 
down  and  the  condenser  discharges  through  the  gap  and  the  primary  L\ 
of  the  oscillation  transformer,  the  antenna  will  receive  the  required  amount 
of  energy. 

2d.  That  when  the  gap  G  breaks  down,  and  thereby  practically  short- 
circuits  the  high-tension  side  of  the  transformer,  the  current  flowing  therein, 
and  also  through  the  gap,  will  be  as  small  as  possible.  The  first  of  these 
requisites  will  be  illustrated  by  means  of  a  numerical  example. 

Antenna 


FIG.  14. — Spark  transmitter  circuit. 

Assume  the  following: 

Antenna  to  be  supplied  with  200  watts. 

Efficiency  of  transformation  from  Ci  to  antenna  =  30  per  cent.1 
Capacity  of  C\  =  0.012  micro-farads. 
Frequency  of  alternator  =  500  cycles  per  second. 
Number  of  sparks  per  second  =  2X500  =  1000. 
Then: 

Power  to  be  supplied  to  condenser  Ci  =  .  ^  =  670  watts.     The  voltage 
to  which  the  condenser  must  be  charged  is  obtained  from  the  formula: 


(3) 


where 

C  =  capacity  of  condenser  in  farads; 

V  =  voltage  to  which  condenser  is  charged; 

N  =  number  of  sparks  per  second; 

W  =  power  in  watts. 

1  This  figure  is,  of  course,  low;  it  has  been  reported  that  a  spark  set  may  have  an 
efficiency  as  high  as  60  per  cent,  measured  by  ratio  of  antenna  high-frequency  power 
to  motor  input;  an  average  figure  is  probably  40  per  cent. 


THE   POWER  TRANSFORMER  295 

Whence: 

V-M- 


The  above  simply  means  that  the  transformer  must  be  able  to  charge 
the  condenser  to  10,500  volts  once  for  every  half  cycle,  and  that  at  this 
voltage  the  gap  shall  break  down. 

The  transformer  must  be  very  well  insulated,  for  the  first  few  turns 
at  any  rate,  not  only  because  it  itself  must  develop  a  high  voltage,  as 
shown  above,  but  also  because,  after  the  gap  has  quenched,1  radio- fre- 
quency e.m.f/s  are  induced  by  the  antenna  circuit  into  the  primary  of 
the  oscillation  transformer  and  are  therefore  inpressed  upon  the  secondary 
winding  of  the  power  transformer.  These  high-frequency  e.m.f.'s  pro- 
duce high-frequency  currents,  which  flow,  by  condenser  action,  from  turn 
to  turn  and  layer  to  layer  through  the  high-tension  side  of  the  power 
transformer  and  even  through  the  low-tension  side;  unless  the  insulation 
has  low  dielectric  loss  and  unless  it  is  especially  heavy  near  the  end  turns 
of  the  high-tension  side,  where  the  dielectric  currents  are  largest,  it  is  likely 
eventually  to  break  down. 

The  second  requisite  of  the  power  transformer  is  of  importance  because 
if,  when  the  gap  breaks  down,  the  current  through  the  power  transformer 
and  the  gap  should  be  large,  not  only  would  there  be  a  large  unnecessary 
waste  of  power  but,  in  addition,  the  large  current  would  maintain  an  "  arc  " 
through  the  gap  and  thus  keep  this  "  closed,"  a  condition  which,  as  is 
pointed  out  on  page  310,  should  be  decidedly  avoided.  In  order  to  meet 
the  above  the  circuit  consisting  of  the  alternator,  the  reactance  V.R.  (see 
Fig.  14),  the  power  transformer,  the  inductances  H-H,  the  condenser  Ci, 
and  the  inductances  L\  and  L'\  are  arranged  so  that,  when  the  gap  is 
open,  the  impedance  of  this  circuit  at  the  alternator  frequency  will  be  low, 
and,  when  the  gap  breaks  down,  the  impedance  of  the  circuit  of  the  alter- 
nator V.R.y  the  power  transformer  H-H,  and  the  closed  gap  will  be  very 
much  higher.  Thus,  when  the  gap  is  open  the  flow  of  current  will  not 
be  impeded,  while  when  the  gap  breaks  down  the  current  from  the  alter- 
nator will  be  very  much  reduced.  A  simple  way  of  obtaining  this  result 
is  by  adjusting  the  circuit  of  A,  V.R.,  P-S,  H-H,  Ci,  LI,  L'i  to  have  a 
natural  frequency  equal2  to  that  of  the  alternator;  so  that,  when  the  con- 
denser Ci  and  the  inductances  L\  and  L'i  are,  by  the  breaking  down  of 
the  gap,  separated  from  the  power  transformer,  the  current  in  this  will  be 
only  a  small  fraction  of  that  flowing  when  the  gap  is  open.  In  other  words, 
the  entire  circuit  from  the  alternator  to  and  including  L\  must  resonate 

1  See  p.  314  for  discussion  of  quenching. 

-  In  practice,  this  circuit  is  adjusted  to  a  natural  frequency  somewhat  lower  than 
that  of  the  alternator,  as  is  pointed  out  on  p.  303. 


296  SPARK  TELEGRAPHY  [CHAP.  V 

at  the  alternator  frequency.  This  requires  that  the  capacity  C\  and  the 
various  inductances,  including  the  inductance  of  the  alternator  and  of  the 
transformer,  be  properly  chosen. 

The  values  of  Ci,  LI,  and  L'\  have  to  be  adjusted  to  give  the  correct 
wave  length,  and  this  makes  them  comparatively  small;  hence  in  order 
that  the  entire  circuit,  from  the  alternator  to  LI,  may  resonate  at  the 
alternator  frequency  the  inductances  to  the  left  of  the  gap  (see  Fig.  14) 
must  be  high. 

To  illustrate,  assume: 
Ci  =  0.012  =  microfarad; 
X  =  wave  length  =  600  meters; 
/=  alternator  frequency  =  500  cycles  per  second; 
L  =  total  inductance  from  the  alternator  to  and  including  LI, 
expressed  in  terms  of  high-tension  side  of  transformer,  in 
henries; 

LI  +L'i  =  inductance  of  LI  and  L'i  in  microhenries. 
From  formula  (15)  page  212, 


27T  VLC 

Therefore,  for  resonance  at  500  cycles  per  second, 


Again,  from  formula  (18),  page  213, 

X  =  1885V0.012(Li-hL'i) 
or 

6002 
Li+Li'=18852)<0()12  =  8.5  microhenries. 

Thus,  while  the  inductance  of  Li  and  L'i  must  be  8.5  microhenries,  the 
inductance  of  the  entire  circuit  may  be  8.5  henries  or  one  million  times 
as  large;  hence,  practically  all  of  the  inductance  necessary  to  bring  about 
resonance  at  the  alternator  frequency  must  be  in  the  alternator,  V.R., 
the  power  transformer  and  the  choke  coils  H-H. 

Up  to  a  few  years  ago  it  was  common  practice  to  design  the  trans- 
former with  the  highest  possible  inductance  or,  in  other  words,  with  a  very 
large  amount  of  magnetic  leakage,  so  that  the  most  of  the  required  induct- 
ance was  in  the  transformer  and  comparatively  little  in  the  alternator 
and  the  choke  coils;  such  a  transformer  was  called  a  "  resonance  trans- 
former," in  so  far  as  its  inductance  alone  was  nearly  capable  of  bringing 
about  resonance  at  the  alternator  frequency.  A  transformer  of  this  type 
was  generally  made  with  an  open  magnetic  circuit,  a  so-called  "  open- 
core  transformer."  The  tendency  of  late  is  to  design  the  transformer 
with  little  leakage  (closed  magnetic  circuit)  and  hence  little  inductance, 


TRANSMITTER  CONDENSERS 


297 


O 

D 

O 


and  place  the  required  inductance  outside  of  the  transformer  in  series 
with  its  low-tension  side,  as  at  V.R.  (Fig.  14)  or  in  the  alternator  armature. 
Some  of  the  power  transformers  for  the  smaller  sets  are  constructed  so  that 
the  leakage,  and  therefore  the  inductance  of  the  transformer,_may  be 
regulated;  thus,  in  Fig.  15  by  moving  the  magnetic  shunt  Tlf,  which  is 
pivoted  at  D,  the  air  gap  A  may  be  varied,  and  in  this  manner  more  or  less 
flux  may  be  caused  to  leak  away  from  the  secondary  coil  S  and  into  the 
shunt  M .  This  arrangement  is  satisfactory  for  small  power  transformers, 
but  not  so  for  large  transformers,  espe- 
cially in  view  of  the  noise  due  to  the  vibra- 
tions of  the  shunt  M,  which  is  difficult  to 
overcome. 

It  is  standard  practice  at  present  for 
any  but  the  smallest-size  sets  to  con- 
struct the  alternator  with  high  induct- 
ance, the  transformer  with  a  closed  core 
and  hence  with  low  inductance,  and  to 
make  up  the  needed  additional  induct- 
ance in  the  form  of  a  coil  V.R.,  inserted 
in  the  primary  of  the  transformer. 

It  has  already  been  pointed  out  that 
the  insulation  of  the  power  transformer 
must  be  of  the  best,1  not  only  because 
of  the  low-frequency  high  voltage  but 
also  because  of  the  trouble  experienced 
due  to  high-frequency  currents  finding 
their  way  into  the  transformer.  If  the  choke  coils  H-H  are  used  (see 
Fig.  14)  they  should  reduce  to  a  minimum  the  high-frequency  currents 
flowing  in  the  transformer;  if  the  choke  coils  are  not  used,  and  this 
is  very  common  in  order  to  simplify  the  equipment,  then  the  insulation 
of  the  transformer  secondary  must  be  augmented  in  order  to  take  care 
of  the  voltages  due  to  the  high-frequency  currents. 

Condensers. — The  Audio  Frequency  Circuit  of  the  Transmitting  Set— 
The  condensers  used  in  a  transmitting  set  are  known  as  "  power  con- 
densers," to  distinguish  them  from  those  used  in  a  receiving  set,  which  are 
known  as  "  receiving  condensers."  A  power  condenser  must,  as  its  very 
name  implies,  be  capable  of  handling  large  amounts  of  power  without 
serious  deterioration  or  breaking  down. 

The  requisites  of  a  power  condenser  are: 

1st.  That  the  insulation  between  plates  shall  be  such  as  to  prevent 
its  being  punctured  by  the  high  voltage  used. 

1  In  American  practice  the  transformer  is  generally  an  open-core  transformer,  air 
cooled;  in  European  practice  an  oil-cooled  transformer  is  generally  used,  this  type  being 
undoubtedly  superior  to  the  air-cooled  type. 


FIG.  15. — Small  radio  transformers 
are  frequently  fitted  with  an 
adjustable  magnetic  shunt. 


298  SPARK  TELEGRAPHY  [CHAP.  V 

2d.  That  the  losses  shall  be  small  (see  page  166,  Chapter  II).  The 
dielectrics  generally  used  in  power  condensers  are:  air,  glass,  oil  and 
mica.  Of  these  air  has  the  minimum  specific  inductive  capacity,  and 
it  causes  practically  no  losses,  while  the  other  dielectrics  have  a  much 
higher  specific  inductive  capacity  but  suffer  more  or  less  energy  loss.  As 
regards  breakdown  voltage  air  is  at  a  disadvantage  as  compared  with  the 
other  dielectrics,  but  at  pressures  higher  than  atmospheric  the  break- 
down voltage  for  air  is  very  high  and  it  increases  in  nearly  direct  propor- 
tion to  the  absolute  pressure.  A  comparison  of  the  characteristics  of 
these  dielectrics  is  given  in  Chapter  II,  page  169. 

It  will  be  seen  from  the  characteristics  of  the  various  dielectrics  that 
if  a  condenser  of  a  certain  capacity  is  to  be  designed,  the  air  condenser 
would  have  the  largest  dimensions  and  the  mica  condenser  the  smallest. 
However,  the  losses  in  the  air  condenser  would  be  very  small,  while  those 
in  a  poorly  constructed  mica  condenser  might  be  so  high  as  to  make  its 
use  prohibitive.  Glass  condensers  in  the  form  of  Ley  den  jars  have  met 
with  much  favor  in  the  radio  field  and  they  are  being  extensively  used. 
Each  jar  has  a  capacity  of  about  0.002  nf,  and  is  capable  of  withstanding 
a  voltage  of  about  15,000;  for  any  particular  desired  voltage  and  capacity 
the  jars  are  grouped  in  series  multiple,  so  that  the  combination  will  have 
the  required  capacity  and  breakdown  voltage.  Condensers  with  glass  as 
the  dielectric  are  also  made  with  flat  pieces  of  glass  covered  with  tin  foil, 
the  spate  requirements  of  such  condensers  being  much  smaller  than  for 
the  Leyden  jars.  They  do  not  stand  continued  use,  however,  as  well 
as  the  Leyden  jars,  because  of  the  greater  amount  of  heating  due  to  smaller 
cooling  surface. 

Oil  condensers  are  not  very  much  used  in  general  practice,  but  their 
use  is  very  commendable  in  places  where  there  is  no  possibility  of  spilling 
the  oil.  It  must  be  borne  in  mind,  that  although  the  dielectric  properties 
of  oil  are  unfavorably  affected  by  a  flash  through  it,  so  that  oil  condensers 
cannot  be  expected  to  give  as  good  service  after  the  oil  has  once 
been  flashed,  they  are  still  serviceable  after  a  breakdown,  whereas 
a  solid  dielectric  condenser,  such  as  mica  or  glass,  is  completely 
spoiled. 

The  mica  condenser  is  a  very  desirable  one,  and  is  apparently  going 

to  largely  supplant  the  Leyden  jar  for  ship  sets  and  similar  installations. 

It  is  compact,  and,  if  properly  constructed,  has  a  loss  so  small  as  to  be 

"  ardly  measurable.     The  impregnation  of  the  condenser  with  suitable  wax 

aij[J  be  done  sufficiently  well  to  drive  out  all  air  completely,  as  the  trapped 

forrri£>bles,  suffering  corona  loss,  are  the    source  of  local  heating  and 

about  rt5en  *ne  dielectric  strength  of  the  mica.     It  must  be  noted  that 

was  gener2sers  are  ma-de  to  be  used  at  the  rated  voltage  and  frequency 

core  transfoi  service  only  and  that  even  a  good  mica  condenser  if  used 

with  little 


TRANSMITTER  CONDENSERS  299 

continuously  at  the  rated  voltage  and  frequency  will  have  its  wax  melted 
after  an  hour  or  so. 

Compressed-air  condensers  are  very  suitable  where  very  high  voltages 
and  low  losses  are  required;  the  structure  of  the  condenser,  i.e.,  the  metal 
plates  and  their  insulating  supports,  is  placed  in  a  steel  container  capable 
of  safely  withstanding  a  pressure  up  to  a  dozen  atmospheres  or  more  and 
dry  compressed  air  is  pumped  in  until  the  required  pressure  is  obtained. 
It  may  be  easily  seen  that  an  air  compressor  and  gauge  are  necessary 
auxiliaries  of  such  condensers,  and  that  their  use  cannot  be  considered, 
except  for  very  large  land  installations,  or  for  laboratories. 

On  the  whole  the  Ley  den  jar  with  its  simplicity  of  construction  and 
large  heat-radiating  surface  affording  cool  operation  is  a  favorite  type 
of  transmitting  condenser  and  would  be  even  more  widely  used  were  it 
not  for  its  large  space  requirements  and  liability  of  breakage. 

Transmitting  condensers  are  very  seldom  constructed  so  that  their 
capacity  may  be  continuously  varied  in  view  of  the  insulation  difficulties 
resulting  from  the  high  voltages  dealt  with. 

The  value  of  the  capacity  of  the  condenser  used  in  the  closed  circuit 
of  a  spark  transmitter  is  fixed  by  the  voltage,  the  spark  frequency,  and 
the  power  set.  This  point  has  already  been  discussed  on  page  295,  from 
the  point  of  view  of  the  high-tension  transformer,  and  it  will  be  more 
fully  emphasized  here  from  the  point  of  view  of  the  condenser.  Rewriting 
formula  (3): 


=  W,    .........     (3) 

where 

C  —  capacity  of  condenser  in  farads; 

V  =  voltage  to  which  condenser  is  charged; 

N  =  number  of  sparks  per  second  ; 

W  =  electrical  power,  in  watts,  given  to  condenser. 

We  immediately  note  that  the  power  varies  directly  with  N,  C  and  V2. 
The  value  of  N  is  more  or  less  fixed,  because  it  represents  the  "  tone  "  of 
the  set  and  the  best  tone  is  supposed  to  be  that  due  to  N  =  1000  per  second. 
Therefore,  if  a  certain  amount  of  power  must  be  imparted  to  the  con- 
denser a  suitable  choice  must  be  made  of  C  and  F.  With  a  very  high 
voltage  the  dielectric  and  leakage  losses  are  likely  to  -be  high,  and  the  dif- 
ficulties of  insulating  the  various  parts  of  the  set  are  such  as  to  make  it 
impractical,  and  a  limit  in  this  direction  is  soon  reached  after  which,  if 
more  power  is  required,  the  condenser  capacity  must  be  increased. 
Voltages  of  100,000  might  be  used  in  large  land  installations,  but  in  small 
land  and  in  ship  installations  the  range  is  10,000  to  20,000  volts. 

It  may  be  easily  seen  that  in  large  power  installations  the  condenser 


SPARK  TELEGRAPHY  [CHAP.  V 

must  have  a  very  large  capacity,  even   though  a  high  voltage  is  used. 
For  instance,  assume: 

W  =  50,000  watts; 

V=  100,000; 

N  =  1000  per  second. 

r™  2X50,000 

=  =  a 


Since  this  capacity  affects  the  wave  length  it  is  plain  that  even  though 
a  small  inductance  be  used  in  the  closed  circuit,  the  wave  length  will  be 
large;  and  this  is  one  reason  -why  the  wave  length  of  high-power  instal- 
lations is  large;  there  are  other  reasons  which  are  taken  up  on  page  196. 
In  the  example  given,  even  if  the  inductance  in  the  closed  circuit  were 
200  nh  (which  is  comparatively  small)  the  wave  length  would  be  : 


1885V  200X0.01  =2660  meters. 
Again,  from  the  formula: 


we  obtain  the  other: 
where 


7  =  the  current  in  the  antenna; 
R  =  effective  resistance  of  antenna; 

t]  —  efficiency  of  transformation  from  condenser  to  antenna. 
Hence, 


=  !   hNC 
2\    R  ' 


(5) 


or  the  antenna  current  varies  with  the  square  root  of  the  capacity. 

To  show  this  a  test  was  made  on  a  transmitter  with  the  apparatus 
connected  as  shown  in  curve  sheet  Fig.  16,  where  the  ammeter  measures 
the  high-frequency  current  in  the  closed  circuit.  Of  course  the  current 
in  the  antenna,  which  is  here  not  shown,  would  be  directly  proportional 
to  the  current  in  the  closed  circuit.  In  this  test  the  gap  length  was  kept 
constant,  the  value  of  the  capacity  was  varied  and  the  voltage  of  the 
alternator  was  regulated  until,  for  every  case,  a  spark  occurred  for  each 
alternation  (as  could  be  approximately  determined  by  the  pitch  of  the 
spark  note);  this  meant  that  the  voltage  to  which  the  condenser  was 
being  charged  was  the  same,  and,  furthermore,  that  the  condenser  was 
being  charged  and  discharged  once  for  every  alternation.  Under  these 
conditions  the  high-frequency  current  should  be  proportional  to  A/C,  and 
the  square  of  the  current  proportional  to  C.  The  curve  obtained  shows 


DESIGN   OF  LOW-FREQUENCY  CIRCUIT 


301 


this  to  be  approximately  the  case,  except  that  an  intercept  is  noted  at 
the  point  corresponding  to  two  jars  due  to  the  fact  that  for  such  a  low 
capacity  the  gap  could  not  be  kept  from  arcing,  which,  in  turn,  prevented 
the  periodic  and  regular  charging  and  discharging  of  the  condenser. 

Design  of  Audio  Circuit. — We  may  now  discuss  more  fully  tne  choice 
of  the  various  parts  of  the  so-called  "  audio  circuit,"  which  comprises  the 
alternator,  the  variable  reactance,  the  step-up  transformer,  the  choke 


VARIATION  OF  HIGH  FREQUEh 
CURRENT  WIjTH  CAPACITY 


CY 


R=4.8  ohms 


Stationary  Gap  used 

Voltage  of  Generator  a'djusted 


5678 
Number  of  jars 


10 


11 


12 


FIG,  16. — Variation  of  the  high-frequency  oscillatory  current  with  the    amount  of 

capacity  used. 


coils,  and  the  condenser.  This  circuit  may  be  simplified  by  noting  that  a 
transformer  may  be  treated  approximately  as  a  simple  circuit  consisting  of 
an  inductance  and  a  resistance  entirely  transferred  to  the  high-  or  to  the 
low-tension  side ;  furthermore,  any  impedance  in  the  secondary  circuit  may 
be  transferred  to  the  primary  by  multiplying  by  a  suitable  factor.  On 
this  basis  the  audio  circuit  may  be  simplified  to  that  of  Fig.  17, 


where 


A   =  alternator  armature,  having  both  resistance  and  inductance: 


302 


SPARK   TELEGRAPHY 


[CHAP.  V 


RI  =  resistance  of  both  transformer  coils  transferred  to  low-ten- 
sion side; 
Lt  =  leakage  inductance  of   both  transformer  coils  transferred  to 

low-tension  side; 
Rp  =  resistance  of  protective  .choke  coils  transferred  to  low- tension 

side; 

Lp  —  inductance  of  protective  choke  coils  transferred  to  low-ten- 
sion side; 

C  =  condenser  capacity  transferred  to  low-tension  side; 
Rv  =  resistance  of  variable  reactance  coil  in  low-tension  side; 
Lp  =  inductance  of  variable  reactance  coil  in  low-tension  side. 

The  circuit  of  Fig.  17  may  be  still  further  simplified  to  that  of  Fig.  18, 
where 

A  =  alternator  without  inductance  or  resistance; 
R  =  resistance  of  entire  circuit,  including  alternator  armature,  trans- 
former coils,  protective  choke  coils,  variable  reactance  coils, 
on  basis  of  low-tension  side; 
L  =  inductance  of  entire  circuit  (ditto) ; 
C  —  capacity  of  condenser  transferred  to  low-tension  side. 

It    has    already    been   stated   that  this   circuit  should  be  adjusted 

so  that  it  will  have  a 
natural  frequency  about 
equal  to  that  of  the 
alternator;  it  has  also 
been  shown  how  the 
c  capacity  of  the  con- 
denser may  be  calcu- 
lated if  the  voltage  to 
be  used  and  the  power 

LV         RV  required   are   known;  it 

FIG.  17.— An  approximate  simplification  of  the  lovv-fre-   follows  then  that,  know- 
quency  circuit  of  a  radio  transmitter.  ing     the     capacity,     the 

value  of  the  total  in- 
ductance L  in  the  circuit  of  Fig.  18  may  be  easily  calculated  from 
formula : 


and  this  inductance  may  then  be  apportioned  between  the  alternator,  the 
variable  reactance,  the  transformer,  and  the  choke  coils.  An  example  of 
this  calculation  has  already  been  given  on  page  296,  where  the  compu- 


DESIGN   OF  LOW-FREQUENCY  CIRCUIT  303 

tations  have  been  based  on  the  high-tension  side  of  the  transformer.    The 
same  computations  will  be  repeated  on  the  basis  of  the  low-tension  side. 

Assume  that  the  transformer  ratio  is  1  :  80;  then,  any  inductance  or 
resistance  in  the  high-tension  side  may  be  transferred  to  the  low-tension 
side  by  dividing  by  802,  or  6400,  while  a 
capacity  in  the  high-tension  side  may  be 
transferred  to  the  low-tension  side  by  mul- 
tiplying by  6400. 

In  our  case: 

Capacity  of  condenser  in  high-tension 
side  =  0.012  /*/.  Hence,  equivalent  low- 
tension  capacity  =  0.012X6400  =  77.0  /*/• 

If  the  audio-circuit  must  resonate  at  500 
cycles  per  second,  FIG.  18.— Simplest  possible  rep- 

Total  equivalent  low  tension  inductance  resentation  of  the  low  frequen- 

cy circuit,  not  quite  equivalent 

1 HOI  QQ  hpnrv  to  tlie  actual  circuit. 

-5002x47r2X77.0X10-6~ 

This  value  of  inductance  should  be  ^j^  of  that  found  on  page  296, 

i.e.,  8.5  henries;  thus: 

8.5 


6400 


.00133  henry. 


Of  this  inductance  probably  the  largest  part  is,  in  a  modern  set,  found  in 
the  alternator,  while  the  transformer  has  comparatively  little  inductance, 
and  the  balance  is  made  up  by  the  choke  coils  in  the  high-tension  side  and 
the  variable  reactance  V.R.  in  the  low-tension  side. 

In  order  to  show  the  manner  in  which  the  whole  audio  circuit  may  be 
made  to  resonate  the  curves  of  Fig.  19  are  here  given  as  being  representa- 
tive of  an  actual  set.  In  obtaining  these  curves  the  field  current  and 
speed  of  the  alternator  were  kept  constant,  while  the  capacity  in  the  high- 
tension  side  of  the  transformer  was  changed  with  the  circuit  connections 
as  shown  in  Fig.  20.  Under  these  conditions,  as  the  capacity,  and,  there- 
fore, the  natural  frequency  of  the  circuit,  was  varied,  the  current  in  the 
primary  of  the  power  transformer  as  well  as  the  voltage  across  it  varied 
and  reached  a  maximum  at  the  point  corresponding  to  resonance  condi- 
tions. A  capacity  of  about  5.5  Leyden  jars  is  seen  to  have  produced 
resonance.  In  an  actual  set  the  adjustment  of  the  capacity,  or  of  the 
inductance,  is  made  about  20  per  cent  to  30  per  cent  larger  than  neces- 
sary to  give  resonance  at  audio  frequency,  thus  making  the  natural  fre- 
quency of  the  circuit  somewhat  lower  than  the  alternator  frequency. 
This  point  will  be  more  fully  emphasized  further  on.  In  the  case 


304 


SPARK  TELEGRAPHY 


[CHAP  V. 


represented  by  the  curves  of  Fig.  19  the  set  was  actually  operated  with 
8  Leyden  jars  across  the  secondary. 

It  now  remains  to  investigate,  as  far  as  the  conditions  will  allow,  the 
transient  phenomena  taking  place  in  the  audio  circuit  as  the  condenser 


RESONANCE  CURVES  OF  THE  AUDIO 
CIRCUIT  2  K.W.,  500  SPARK  SET. 
ALTERNATOR  F4ELD  CURRENT  CONSTANT 


'0  1  2  3  4  6  6  7  8  9  10  11  12 

Number  of  Leyden  jaia  connected  in  multiple  across  the  secondary  of  tfle  transformer 

FIG.  19. — Variation  of  alternator  voltage  and  primary  current  of  a  2  k.  w.  spark  trans- 
mitter as  the  capacity  in  the  secondary  of  the  transformer  was  varied;  field  cur- 
rent of  alternator  and  speed  held  constant.  Gap  set  too  long  to  permit  sparking 
at  voltage  of  test. 

is  charged  and  discharged;  we  especially  mean  to  refer  to  the  variation 
of  the  condenser  current  and  voltage  as  the  alternator  e.m.f.  is  impressed 
upon  the  audio  circuit  and,  thereafter,  as  the  gap  breaks  down.  As  shown 
in  Fig.  18,  we  are  dealing  with  an  oscillatory  circuit,  having  the  resistance, 
inductance,  and  capacity  R,  L,  and  C,  respectively,  upon  which  there  is 


TRANSIENT  CURRENT  IN  AUDIO  CIRCUIT  305 

impressed  a  harmonic  e.m.f.  The  equation  for  the  instantaneous  value 
of  current  for  such  a  circuit  (Eq.  (79))  was  derived  in  Chapter  IV,  page 
252,  and  is 

E  J*L 

?'=  sin  (pt-tfi  +  Ae.  2LSinco£',    —  -.-.     (6) 


in  which  p  =  angular  velocity  of  impressed  force; 

co  =  angular  velocity  of  natural  oscillations  of  the  circuit; 

0  =  phase  difference  of  E  and  7  in  the  steady  state; 

A  =a  constant  to  be  determined; 

tf  =  time  of  duration  of  the  transient  term. 

In  deriving  this  equation  (page  254)  it  was  shown  how  to  solve  for  A  and  t', 
these  depending  for  their  value  on  the  time  the  voltage  is  introduced  into 
the  circuit.  In  a  radio  set  there  is  no  switch  actually  used,  but  the  equiv- 
alent effect  is  caused  by  the  operation  of  the  spark  gap;  when  the  gap  is 
sparking  its  resistance  is  so  low  that  the  secondary  of  the  power  trans- 

S~* 
Am. 


FIG.  20. — Circuit  used  in  getting  curves  of  Fig.  19. 

former  is  short-circuited  and  this  is  the  condition  for  comparatively  small 
current  in  the  armature  circuit.  When  the  gap  opens  (ceases  to  carry 
current)  the  effect  of  the  condenser  of  the  closed  oscillating  circuit  is  to 
so  neutralize  the  inductance  of  the  transformer  and  armature  that  the 
current  rises  to  comparatively  large  values.  We  may  get  a  fair  idea  of 
the  behavior  of  the  actual  radio  circuit,  therefore,  by  supposing  that  Eq. 
(6)  holds  good,  the  voltage,  E  sin  pt,  being  introduced  into  the  circuit  at 
the  instant  when  the  gap  opens.  As  mentioned  when  analyzing  the  action 
of  this  circuit  before  (page  258)  the  general  solution  is  difficult,  but  we  can 
get  fairly  easy  solutions  if  we  assume  that  the  condenser  is  completely 
discharged  at  every  oscillation  and  that  the  gap  opens  when  the  voltage 
of  the  generator  is  zero;  this  latter  condition  may  be  approximately  satis- 
fied by  suitable  adjustment  of  the  set. 

Assuming  that  the  low-frequency  circuit  is  resonant  to  the  alternator 
voltage,  that  the  gap  opens  when  generator  voltage  is  zero,  and  that  the 
condenser  is  discharged,  Eq.  (6)  becomes 

E  E  _:?£  E  _£*. 

i  =  -f*  sin  pi—  -^€*"2i/sin  <o£=^  sin  pt(l  -e  2L).    .      .    r     (7) 
ij  fj  ti 


306  SPARK   TELEGRAPHY  [CHAP.  V 

From  this  we  find  the  voltage  across  the  condenser;  it  is 

-— 

~cos +S sin pi+p cos pt)  ' 


f  R  \2 
which  when  (or"]    ^s  small  compared  to  (p)2  gives 


This  equation  shows  that  the  condenser  voltage  rapidly  changes  its 

phase  during  the  first  few  alternations,  the  sin  pt  term   predominating 

_ft£ 
at  first,  the  cos  pt  term  being  zero;   as  soon  as  e  2L  departs  appreciably 

from  unity  the  cos  pt  begins  to  predominate  and  this  continually  increases 

_m 
with  increasing  time  due  to  the  increasing  value  of  (1  —  e  2L).     Thus  in 

_m 
the    steady    state    (c  2L  ^  0)    Eq.    (8)    reduces    to    the    familiar    form 


The  curves  of  Fig.  21  show  the  form  of  current  and  voltage  across 
the  condenser  for  a  typical  circuit,  the  values  of  the  various  constants 
being  noted  on  the  curve  sheet.  It  will  be  noticed  that  the  condenser 
voltage  reaches  its  maximum  values  at  approximately  the  times  when 
the  impressed  voltage  is  zero,  and  hence  the  spark  gap  will  break  down 
at  about  this  time;  the  resulting  oscillatory  current  in  the  closed  oscil- 
lating circuit  at  once  discharges  the  condenser  the  spark  gap  opens  and 
the  voltage  of  the  alternator,  passing  through  its  zero  value  is  again 
impressed  on  the  circuit  to  produce  the  next  transient.  It  is  to  be  seen 
that  if  events  follow  the  order  given  here  the  assumed  condition  (e  =  o 
when  gap  opens)  is  satisfied. 

It  is  found  in  practice  that  the  condition  of  resonance  assumed  in  this 
analysis  tends  to  produce  irregular  sparking,  giving  the  signal  a  ragged 
note,  so  actually  the  natural  frequency  of  the  circuit  is  made  about  20 
per  cent  lower  than  the  frequency  of  the  alternator.  On  the  assumption 
that  the  spark  gap  again  opens  when  the  generator  voltage  is  passing 
through  zero  the  curves  of  Fig.  22  have  been  constructed  for  the  same  cir- 
cuit as  used  for  Fig.  21  with  the  exception  that  the  capacity  has  been 
increased  from  20/xf  to  30#/,  this  giving  about  the  same  amount  of  de-tuning 
as  is  used  in  practice. 

For  this  case  the  form  of  current  and  condenser  voltage  are  obtained 
by  the  use  of  Formulae  (80)-(83)  of  Chapter  IV.  Supposing  that  the 
gap  opens  the  circuit  at  the  instant  the  circuit  voltage  (that  produced 
by  the  alternator)  is  zero  and  increasing,  it  is  found  that  for  the  steady 


TRANSIENT  CURRENT  IN  AUDIO   CIRCUIT 


307 


state  the  current  should  be  -23.5  amperes  and  the  voltage  across  the 
condenser  should  be  -92  volts.  To  satisfy  the  condition  that  the  actual 
current  must  be  zero  as  well  as  the  drop  across  the  condenser  a  transient 
term  must  be  added  to  the  steady  state  solution;  by  the  process  outlined 
in  Chapter  IV  this  transient  is  found  to  be  satisfied  by  charging  the  con- 
denser to  -385  volts  and  starting  this  transient  term  .000756  second 
before  the  alternator  voltage  goes  through  its  zero  value — this  transient 
term  has  the  natural  frequency  of  the  circuit  (given  practically  correct 


o 
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FIG.  21. — Transient  current  in  audio  circuit  of  a  spark  transmitter,  circuit  tuned  tor 

alternator  frequency, 

by  putting  co  =  (•  -T==\  and  a  damping  fixed  by  the  R  and  7^  of  the  circuit. 

\vLG7 

The  actual  current  is  obtained  by  taking  the  sum  of  the  steady  term  and 
transient  term  and  is 
150 


3000  X. 0056- 


106      \2 


sin  (3000  t  -70  .7) 


3000  X30/ 

2«  +.000756) 

+28.2  €      2X.0056 


{24400  +.000756)) 


308 


SPARK  TELEGRAPHY 


[CHAP.  V 


Similarly  the  equation  for  voltage  drop  across  the  condenser  is  found 
to  be  represented  by  the  equation 

150  X106 


Ve=— 


3000X30 


V22+( 


3000 X .0056 


=  sin  ( 


3000  «- 


2  (t  +.000756) 

-385  e      2X-0056     cos  {2440(*+. 000756)} 


«2        8 

1     1 

1 

1     1 

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(pi-4) 

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200     20 
150     15 
100     10 
50       5 
0 

50      5 
100     10 
150     15 
200     20 
250     25 
300    30 

1 

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+  ( 

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ms 

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JT 

C  =  30  m'icr 

ofz 

ira 

ds 

L  f  .0056  h< 

nries 

1 

1 

1 

FIG.  22.— Transient 
being 


current  in  audio  circuit  of  a  spark  transmitter,  circuit  frequency 
about  20  per  cent  lower  than  alternator  frequency. 


It  may  be  seen  from  Fig.  22  that  the  voltage  across  the  condenser 
is  rising  more  rapidly,  at  times  t=ir,  than  was  the  case  for  the  resonant 
condition  depicted  in  Fig.  21;  it  is  quite  likely  this  more  rapid  rise  in 
condenser  voltage,  by  causing  the  spark  to  take  place  at  a  more  definite 
time,  accounts  for  the  more  regular  behavior  of  the  spark  when  the  cir- 
cuit is  detuned  as  supposed  in  Fig.  22,  than  when  the  circuit  is  resonant. 

In  Figs.  21  and  22  the  forms  of  current  and  condenser  voltage  have 
been  shown  for  nearly  two  cycles;  actually  if  a  spark  occurs  at  the  time 
indicated  by  the  letter  A  on  the  condenser  voltage  curve  (which  is  the 
time  the  spark  should  actually  occur)  the  condenser  voltage  drops  to  zero 


THE  COMMON  SPARK  GAP  309 

and  it,  as  well  as  the  current,  goes  through  the  same  changes  from  TT  to  2ir 
as  it  did  from  0°  to  TT.  The  actual  forms  of  the  condenser  voltage  for  the 
circuits  analyzed  in  Figs.  21  and  22  are  shown  in  Figs.  48  and  49  of  Chap- 
ter IV,  page  259).  It  will  be  seen  that  the  above  analysis  does  give  fairly 
accurate  results. 

Types  of  Spark  Gaps.  —  The  construction  of  the  several  commercial 
types  of  spark  gaps  in  use  at  the  present  time  may  be  conveniently  sub- 
divided into  the  following  classes* 

(a)  Open  gap. 

f  synchronous 
(6)  Rotating  gap  \   ' 

[  nonsynchronous 

f  self-cooled 
(c)  Quenched  gap 


The  Open  Gap  and  Operating  Conditions.  —  Fig.  23  below  illustrates 
one  form  of  the  open  gap.  This  type  is  also  known  as  a  plain  spark  dis- 
charger. 

In  considering  the  requirements  which  such  a  gap  must  fulfill,  it  is 
desirable  to  review  briefly  that  part  which  it  plays  in  the  production  of 
high-frequency  oscillations.      It   will   be 
recalled  that  a  high  voltage  is  impressed 
on  the   gap    and    condenser-inductance 
circuit   connected  in   parallel,  and  at  a 
certain  critical  voltage,  the  insulation  of 
the  dielectric,   usually  air,  between  the  FlG<  23.—  Small    open    spark     gap 
terminals,  breaks  down,  and  permits  a      having  cooling  vanes  on  the  spark 
high-frequency    oscillatory    discharge      knobs. 
to  take  place.       The  gap  must    there- 

fore possess  high  dielectric  strength  or  resistance  to  puncture,  pre- 
vious to  breakdown  so  that  the  condenser  may  be  charged  to  a  high  poten- 
tial difference,  as  otherwise  the  high-frequency  energy  is  reduced,  and  the 
efficiency  of  the  transmitter  is  lowered,  due  to  the  breakdown  occurring 
at  too  low  a  voltage. 

After  the  gap  has  broken  down  it  must  possess  a  very  low  resistance, 
otherwise  the  damping  of  the  oscillations  will  be  excessive,  and  the  trans- 
mitter inefficient,  most  of  the  energy  being  dissipated  as  PR  loss  in  the 
gap.  The  gap  must  be  conducting  only  during  the  interval  of  the  passage 
of  a  wave-train.  If  we  assume  a  300-meter  wave  and  a  decrement  of  .2, 
the  duration  of  the  train  is  .000024  second.  The  time  during  which  the 
gap  is  conducting  is  thus  very  small.  If  we  consider  1000  wave-trains 
per  second,  the  period  between  trains  is  .001  -  .000024  =  .000976  second, 
and  in  this  period  the  gap  must  recover  its  insulating  properties.  These 
figures  indicate  the  short  time  intervals  involved  in  the  functioning  of 


310  SPARK  TELEGRAPHY  [CHAP.  V 

the  gap,  and  special  precautions  must  be  taken  to  insure  satisfactory 
operation. 

Open  Gap — Requirements  for  Satisfactory  Operation. — First. — The  gap 
electrodes  and  dielectric  between  them  should  remain  cool.  This  will 
assist  to  prevent  arcing  and  permit  the  gap  to  return  quickly  to  its  con- 
dition of  high  dielectric  strength.  It  will  be  recalled  that  a  cumulative 
ionization  (ionization  by  impact)  causes  the  gap  suddenly  to  become  a 
conducting  medium,  and  that  an  extremely  rapid  de-ionization  causes 
the  dielectric  between  the  electrode  to  become  a  good  insulator  again. 
If  the  dielectric  is  hot,  this  de-ionization  is  hindered  and  delayed,  and  the 
gap  may  be  conducting  after  the  high-frequency  discharge  has  passed. 
Under  this  condition  an  arc  current  will  flow,  that  is,  arcing  occurs  and 
the  voltage  across  the  gap  will  be  unable  to  increase.  No  energy,  or  at 
best,  very  little  energy,  will  thus  be  stored  in  the  condenser.  Also  the 
gap  electrodes  will  be  rapidly  eaten  away  under  the  arcing  conditions, 
requiring  frequent  cleaning  and  adjustment. 

For  these  reasons  cooling  flanges  are  usually  provided,  or  a  blast  of 
air  may  be  blown  through  one  electrode.  In  this  latter  case  the  electrode 
may  be  supported  on  a  hollow  shaft,  through  which  the  cooling  air  is 
blown,  leaving  the  electrode  through  perforations  in  the  sparking  surface. 

The  air  blast  also  assists  the  gap  to  return  to  its  high  resistance  con- 
dition by  blowing  away  the  ionized  air. 

Second. — The  electrodes  should  be  constructed  of  non-arcing  metal, 
such  as  zinc  or  magnesium,  in  preference  to  copper,  which  represents  an 
arcing  metal. 

Open  Gap — Operation  and  Adjustment. — This  gap  is  intended  only 
for  the  smaller,  low-powered  sets,  due  to  the  difficulty  of  preventing  arc- 
ing and  irregular  discharges  (partial  discharges).  The  amount  of  energy 
radiated  is  small,  and  the  signal  note  received  may  not  possess  a  clear 
tone,  due  to  the  irregular  timing  of  the  wave  trains  sent  out.  On  the  low- 
powered  set,  the  charging  voltage  is  rather  low,  in  the  neighborhood  of 
2000  volts,  and  the  gap  separation  is  very  small  (about  .02  inch).  It  is 
therefore  important  that  the  gap  separation  be  easily  adjustable  and  that 
means  be  provided  for  rigidly  holding  the  electrodes  in  position  when  once 
set.  The  electrodes  are  usually  very  heavy  and  massive  to  assist  in  con- 
ducting away  the  heat,  and  are  provided  with  large  sparking  surfaces, 
so  their  replacement  is  not  required  at  frequent  intervals.  It  should  be 
noted,  however,  that  the  replacement  of  defective  electrodes  should  not 
be  made  difficult,  but  the  gap  designed  with  their  removal  and  renewal 
in  mind. 

With  the  small  separation  mentioned  above,  it  is  also  important  to 
have  the  gap  faces  properly  aligned.  If  this  is  not  done,  the  spark  will 
always  jump  at  the  same  point,  and  the  electrodes  will  be  consumed 


SYNCHRONOUS   ROTATING   GAP 


311 


more  rapidly  at  this  point.  It  is  desirable  that  the  wear  on  the  gap  faces 
be  uniform,  as  in  this  way  the  most  effective  use  of  the  electrodes  will  be 
secured.  In  addition  to  alignment,  it  is  essential  that  the  faces  be  clean 
and  polished.  If  they  are  neglected,  oxide,  dust,  and  dirt,  etc.,  will  collect, 
and  form  an  uneven  surface.  The  spark  will  jump  wherever  th*  surfaces 
may  be  closest  together,  and  thus  for  this  condition  also  the  sparks  occur 
at  a  particular  spot  on  the  electrode.  Since  the  oxide  or  dirt  is  not  metal, 
it  will  not  conduct  the  heat  away  as  rapidly  as  required.  A  hot  spot  will 
thus  be  formed,  causing  arcing  to  take  place,  and  operation  to  be  inefficient 
and  unsatisfactory. 

The  following  table  indicates  approximate  minimum  discharge  volt- 
ages required  for  sphere  gaps  of  2.5  cm.  and  1.0  cm.  radius  in  air  at 
atmospheric  pressure : 

TABLE  I 


MINIMUM  DISCHARGE,  VOLTS. 

MINIMUM  DISCHARGE,  VOLTS. 

Gap  Length 

Gap  Length 

in  Cm. 

in  Cm. 

R=2.  5  Cm. 

72=1  Cm. 

R  =2.5  Cm. 

«=1  Cm. 

.1 

5,000 

5,000 

.1.0 

33,000 

31,000 

.2 

8,500 

8,000 

1.1 

35,500 

33,500 

.3 

12,000 

11,000 

1.2 

38,400 

35,200 

.4 

15,000 

14,000 

1.3 

41,000 

37,000 

.5 

19,000 

17,500 

1.4 

43,600 

38,500 

.6 

21,500 

20,000 

1.5 

46,000 

40,000 

.7 

25,000 

23,000 

2.0 

56,000 

44,000 

.8 

27,500 

27,000 

3.0 

74,000 

50,000 

.9 

30,000 

29,000 

Open-gap  Limitations. — As  previously  mentioned  the  open  gap  is 
inherently  limited  in  application  to  small  power  sets,  due  to  the  impos- 
sibility of  preventing  arcing,  and  also  the  small  number  of  breakdowns 
permissible  per  second  (group  frequency)  without  causing  excessive  arc- 
ing. It  will  be  recalled  that  the  high-frequency  power  equals  %NCE2, 
wherein  N  is  the  group  frequency,  and  thus  the  low-group  frequency  to 
which  the  open  gap  is  limited  causes  a  corresponding  decrease  in  the 
high-frequency  power,  which  may  be  generated  by  the  set. 

Synchronous  Rotating  Gap — Construction  and  Operation. — The  con- 
struction of  the  synchronous  rotating  gap  is  indicated  in  Fig.  24,  where 
the  rotating  electrode  shown  is  simply  a  toothed  wheel,  rigidly  fastened 
to  the  alternator  shaft.  The  spark  jumps  from  one  fixed  electrode  to  the 
disk,  through  the  disk  and  thence  back  through  the  second  gap  to  the 
other  electrode. 

The  position  of  the  disk  on  the  shaft  is  adjusted  permanently  so  that 
the  teeth  line  up  with  the  fixed  electrodes  at  the  time  of  maximum  values 


312 


SPARK  TELEGRAPHY 


[CHAP.  V 


(positive  and  negative)  of  the  voltage  wave,  and  the  gap  separation 
adjusted  so,  that  the  breakdown  voltage  is  slightly  below  the  maximum 
voltage.  Under  these  conditions  the  gap  breaks  down  once  during  each 
half  cycle,  and  assuming  a  500-cycle  supply,  the  group  frequency  is  evi- 
dently 1000.  The  number  of  teeth  on  the  disk  is  determined  by  the  number 
of  alternator  field  poles.  For  instance,  if  the  alternator  be  equipped 
with  24  poles,  the  disk  would  have  24  teeth,  and  24  breakdowns  would 
occur  per  revolution.  This  would  correspond  to  an  alternator  speed  of 
2500  r.p.m.  if  a  group  frequency  of  1000  were  desired. 

Clearly,  the  number  of  breakdowns  per  revolution  may  be  controlled 
by  substituting  disks  with  different  tooth  spacing.     Thus,  we  could  omit 

Housing  rotatable  thru  twice  the 
distance  between  studs 


Renewable  stud 


^s 


Renewable  studs  uniformly 
spaced,  one  for  each  pole  om 
the  alternator 

FIG.  24. — Arrangement  of  parts  of  a  synchronous  rotating  gap;  instead  of  using  a  metal 
disk  for  the  rotating  member  this  is  sometimes  made  of  a  disk  of  bakelite  or  similar 
material,  the  rotating  studs  being  then  all  connected  together  by  a  metal  strip. 

alternate  teeth,  and  cut  the  group  frequency  in  half,  etc.  The  tone  of 
a  signal  may  thus  be  altered  easily  and  quickly,  in  case  this  is  found 
desirable  due  to  interference  effects  present.  The  quality  of  the  note 
may  be  made  quite  distinctive  by  introducing  regular  irregularities  in 
the  arrangement  of  teeth  as,  e.g.,  omitting  every  third  tooth. 

The  action  of  the  gap,  assuming  one  breakdown  to  occur  every  half 
cycle  is  indicated  conventionally  in  Fig.  25.  Actually  the  condenser  voltage 
is  not  a  sine  wave,  but  has  the  peculiar  form  shown  in  Figs.  21  and  22. 

Synchronous  Gap  Application. — The  synchronous  gap  possesses  a  low 
operating  resistance,  due  to  the  electrodes  being  close  together  at  the  time 
of  discharge,  and  automatically  recovers  its  insulating  properties  between 


NON-SYNCHRONOUS  GAP 


313 


discharges  due  to  the  electrodes  being  widely  separated  during  this  interval. 
Arcing  is  prevented  by  the  separation  of  the  electrodes  increasing  as  the 
wave  train  passes,  and  also  by  the  fanning  and  cooling  action  of  the  rapidly 
moving  electrodes.  Partial  discharges  cannot  occur,  as  the  gap  separation 
may  be  adjusted  for  breakdown  near  the  voltage  maximum.  This  form 
of  gap  will  successfully  handle  large  amounts  of  power  and  high  spark 
frequencies,  and  is  at  present  widely  used  on  commercial  spark  trans- 
mitters of  large  capacity. 

Non-synchronous  Gap — Operation  and  Application. — The  non-syn- 
chronous gap  is  essentially  similar  to  the  synchronous  rotary  gap  described 
above,  with  the  exception  that  the  moving  electrode  disk  is  not  attached 
to  the  alternator  shaft,  but  is  driven  by  an  independent  motor.  If  the 


-Gap  Breakdown 


Condenser 
Voltage 


FIG.  25. — Conventional  representation  of  audio  and  radio  frequency  currents;  actually 
the  voltage  across  the  condenser  does  not  have  the  sinusoidal  shape  given  here  but 
has  the  form  given  in  Figs.  21  and  22. 

motor  runs  at  exactly  synchronous  speed,  and  the  phase  relation  is  correct, 
the  operation  will  be  equivalent  to  the  synchronous  type. 

This,  however,  is  an  unusual  condition,  and  one  which  would  be  dif- 
ficult to  maintain  for  any  length  of  time.  Normally  the  disk  is  run  at 
speeds  greater  than  synchronous,  the  gap  separation  being  adjusted  for 
some  voltage  somewhat  less  than  the  peak  value.  The  action  under  these 
conditions  is  shown  conventionally  in  Fig.  26. 

It  will  be  noted  that  several  breakdowns  may  occur  during  each  half 
cycle  and  that  the  voltage  at  which  breakdown  occurs  is  not  of  a  definite 
nor  constant  value.  Thus  the  wave-trains  do  not  occur  at  regular  intervals, 
nor  is  the  energy  of  the  several  discharges  the  same.  The  received  signal 
is  therefore  of  a  higher  pitch,  and  of  a  different  musical  quality  than  that 
produced  by  the  synchronous  type.  It  finds  its  greatest  application  for 
those  installations  where  commercial  frequencies  only  are  available  as  a 
supply.  A  60-cycle  service  may  thus  be  used  to  supply  a  transmitter 


314 


SPARK   TELEGRAPHY 


[CHAP.  V 


radiating,  by  means  of  the  non-synchronous  gap,  in  the  neighborhood  of 
1000  groups  per  second.  The  power  radiated  is  thus  greatly  increased  and 
the  tone  high  enough  to  make  the  ear  and  telephone  both  more  efficient 
than  they  would  be  with  a  60-cycle  note;  the  result  is  a  material  increase 
in  the  range  of  a  station. 

Quenched  Gap. — The  property  which  a  gap  possesses  of  returning 
very  quickly  to  its  un-ionized  condition  is  termed  "  quenching."  In 
the  rotating  gaps,  quenching  is  obtained  principally  by  the  air  blast  which 
occurs  at  the  sparking  contacts,  and  also  to  some  extent  perhaps  by  the 
high  velocity  of  the  moving  electrodes,  thus  preventing  arcing  and  per- 
mitting the  voltage  to  build  up  again  across  the  condenser,  as  already 
noted.  Rapid  quenching  also  possesses  additional  advantages  as  dis- 
cussed on  page  247. 


Condenser 
Voltage 


.0001  sec. 


FIG.  26. — Conventional  illustration  of  the  action  of  a  transmitter  set  having  a  non- 
synchronous  rotating  gap. 

In  place  of  a  mechanical  quenching  action,  as  illustrated  by  the  rotary 
gaps,  an  electrical  quenching  type  is  also  widely  used,  which  is  known 
as  the  "  quenched  gap."  In  this  type,  the  return  of  the  gap  to  a  con- 
dition of  high  dielectric  strength  is  obtained  through  very  rapid  de-ioni- 
zation  of  the  gap  between  the  electrodes.  The  construction  of  a  typical 
gap  is  shown  in  Fig.  27.  The  following  description  of  its  action  will 
explain  the  peculiar  cellular  form  of  construction  illustrated. 

Quenched  Gap — Requirements  for  Rapid  De-ionization. — For  the  gap 
to  operate  satisfactorily,  that  is,  return  to  its  un-ionized  condition  in  an 
extremely  short  time,  the  following  conditions  must  be  fulfilled. 

1.  The  spark  must  take  place  in  a  space  in  which  no  oxide  is  formed. 
This  is  because  the  oxide  will  deposit  on  the  sparking  surface  of  the  gap 
and  soon  short-circuit  it. 

2.  The  metal  surfaces  must  be  kept  cool  and  the  electrodes  must  there- 
fore be  good  heat  conductors.     Silver  or  copper  are  the  metals  which  best 
fulfill    this   requirement.     Usually   silver-plated    copper    electrodes   are 
employed. 


QUENCHED  GAP  315 

3.  No  part  of  the  gas  which  forms  the  gap  dielectric  must  be  far  from 
a  cool  metal  surface,  that  is,  a  very  short  gap  only  may  be  used. 

Quenched  Gap — Construction. — The  above  requirements  are  satisfied 
in  the  commercial  form  of  gap  as  follows : 

1.  The  spark  takes  place  in  a  practicially  air-tight  chamber.  The 
several  elements  or  sections  of  the  gap  are  separated  from  one  another 
by  the  insulating  gaskets  as  shown  (Fig.  28A)  and  the  whole  clamped 
tightly  together.  When  the  gap  is  first  operated,  the  air,  which  is  initially 
between  the  gap  faces,  becomes  separated  into  its  elements,  mainly  oxygen 


FIG.  27. — Photograph  of  a  commercial  type  of  quenched  gap;  three  disks  clamped 
together  by  insulating  screws  make  up  a  unit,  there  being  two  gaps  in  series  per 
unit. 

and  nitrogen,  the  oxygen  combining  with  the  copper  electrodes  to  form 
copper  oxide,  thus  leaving  an  atmosphere  of  essentially  pure  nitrogen 
between  the  gap  faces.  The  black  oxide  of  copper  disappears  after  the 
gap  has  been  in  operation  a  short  while,  the  gap  faces  being  found  bright 
and  clean  if  the  gap  is  disassembled  for  inspection.  (The  exact  reason 
for  the  disappearance  of  this  oxide  is  not  apparent — it  is  probably  absorbed 
into  the  material  of  the  separating  gasket,  under  conditions  present  when 
the  gap  is  in  operation.) 

2.  In  addition  to  using  good  heat-conducting  materials,  such  as  silver 
and  copper,  for  the  electrodes,  the  efficient  cooling  of  the  gap  is  assisted 
by  means  of  cooling  vanes  or  fins,  which  radiate  the  heat  produced  during 
the  operation  of  the  gap.  These  fins  are  clearly  indicated  in  the  diagram 


316  SPARK  TELEGRAPHY  [CHAP.  V 

(Fig.  27).  There  has  been  recently  developed  a  staggered  form  of  gap 
construction,  which  permits  air  circulation  on  both  sides  of  each  element. 
This  construction,  whereby  cooling  is  accomplished  by  increased  radi- 
ating surface,  represents  what  is  known  as  the  self-cooled  type.  It  is 
sometimes  necessary,  with  the  higher-powered  sets,  to  supply  a  small 
motor  driven  fan  to  cool  the  gap  satisfactorily.1  This  form  may  be  of 
the  type  illustrated  in  Fig.  28,  where  the  gap  is  supported  in  a  trough  of 
insulating  material,  the  cooling  air  blast  provided  by  the  motor-driven 


FIG.  28. — Another  type  of  quenched  gap  in  which  each  copper  disk  is  assembled  sep- 
arately; the  small  blower  forces  cool  air  around  the  cooling  vanes  to  prevent  over- 
heating 

fan,  coming  up  through  the  trough,  and  thus  effectually  cooling  the  gap. 
The  cross-sectional  detail  of  this  gap  is  indicated  in  Fig.  28 A. 

3.  The  requirement  that  no  particle  of  gas  in  the  gap  shall  be  remote 
from  a  metal  surface  is  satisfied  by  subdividing  the  gap  into  sections, 
the  number  of  sections  increasing  as  the  "  break-down  "  voltage  value 
is  increased.  Each  gap  provides  somewhat  less  than  .01  inch  separation, 
with  a  breakdown  voltage  of  approximately  1200  volts.  Thus  no  particle 
of  gas  in  the  gap  is  more  than  .005  inch  away  from  the  metal,  and  the  gap 
is  rapidly  de-ionized.  This  rapid  de-ionization  is  due  principally  to  the 
loss  of  electrons  by  diffusion,  although  recombination  of  electrons  and 
positive  ions  is  also  a  factor.  By  loss  of  electrons  by  diffusion  is  meant 

1  Most  modern  gaps  receive  their  supply  of  cooling  air  from  a  fan  mounted  on  the 
llternator  shaft,  thus  dispensing  with  the  extra  motor  required  for  blower. 


CHAFFEE  GAP 


317 


Insulating  Gasket- 


Copper  or  silver 
sparking  surface 

Copper  Element 
•Cooling  Flange 

FIG.  28A. — Cross-sectional 
sketch  of  part  of  the  gap 
shown  in  Fig.  28. 


the  removal  of  electrons  from  the  gas  to  the  face  of  the  gap,  due  to  the 
attraction  of  the  induced  positive  charges  on  the  gap  faces.  As  the  most 
distant  electron  has  only  a  short  distance  (.005  inch)  to  go  before  arriving 
at  the  gap  face  and  the  attracting  charge,  the 
time  required  is  extremely  small. 

Quenched  Gap — Application. — The  quenched 
gap  is  used  on  spark  transmitters  of  all  powers, 
from  the  very  small  sets  used  in  military  field 
work  and  aeroplanes,  up  to  the  500-600  h.p. 
(Input)  equipment  at  the  Nauen  Station  (Tele- 
funken  System).  Quietness  in  operation,  small 
space  requirements,  simplicity,  and  desirable 
operating  characteristics  (see  page  324)  are 
the  particular  advantages  of  this  type  of 
gap. 

The  Chaffee  Gap1 — Construction. — The  construction  of  this  gap  is 
quite  similar  to  that  of  the  quenched  gap  described  above.  The  electrodes 
consist  of  a  copper  anode  and  an  aluminum  cathode,  the  spark  occurring 
between  them  in  an  air-tight  chamber  containing  an  atmosphere  of  moist 
hydrogen.  One  electrode  is  mounted  on  a  flexible  diaphragm  to  permit 
adjustment  of  the  gap  length,  while  the  other  is  held  fixed  in  a  bakelite 
mounting  as  indicated.  As  with  the  quench  gap,  it  is  highly  important 
that  the  electrodes  and  gap  faces  be  kept  cool,  hence  the  large  radiating 
fins  with  which  each  electrode  is  equipped. 

Operation  of  the  Chaffee  Gap. — This  gap  is  supplied  from  a  d.c.  source 
through  resistances  and  high-frequency  choke  coils  as  shown  in  Fig.  29, 

and    is    connected    in 


shunt  with  the  oscillat- 
ing circuit  CiLi.  Nor- 
mally the  gap  separa- 
tion is  2  or  3  mm.  and 
under  these  conditions 
the  gap  acts  as  a  recti- 
fier, permitting  current 
FIG.  29.— Circuit  used  with  Chaffee  type  of  quenched  gap,    pulses    to    flow   in    one 
by  which  the  high-frequency  current  is  maintained  by   direction       onlv       6  £ 
impulse  excitation.  <y'          ," ' 

from  the  copper  to  the 

aluminum  electrode.  One  of  these  impulses  sets  the  secondary  circuit 
into  oscillation,  the  retro-action  of  which  sets  off  successive  primary 
impulses  at  the  proper  time  2  for  maintaining  the  oscillations  in  the  second- 
ary. These  secondary  oscillations  are  not  constant  in  amplitude,  but 

1  This  is  only  one  of  several  gaps  of  this  general  type  which  have  been  developed  in 
recent  years.     Tungsten  is  quite  a  favorite  metal  for  making  the  terminals. 

2  Spark  frequencies  as  high  as  100,000  per  second  have  been  reported  for  gaps  of 
this  type, 


r- vwv-~yjj^ 


500V. 


' ww — fj^J, — 


318  SPARK  TELEGRAPHY  [CHAP.  V 

grow  to  a  maximum  amplitude  in  one  or  two  cycles,  and  decay  thereafter 
more  or  less  quickly.  Normally  the  current  consists  of  distinct  groups  of 
trains  of  waves  separated  by  a  few  cycles  only;  under  certain  conditions 
(high  secondary  resistance)  the  trains  join,  and  the  current  then  is  a  high- 
frequency  oscillation,  the  amplitude  of  which  periodically  rises  and  falls. 

This  gap  has  not  been  extensively  employed  up  to  the  present  time, 
as  the  power  limitations  do  not  permit  its  application  to  the  higher 
powered  stations.  Thus  one  gap  is  capable  of  200  watts  input.  It  is 
to  be  noted  that  several  gaps  may  be  connected  in  series,  the  power  rating 
increasing  as  the  square  of  the  number  of  gaps  used. , 

Oscillation  Transformer. — As  previously  noted,  the  function  of  the 
oscillation  transformer  is  to  transfer  the  high-frequency  power  from  the 


V.R. 


FIG.  30. — For  small  portable  sets  the  oscillation  transformer  is  sometimes  made  with 

only  one  coil  as  shown  here. 

closed  circuit  to  the  open  or  antenna  circuit ;  it  is,  in  other  words,  a  trans- 
former of  high-frequency  currents  or  oscillations.  Because  of  these  it  is 
important  that  it  be  constructed  without  iron  core  or  other  masses  of 
any  metal  whatever,  for  the  hysteresis  and  eddy  current  losses  would  be 
so  large  as  to  make  the  transformer  efficiency  very  low. 

Two  general  types  of  oscillation  transformer  are  available,  i.e.,  (a) 
the  two-coil  type,  (6)  the  single-coil  type.  As  the  names  imply,  the  two- 
coil  type  is  made  up  of  two  separate  and  distinct  coils  more  or  less  sepa- 
rated from  each  other,  while  the  single-coil  type  consists  of  a  single  coil 
connected  as  shown  at  YQW  T  in  Fig.  30. 

In  the  figure  above,  WT  represents  the  part  of  the  oscillation  trans- 
former in  the  closed  circuit,  while  QT  is  the  part  used  in  the  open  circuit. 
It  will  be  seen  that  here  we  have  what  is  known  in  general  electrical 
engineering  as  an  "  auto-transformer,"  which,  in  turn,  is  a  modification 
of  the  simple  transformer.  The  practical  construction  of  the  oscillation 
transformer  varies  widely  with  different  makes.  In  every  case  means 
must  be  provided  for  changing  the  number  of  turns  in  the  closed  circuit 


OSCILLATION   TRANSFORMER 


319 


and  in  the  open  circuit  and  also  (in  the  case  of  the  two-coil  transformer) 
for  changing  the  position  of  one  coil  relative  to  the  other.  As  regards 
the  former  of  these  two  requirements  two 
general  methods  are  used:  one  consists  of 
using  a  clip  as  shown  in  Fig.  31,  and  shift- 
ing this  by  hand  until  the  required  number 
of  turns  is  obtained;  and  the  other  consists 
of  a  roller  contact  which  is  rotated  by  means 
of  a  suitable  handle  so  as  to  make  contact 
with  different  turns  as  shown  in  Fig.  32. 

The  changing  of  the  position  of  one  coil 
relative  to  the  other  may  be  accomplished  by 
any  one  of  several  methods,  two  of  which  are 
represented  by  Figs.  33  and  34,  which  are 

self-explanatory.  These  figures  also  show  the  general  construction  of  the 
various  types  of  transformers;  in  all  cases  either  ribbon  or  braided  copper 
is  used,  and  is  supported  in  various  ways  as  shown  by  the  illustrations. 


Copper  Strip  of 
Oscillation  Transformer 


Spring  Clip 


FIG.  31. — For  making  connec- 
tion at  any  desired  point  on 
the  coils  of  an  oscillation 
transformer  a  spring  clip  of 
this  form  is  useful. 


FIG.  32. — An  adjustable  transmitting  coil  is  sometimes  made  with  a  rolling  contact;  on 
the  opposite  end  of  the  arm  is  placed  a  roller  of  some  insulation  material  to  avoid 
having  a  short  circuited  half-turn  which  would  occur  if  both  rollers  were  conductors. 

The  variation  of  the  coefficient  of  coupling  between  the  closed  and 
open  circuits  is  accomplished,  in  the  case  of  the  two-coil  transformer,  by 
changing  the  position  of  the  two  coils  relative  to  each  other  and  also 
changing  the  inductances  outside  of  the  transformer  coils;  in  the  case  of 


320 


SPARK  TELEGRAPHY 


[CHAP.  V 


the  single-coil  type,  the  coefficient  of  coupling  is  changed  by  changing  the 
number  of  turns  WT  (Fig.  30),  which  are  common  to  both  circuits,  and 


FIG.  33. — A  type  of  oscillation  transformer  in  which  one  coil  telescopes  with  the  other 

to  vary  coupling. 


FIG.  34. — An  oscillation  transformer  made  of  flat   spirals;  variation  of  coupling  is 
obtained  by  sliding  one  of  the  coils  back  and  forth  on  the  central  shaft. 

also  by  changing  the  position  of  the  point  Q  on  the  loading  inductance 
in  the  antenna  circuit. 


RADIO   FREQUENCY  CIRCUITS  OF  TRANSMITTER  321 

It  must  be  remembered  that,  in  the  case  of  the  two  coil  type : 

M 

k  =  -/= , 

where 

k  =  coefficient  of  coupling; 
M  —  mutual  inductance  between  the  two  coils  of  the  oscillation 

transformer; 

LI  =  total  inductance  in  the  closed  circuit; 
Z/2  =  total  inductance  in  the  open  circuit, 
and  in  the  case  of  the  single  coil  type, 

k-      L 

A/  ~-          i         •    n^ 

where 

L  =  inductance  common  to  both  circuits. 
k,  Z/i,  Z/2  have  the  same  significance  as  above. 

The  Radio-frequency  Circuits. — This  consists  of  the  closed  and  open 
oscillatory  circuits,  coupled  together  through  the  oscillation  transformer. 
The  whole  of  the  radio-frequency  cir- 
cuit for  a  two-coil  oscillation  trans- 
former is  shown  in  Fig.  35.  The 
closed  and  open  circuits  are  tuned  to 
the  same  frequency.  spark  db  Lijl 

The  theory  applying  to  the  above 
is  that  which  has  been  discussed 
in  connection  with  two  inductively 

couple  oscillatory  circuits  (see  Chapter 

TTr  *  „,,  FIG.  35.— The  two  coupled  radio  fre- 

IV,  pages  226-246).      The  mam  point     quency  circuitg  of  a  gpark  transmitter> 

to  be  considered  is  that  when  the  two 

circuits  are  closely  coupled  there  are  produced  in  each  two  currents  of 
frequencies  differing  from  the  natural  frequency  of  the  two  circuits;  when 
the  natural  frequencies  of  the  circuits  are  the  same,  then  the  frequency 
and  wave-length  of  the  component  currents  are  given  by  (see  Chapter 
IV,  pages  229-231) 


where 

/and  X  =  natural  frequency  and  wave-length  of  either  circuit; 
f '  and  X'  =  frequency  and  wave-length  of  one  of  the  component  cur- 
rents; 


322 


SPARK  TELEGRAPHY 


[CHAP.  V 


/"  and  X"  =  frequency  and  wave-length  of  the  other  component  cur- 
rents; 
k  —  coefficient  of  coupling. 

The  relative  amplitudes  of  the  two  currents  have  been  discussed  in 
Chapter  IV,  pages  230-237;  generally  the  higher-frequency  current  has  the 
greater  amplitude.  Futhermore  the  higher-frequency  currents  of  the 
primary  and  secondary  are  about  180°  apart,  while  the  lower-frequency 
currents  of  the  primary  and  secondary  are  about  in  phase.  The  effect 
of  all  this  is  to  produce  current  "  beats  "  in  the  primary  and  secondary 
with  a  frequency  equal  to  the  difference  of  the  frequencies  of  the  com- 
ponent currents;  again,  while  the  resultant  current  in  the  primary  is  pass- 

A •=  Low  Wave  Length  Component] 
B=High     ••  »  ••  I  F«r  Primary 

/C    C  —  Resultant 


; 


D  =  Low  Wave  Length  Component! 

F~=High      "          "  "  >  For  Secondary 


Time 


CURVES  OF  CURRENT  IN  COILS  OF  AN  OSCILLATION  TRANSFORMER 
•FOR  A  NON-QUENCHING  GAP  AND  ZERO  DECREMENT 

FIG.  36. — Currents  in  the  two  circuits  of  Fig.  35,  no  damping  assumed. 

ing  through  the  small  amplitude  values  of  the  "  beat  cycle,"  the  secondary 
current  is  passing  through  the  high  amplitude  values  of  the  "  beat  cycle," 
and  vice  versa.  This  is  illustrated  by  the  curves  of  Fig.  36,  where  the 
dotted  line  curves  represent  the  resultant  primary  and  secondary  currents; 
it  will  be  noted  that  the  primary  resultant  current  starts  with  a  high 
amplitude  at  Q  and  decreases  to  a  low  amplitude  at  R,  while  the  secondary 
resultant  current  does  just  the  opposite.  In  plotting  the  curves  it  has 
been  assumed  that  neither  circuit  suffers  any  losses,  and  the  result  is  that 
the  decrement  of  the  component  currents  is  zero,  while  the  resultant  cur- 
rents would  also  periodically  repeat  themselves  through  the  "  beat  cycle  " 
without  any  decay.  This  of  course  is  not  true  of  an  actual  case,  where, 
on  account  of  the  losses  in  both  circuits,  the  decrement  would  have  a 
definite  value,  and  the  resultant  currents  would  "  decay  "  somewhat  as 


RADIO  FREQUENCY  CURRENTS 


323 


shown  in  Fig.  37,  which  represents  the  component  and  the  resultant  pri- 
mary and  secondary  currents  for  circuits  with  decrements.  Another 
assumption  made  is  that  the  gap  used  is  such  (open-spark  gap)  that  it 
remains  closed  for  considerable  time  after  its  breaking  down,  so  that  the 
currents  may  flow  through  the  closed  circuit. 

The  phenomenon  of  the  "  beats  "  takes  place  most  pronouncedly  when 
the  coupling  between  the  primary  and  secondary  of  the  oscillation  trans- 
former is  closest.  For  loose  coupling  the  two  circuits  oscillate  at  very 
nearly  a  single  frequency  equal  to  their  natural  frequency,  but  when  this 

CURVES  OF  CURRENT  IN  COILS  OF  AN  OSCILLATION 
TRANSFORMER   FOR  A  NON-QUENCHING  GAP 


Time 


A=Low  Wave  Length  Component 

B=High      "          "  "  J>  For  Primary 

C=Resultant 


D*=Low  Wave  Length  Component 


For 

Primary 
Circuit 


For 

Secondary 
Circuit 


Time 


FIG.  37. — Currents  in  the  two  circuits  of  Fig.  35,  high  damping  assumed. 


is  the  case  the  secondary  current  is  generally  low.  On  the  other  hand, 
when  the  coupling  is  very  close,  although  the  current  in  the  antenna  is 
large,  yet  since  it  is  made  up  of  two  component  currents  of  two  widely 
different  frequencies  the  antenna  will  radiate  energy  at  these  two  different 
frequencies;  this  is  very  objectionable  because  the  total  available  energy 
is  subdivided,  and  hence  the  range  of  transmission  diminished,  and  also 
because  it  would  interfere  with  other  stations.  As  a  matter  of  fact,  the 
law  in  the  United  States  requires  that  the  energy  of  no  other  frequency 
shall  exceed  10  per  cent  of  that  of  the  frequency  on  which  the  station  is 
transmitting. 


324  SPARK  TELEGRAPHY  [CHAP.  V 

As  outlined  above,  we  find  that  when  an  open  spark  gap  is  used,  which 
remains  closed  for  some  time  after  its  breaking  down  and  thus  permits 
a  current  to  be  maintained  in  the  closed  circuit,  we  are  confronted  by 
either  one  of  two  evils,  i.  e.,  low  current  in  antenna  at  a  single  frequency 
for  loose  coupling,  and  large  antenna  current  of  two  frequencies  for  close 
coupling;  besides,  for  both  loose  and  close  coupling,  energy  is  wasted  in 
the  primary,  since  the  latter  has  a  current  flowing  in  it  for  a  longer  time 
than  necessary,  which  produces  unnecessary  losses,  and  subtracts  from 
the  energy  which  might  otherwise  be  given  to  the  antenna. 

In  order-  to  overcome  these  difficulties  advantage  is  taken  of  the  fact 
that,  as  has  already  been  pointed  out,  and  as  shown  in  Fig.  37,  the  pri- 
mary and  secondary  currents  (for  close  coupling  and  an  open  spark 

CURVES  OF  RESULTANT  CURRENT  IN  COILS  OF  AN 
OSCILLATION  TRANSFORMER  FOR  A  QUENCHED  GAP 


Time 


A    A    A 

Time 


Decrement  and  wave  length  for  this  current 
are  fixed  by  the  antenna  circuit  only 

FIG.  38. — Currents  in  the  two  circuits  of  Fig.  35  if  the  gap  used  in  the  closed  circuit  is 

of  the  quenching  type. 

gap)  pass  through  beat  cycles,  and  that  the  amplitude  of  the  primary 
current  has  minimum  values  at  the  same  time  that  the  amplitude  of 
the  secondary  current  has  maximum  values.  It  is  plain  that  if  the 
primary  current  were  automatically  interrupted  when  passing  through 
its  minimum  amplitude  values,  the  secondary  circuit  would  then  go  on 
oscillating  at  its  own  frequency  and  damping.  This,  of  course,  would 
be  made  possible  by  the  fact  that  the  primary  current  would  be  inter- 
rupted when  the  secondary  current  amplitude  values  are  a  maximum 
and  hence  when  almost  the  entire  energy  is  in  the  secondary.  Accord- 
ing to  this  plan  the  current  would  be  interrupted  in  the  primary  at 
the  completion  of  the  first  one-half  of  a  "  beat-cycle  "  as  shown  at  A 
in  Fig.  38.  To  interrupt  the  primary  current  several  methods  may 
be  used,  the  simplest  of  which  is  by  replacing  the  ordinary  open  gap 


RADIO  FREQUENCY  CURRENTS 


325 


by  the  so-called  "  quenched  gap."  The  construction  of  this  already  has 
been  described  on  page  316.  Its  characteristic  is  that  it  "  opens  "  when 
the  current  in  the  primary  of  the  oscillation  transformer  passes  through 
its  low  values,  probably  because  the  comparatively  few  ions,  which  are 
formed  between  the  sparking  surfaces  during  the  time  of  low  current 
amplitude,  recombine  very  quickly,  thus  making  it  impossible  to  maintain 
low  currents  through  the  gas  between  the  sparking  surfaces.  Such  a  gap 
is  said  to  "  quench  "  the  spark  formed  upon  the  discharge  of  the  condenser. 
A  quench  gap  may  be  and  is  generally  operated  with  a  close  coupling  of 
the  oscillation  transformer,  because  the  closer  the  coupling  the  greater 
the  amount  of  energy  transferred  to  the  antenna  circuit ;  but  if  the  coupling 
should  be  made  extremely  close  then  it  is  possible  that  the  gap  may  refuse 
to  quench,  because  of  the  very  short  time  during  which  the  closed  circuit 
has  its  low  amplitude  current;  this  may  not  be  sufficient  to  permit  the 
gap  to  quench.  A  critical  coupling,  therefore,  exists  at  which  the  gap 
quenches  best;  this  coupling  is  quite  close  and  far  closer  than  could  be 
used  with  an  ordinary  open  gap;  the  secondary  current  as  indicated  by  an 
ammeter,  is  a  maximum  for  the  critical  coupling.  Of  course  if  the  gap 
is  quenching  properly  the  secondary  current  should  have  a  frequency 
equal  to  its  natural  frequency,  and,  since  no  current  flows  in  the 
primary,  the  efficiency  is  higher  and  the  decrement  lower  than  for  the 
"  open  gap." 

The  adjustment  of  a  transmitting  set  as  regards  the  coupling  of  the 
closed  and  open  circuits,  the  gap,  and  the  tuning  of  the  two  circuits  is 
best  determined  by  obtaining  the  "energy 
distribution  curve."  Such  a  curve  is 
obtained  in  the  following  manner:  a 
search  coil  of  one  or  two  turns  is  intro- 
duced in  the  antenna  circuit  as  shown 
at  S,  Fig.  39,  and  a  wave-meter  circuit, 
consisting  of  L±,  C±  and  a  hot-wire  meter 
A  is  loosely  coupled  to  S.  With  the 
transmitter  in  operation  the  capacity  €4 
is  set  at  different  values,  and  the  reading 
of  A  is  obtained;  thus,  as  the  natural 
wave-length  of  the  circuit  of  C±  -L4  -A 
is  varied,  the  ammeter  reading  varies. 
A  curve  plotted  with  values  of  the  natural  wave-lengths  of  circuit 
C4-Z/4  —  A  against  squares  of  ammeter  readings  is  known  as  "energy- 
distribution  curve,"  and  shows  the  relative  amounts  of  energy  radiated 
by  the  antenna  at  each  wave-length.  Another  way  to  look  at  it  is  that, 
since  the  circuit  €4—  L±  —  A  is  nothing  but  a  receiving  circuit  loosely 
coupled  to  the  transmitting  antenna,  it  follows  that  the  energy  distribution 


FIG.  39. — Use  of  wave-meter  for 
getting  wave-length  of  antenna 
circuit. 


326 


SPARK  TELEGRAPHY 


[CHAP.  V 


curve  also  represents  the  energy  reaching  the  receiving  circuit  when  it 
is  adjusted  to  different  natural  wave-lengths.  Whichever  way  one  chooses 
to  look  upon  the  "  energy  distribution  curve/'  it  is  plain  that  it  is  of  great 
importance  in  the  study  and  adjustment  of  a  transmitting  set.  Two 
typical  sets  of  such  curves  are  given  in  Figs.  40  and  41  and  a  study  of  these 
will  bear  out  some  of  the  points  brought  out  in  the  previous  discussion. 
In  these  curves  the  ordinates  represent  squares  of  currents,  and  they  were 
in  one  case  read  on  a  so-called  "  Wattmeter  "  1  and  in  the  other  on  a 
thermo-galvanometer. 


SEPARATION  OF  ANTENN 

CURVE     COILS  OF  OSCILL     COEFF.    OF  CURREN 

TRANSFORMER         COUPLING      AMp.s 


400     420     440     460     480     500     520,.  540     560     580     600     620     640     660     680     700     720     740     760    780 

Wave-length  in  meters 

FIG.  40. — A  set  of  resonance  curves  for  a  spark  transmitter  having  a  non-quenching  gap; 
even  when  the  coupling  is  as  low  as  5  per  cent  two  distinct  waves  are  emitted  from 
the  antenna. 


Fig.  40  shows  curves  for  an  open  gap  and  for  different  amounts  of 
coupling,  curve  (1)  being  for  the  closest  and  curve  (8)  for  the  loosest 
coupling.  It  will  be  seen  that  for  any  but  the  loosest  coupling  there  are 
two  maxima  in  the  radiation  of  the  antenna  at  two  different  wave-lengths 
more  or  less  separated  from  each  other;  thus,  for  curve  1,  the  two  wave- 
lengths are  732  and  415  meters,  while  for  curve  7  they  are  616  and  588 
meters.  On  the  other  hand,  for  curve  8  maximum  energy  is  radiated  at 

1  Wattmeter  is  the  name  often  given,  in  radio  measurements,  to  a  hot-wire  ammeter 
the  scale  of  which  is  calibrated  to  indicate  the  power  expended  in  the  resistance  of  the 
instrument  itself. 


ENERGY  DISTRIBUTION  CURVES 


327 


the  one  wave-length  of  602  meters,  i.e.,  the  natural  wave-length  of  the  closed 
and  open  circuits.  Again,  by  referring  to  the  table  inserted  in  Fig.  40  we 
note  that  the  antenna  current  was  a  minimum  for  curve  (8)  (1.25  amperes) 
and  a  maximum  for  curve  (1)  (1.57  amperes).  Or,  as  already  pointed  out, 
the  loose  coupling  produces  an  antenna  current  which,  though  smaller 
than  for  close  coupling,  radiates  maximum  energy  at  a  single  frequency 
or  wave-length. 


30 


1   5  24 

a    o 

|  5  22 
*   a 

.£   §  20 
k.  '£ 

£  fe 
«   a  18 


tC     4) 


12 


10 


-u 


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ffi 


Effect  of 


rad 


iatibn 


having,  a  qu 


upling 


Curve  1      3|4* 


•oup  my  i  n 


from  a  'set 


24* 


20* 


1000 


1100 


1200 


1300  1400  1500 

Wave-length  in  meters 


1600 


1700 


FIQ.  41. — Resonance  curves  of  a  spark  transmitter  using  a  quenching  gap;  the  gap 
would  not  properly  quench  if  the  coupling  exceeded  20  per  cent.  For  curves  1,  2 
and  3  partial  quenching  is  indicated  by  the  presence  of  three  "humps"  on  the 
resonance  curve. 

In  Fig.  41  are  shown  some  energy  distribution  curves  for  a  set  having 
a  quenched  gap,  the  values  of  coupling  used  being  noted  on  the  curve  sheet. 
It  will  be  seen  that  the  radiation  for  any  but  the  weakest  coupling  was 
impure,  i.e.,  took  place  at  more  than  one  frequency.  As  the  coupling 
is  increased,  in  a  quenched  gap  transmitting  set,  from  very  low  values 
the  antenna  current,  as  read  on  the  ammeter,  will  increase  with  the  increas- 
ing coupling;  for  a  certain  coupling  the  antenna  current  reaches  a  maxi- 


328 


SPARK  TELEGRAPHY 


[CHAP.  V 


mum  and  then  decreases  sharply  for  a  further  small  increase  in  coupling. 
The  value  of  coupling  just  less  than  that  at  which  the  antenna  current 
decreases  is  the  proper  one  to  use;  it  is  the  maximum  value  which  can 
be  used  and  still  maintain  the  quenching  action  of  the  set. 

Adjusting  the  Spark  Transmitter. — In  adjusting  the  transmitter 
shown  in  Fig.  1,  to  radiate  at  a  certain  wave-length  and  energy  output, 
the  following  schedule  of  procedure  should  be  followed.  (Fig.  1  is  repro- 
duced here  as  Fig.  42  for  convenience  in  following  the  directions  given.) 

1.  With  the  antenna  circuit  open,  the  closed  oscillating  circuit  is 
adjusted  to  the  wave-length  desired,  by  varying  the  value  of  inductance 
I/i.1  The  primary  capacity  is  usually  fixed  in  value  and  is  not  readily 
changed,  whereas  the  inductance  LI,  forming  also  the  primary  of  the 
oscillation  transformer,  is  always  of  the  variable  type,  its  construction 
being  as  previously  described  (page  320).  The  wave-length  at  which 


Antenna 


FIG.  42. — Spark  transmitter  circuit. 

the  circuit  will  oscillate  may  be  marked  on  the  inductance  Li,  different 
values  of  LI  corresponding  to  different  wave  lengths,  since  Ci  is  fixed  and 

X  meters  =  1885  VLlCi, 

LI  and  C\  being  given  in  micro-units. 

This  calibration  is  usually  made  by  the  manufacturer  before  the  set 
is  delivered.  In  certain  emergency  or  special  conditions,  however,  this 
may  not  have  been  done,  in  which  case  a  wave-meter  is  loosely  coupled 
to  Li,  and  LI  adjusted,  until  the  wave-meter  indicates  a  maximum  deflec- 
tion for  the  wave-length,  at  which  the  set  is  to  transmit. 

The  student  is  referred  to  Chapter  X  for  a  detailed  treatment  of  the 
wave-meter.  For  the  present  discussion  it  will  suffice  to  say  that  it  is 
simply  a  calibrated  oscillating  circuit,  the  wave-length  of  which  is  known 
for  any  and  every  position  of  a  variable  condenser  element,  the  other 
element  consisting  of  a  fixed  inductance.  An  indicating  device,  e.g.,  hot- 

1  In  the  discussion  Li  stands  for  the  total  inductance  in  the  closed  oscillating  circuit, 
i.e.,  the  sum  of  the  inductances  of  Li  and  L\  of  the  diagram;  as  previously  noted,  the 
extra  inductance  in  the  closed  oscillating  circuit,  L'i,  is  very  seldom  used. 


ADJUSTMENT  OF  A  SPARK  TRANSMITTER  329 

wire  ammeter,  completes  the  instrument,  the  connections  of  which  are 
shown  in  Fig.  43. 

The  ammeter  deflection  is  a  maximum,  when  the  wave-meter  circuit 
is  in  tune  or  in  resonance  with  the  closed  circuit  of  the  transmitter.  Since 
L  is  constant,  and  \=1885V~LC  =  K\/1LC,  we  have  \  =  K'VC,-and  the 
condenser  scale  may  be  calibrated  directly  in  wave-lengths.  When  the 
ammeter  reading  is  a  maximum,  the  wave-length  of  the  set  is  the  same 
as  the  wave-length  of  the  wave-meter,  and  is  thus  readily  obtained  from 
the  calibrated  condenser  scale. 

2.  After  the  closed  circuit  has  been  adjusted  to  the  desired  wave-length, 
the  antenna  circuit  is  closed  and  loosely  coupled  to  the  closed  circuit. 
The  antenna  inductance  1/2  (or  L%  if  in  circuit)  is  then  varied  until  maxi- 
mum current  is  indicated  on  the  antenna 
ammeter,  under  which  condition  the  two 
circuits  are  in  resonance.  This  adjust- 
ment may  be  checked,  by  coupling  the 
wave-meter  loosely  to  the  loading  coil, 
if  in  circuit,  and  noting  the  wave-length 
at  which  maximum  deflection  of  the 
wave-meter  ammeter  is  obtained.  This  FlG-  43.— Simple  wave  meter  circuit, 
should  be  the  same  as  the  wave-length  for 

which  the  closed  circuit  was  adjusted.  It  is  important  to  note,  that  the 
wave-meter  should  not  be  coupled  to  the  oscillation  transformer  secondary 
when  making  this  check,  but  to  some  coil  remote  from  £2.  If  no  loading 
coil  is  used,  a  small  search  coil,  consisting  of  a  turn  or  two  of  wire,  should 
be  inserted  in  the  circuit,  remote  from  the  oscillation  transformer,  and  the 
wave-meter  coupled  to  this  coil. 

This  procedure  is  required  because  of  the  relations  of  the  flux,  which 
surrounds  both  windings  of  the  oscillation  transformer,  when  both  wind- 
ings are  carrying  current,  and  under  which  condition,  double-frequency 
current  flows  in  each  circuit.  It  was  shown  (see  page  231)  that  the 
lower-frequency  currents  in  each  winding  are  practically  in  phase,  while 
the  higher-frequency  currents  are  practically  180°  out  of  phase.  The  flux 
relations  of  the  oscillation  transformer,  assuming  a  flat  spiral  construc- 
tion, are  thus  as  illustrated  in  Fig.  44. 

It  is  apparent  that  a  wave-meter  placed  between  the  two  coils,  as 
indicated  in  Fig.  44,  will  indicate  resonance  at  the  higher-frequency  value, 
while  if  placed  in  the  axial  position  will  show  resonance  at  the  lower- 
frequency  value.  Intermediate  positions  will  result  in  a  combination 
of  effects  of  the  two  fluxes,  and  the  indications  would  therefore  be  inac- 
curate and  confusing.  It  is  thus  always  advisable  to  couple  the  wave- 
meter  to  a  single  remote  coil  in  the  antenna  circuit.  The  disturbing 
effects  of  the  oscillation  transformer  fluxes  in  the  wave-meter  indication, 


330 


SPARK   TELEGRAPHY 


[CHAP.  V 


exist  to  some  extent  even  with  loose  coupling  and  both  circuits  correctly 
tuned.  However,  a  wave-meter  coupled  to  the  loading  coil  or  search  coil 
would  give  true  indications  under  any  condition.  When  the  antenna  is 


^Oscillation  Transformer 

Windings-  ( Sectional  View  through 
center  of  each  helix) 


/<—  Low  Frequency  Flur 


High  Frequency  Flux 


Indicates  Wavemeter  CoU 


FIG.  44 — Cross-section  through  an  oscillation  transformer  showing  the  distribution  of 
flux  due  to  the  high-  and  low-frequency  currents.  With  wave-meter  coil  on  the  axis 
low-frequency  resonance  is  obtained,  whereas  with  coil  between  the  two  parts  of 
the  transformer  high-frequency  resonance  is  obtained. 

carrying  much  current,  no  search  coil  at  all  is  required;  if  the  coil  of  the 

wave-meter  is  placed  near  the  earth  lead  sufficient  coupling  will  be  obtained. 

It  is  interesting  to  note  the  variation  of  antenna  current  when  £2 

or  LS  is  varied.     Fig  45 A  indicates  the  characteristics  obtained  when  La 


4 


4  6 

Turns  in  L3 


10 


4  6 

Turns  in  L2 


10 


12 


FIG.  45. — Tuning  the  antenna  to  the  closed  circuit  by  coil  Lz  will  give  a  different  form  of 
resonance  curve  than  that  obtained  by  varying  L3. 

alone  is  varied,  while  Fig.  45/2  indicates  the  results  obtained  when  LZ 
only  is  varied. 

The  difference  is  due  to  the  fact  that  in  Fig.  45 A,  the  e.m.f.  induced 
in  the  antenna  circuit  is  not  varied,  but  remains  constant.  Thus,  as  the 
resonant  condition  is  reached,  the  current  becomes  a  maximum,  and 


ADJUSTMENT  OF  SPARK   TRANSMITTER  331 

therefore  decreases  nearly  symmetrically,  as  the  turns  in  L$  are  continu- 
ally increased.  In  Fig.  45£,  however,  the  induced  e.m.f.  is  not  of  con- 
stant value,  but  will  increase  as  the  turns  increase,  somewhat  in  the  man- 
ner indicated  by  the  dotted  line.  The  current  curve  is  thus  unsymmeirical, 
but  will  have  the  same  kind  of  symmetry  as  the  curve  of  Fig.  45  A  if  proper 
regard  is  had  to  the  change  in  induced  voltage. 

3.  The  set,  after  adjustment  of  the  closed  and  open  circuits  as  out- 
lined above,  is  in  condition  for  sending  at  the  given  wave-length.  The 
coupling  should  then  be  adjusted  so  that  the  energy  radiated  at  this  wave- 
length will  be  a  maximum.  This  will  not  be  at  the  highest  value  of 
coupling  obtainable,  nor  will  the  antenna  current  be  a  maximum  neces- 
sarily for  this  condition.  Maximum  antenna  current  indicates  a  maximum 
energy  radiation,  but  the  distribution  of  this  energy,  as  discussed  on  page 
326,  is  of  more  importance  than  the  total  radiation,  and  if  the  coupling 
is  too  close,  the  radiated  energy  may  be  distributed  over  a  large  range  of 
wave-lengths.  Thus  the  efficiency  of  the  set,  as  measured  by  the  energy 
reaching  the  receiving  station,  which  is  tuned  to  the  wave-length  for  which 
the  transmitter  is  adjusted,  may  be  very  much  reduced.  This  is  a  very 
important  point  and  one  often  overlooked;  namely,  that  the  criterion  for 
best  operation,  is  maximum  energy  radiation  at  the  wave-length  for  which 
the  set  is  adjusted  and  not  maximum  antenna  current. 

Characteristics  of  the  Spark  Transmitter  —  Energy  Distribution 
Curves. — The  energy  distribution  curves  of  a  transmitter  under  different 
coupling  values  are  shown  in  Fig.  46.  The  manner  in  which  these  curves 
are  determined  is  described  in  detail  in  Chapter  X,  page  798.  Briefly 
stated,  a  wave  meter  is  loosely  coupled  to  the  antenna,  remote  from  the 
oscillation  transformer,  and  the  deflections  of  the  hot-wire  ammeter  (I2) 
noted  as  the  variable  condenser,  is  adjusted  to  the  different  values  of 
wave-length.  The  energy  received  by  the  wave-meter  is  proportional 
to  the  deflection  of  the  hot-wire  meter  (if  a  hot-wire  ampere  meter  is 
used  as  is  generally  the  case)  which  is  thus  indicative  of  the  energy  radi- 
ated by  the  transmitter  at  the  corresponding  wave-length.  The  curve 
plotted  from  the  data  thus  obtained  is  called  the  "  energy  distribution  " 
curve  and  is  of  the  greatest  importance  in  determining  the  characteristics 
and  action  of  the  transmitter. 

The  form  of  the  energy  distribution  curve  will  be  determined  by  the 
coupling  used,  which  in  turn  will  be  dependent  on  the  following  factors: 

First. — The  total  amount  of  energy  to  be  radiated.  If  the  receiving 
station  is  at  a  considerable  distance,  more  energy  will  be  required  and 
vice  versa.  This,  however,  is  a  minor  factor,  as  the  energy  control  is 
primarily  obtained  by  spark  gap  adjustment. 

Second. — The  desired  distribution  of  the  energy  radiated  over  the  dif- 
ferent wave-lengths  as  illustrated  by  the  curves  (Fig.  46). 


332 


SPARK  TELEGRAPHY 


[CHAP.  V 


Under  certain  conditions,  as,  for  instance,  the  sending  out  of  distress 
signals,  etc.,  a  broad  distribution  of  the  energy  radiated  is  of  prime  impor- 
tance and  close  coupling  would  be  used.  A  large  number  of  stations,  all 
of  which  may  be  tuned  to  different  wave-lengths,  would  thus  be  reached. 
This  condition  is  shown  by  curve  C-C,  Fig.  46. 

Under  normal  operating  conditions,  however,  the  distribution  of  the 
radiated  energy  is  of  greater  importance,  and  the  coupling  is  adjusted  so 
as  to  cause  a  minimum  of  interference  with  other  stations,  within  range, 
for  whom  the  message  is  not  intended.  Under  this  conditionfthe  maximum 
energy  is  radiated  at  the  wave-length  for  which  the  receiving  set  is  tuned 


500 


550  600  650 

Wave  Length  in  Meters 


FIG.  46. — Energy  distribution  curve  of  a  spark  transmitter  for  three  degrees  of  coupling. 

(as  indicated  by  curve  B)  and  thus  a  maximum  strength  of  signal 
would  be  obtained  at  the  receiving  station,  although  the  coupling  used 
would  probably  be  considerably  less  than  that  used  in  curve  C. 

Adjustment  of  Power  Input  to  the  Transmitter. — The  above  descrip- 
tion has  considered  the  adjustment  of  the  set  for  desired  power  output 
conditions.  Power  input  adjustments  will  now  be  considered. 

Since  the  high-frequency  power  input  is  equal  to  %CiE2N,  this  power 
may  be  controlled  by  varying  the  quantities  Ci,  E,  and  N. 

Normally,  the  group  frequency  (N)  will  not  be  varied,  as  the  operating 
efficiency  of  the  set  will  probably  be  considerably  decreased  for  speeds 
other  than  noted.  Also,  as  mentioned  previously,  the  characteristics 
of  the  phones  at  the  receiving  station-  are  usually  such  as  to  make 


CARE  OF  SPARK  GAP  333 

them  most  sensitive  to  a  group  frequency  of  about  1000  cycles  per  second, 
and  it  is  therefore  undesirable  to  deviate  from  this  value  to  any  consider- 
able extent. 

In  practical  installations,  the  closed-circuit  capacity  (Ci)  is  usually 
fixed  in  value,  and  could  not  be  varied  to  secure  a  change  in  the- power 
input. 

The  voltage  to  which  C\  is  charged,  E,  is  readily  controlled,  however, 
by  adjusting  the  separation  of  the  spark  gap  in  the  proper  manner.  This, 
therefore,  forms  the  means  whereby  the  power  input  may  be  controlled, 
and  although  limited  in  range,  as  discussed  below,  is  widely  used  in 
practice. 

In  case  a  quenched  gap  is  used  the  power  input  is  controlled  by  using 
the  proper  number  of  gaps  in  series,  many  for  high  power  and  perhaps 
only  one  or  two  for  short-range  sending.  It  must  be  remembered  that 
as  the  gap  length  is  changed,  or  the  number  of  sections  of  a  quenched  gap 
varied,  the  voltage  of  the  alternator  must  be  correspondingly  altered  to 
prevent  arcing  and  irregular  discharges. 

Care  of  a  Spark  Gap.1 — As  previously  mentioned,  the  power 
input  to  the  closed  circuit  condenser  is  immediately  decreased  if  arcing 
occurs  across  the  spark  gap.  To  prevent  this  condition  it  is  essential 
that  the  gap  faces  be  clean  and  smooth.  The  electrode  faces  should  there- 
fore be  periodically  cleaned  and  polished  with  sandpaper  or  emery  cloth, 
the  necessity  and  frequency  of  this  cleaning  being  determined  by  the 
time  which  the  gap  is  in  service.  The  alignment  and  separation  of  the 
electrodes  must  also  be  very  carefully  adjusted,  if  the  maximum  efficiency 
of  the  set  is  to  be  obtained  and  a  pure  note  radiated. 

If  this  is  neglected  one  or  more  partial  discharges  may  occur  per  alter- 
nation, and  a  constant  group  frequency  will  not  be  obtained,  nor  will 
successive  trains  possess  equal  energy.  The  action  is  similar  to  that  of 
the  non-synchronous  rotary  gap,  but  the  group  frequency  may  be  more 
erratic,  since  it  depends  on  the  complex  arc  conditions  existing  in  the  gap, 
whereas  in  the  former,  the  group  frequency  is  partially  controlled  and 
fixed  by  the  rotating  element.  These  partial  discharges,  which  may  occur 
considerably  below  the  peak  value  of  the  charging  potential  and  at  indefi- 
nite intervals,  produce  a  non-musical  note  in  the  phones  at  the  receiving 
station,  which  varies  in  intensity  and  pitch,  and  is  disagreeable  and  fatigu- 
ing to  the  operator.  It  is  also  more  difficult  to  hear  the  signal  through 
interference  than  if  the  transmitter  gap  were  properly  adjusted  and  energy 
radiated  at  a  single-group  frequency.  The  above  refers  also  to  the  syn- 
chronous rotary  gap  and  quench  gap  if  the  separation  of  the  electrodes 
is  too  small. 

1  The  following  remarks  apply  only  to  open  gaps — A  quenched  gap  should  never  be 
opened  for  inspection  until  it  actually  fails  (by  short-circuiting)  as  can  be  detected  by 
seeing  how  long  a  spark  will  jump  across  the  gap  section  outside. 


334  SPARK  TELEGRAPHY  [CHAP.  V 

Improper  adjustment  of  the  gap  (except  the  quenched  type)  is  readily 
detected  by  observing  the  character  of  the  spark.  If  the  separation  is 
too  small,  the  discharge  will  be  yellowish  in  color  and  emit  a  roaring  sound, 
which  is  characteristic  of  the  arc,  whereas  under  proper  conditions,  the 
discharge  is  white,  with  a  snappy  crackling  sound. 

Too  great  a  separation  of  the  electrodes  results  in  uncertain  operation 
due  to  the  gap  not  breaking  down  regularly  once  every  alternation,  but 
every  other  alternation  or  once  every  third  or  fourth  alternation  perhaps; 
that  is,  there  occurs  a  resonant  rise  of  voltage  with  corresponding  energy 
storage  before  the  breakdown  voltage  value  is  reached.  (See  Figs.  21 
and  22,  pp.  307,  308.)  The  condenser  and  step-up  transformer  may  be 
severely  stressed  under  these  conditions  and  their  failure  may  occur  unless 
designed  specifically  for  these  operating  conditions.  A  hot-wire  ammeter, 
suitably  insulated,  and  inserted  in  the  closed  circuit,  forms  an  effective  aid 
in  securing  proper  adjustment  of  the  gap,  for  the  high-frequency  power 
(and  current)  in  the  closed  circuit  is  then  a  maximum,  as  shown  by  the 
ammeter  indication. 

Proper  Motor  Speed. — The  proper  motor  speed  will  evidently  depend 
on  the  rated  frequency  of  the  connected  alternator  and  the  pairs  of  poles, 

since 

_,    pXr.p.m.  ,. 

/=*- — gjy —  (in  cycles  per  second) 

60  X/ 
r.p.m.  =  — 

Thus,  assuming  a  500-cycle  alternator  with  20  pairs  of  poles,  we  have, 

60X500 

r.pjn.  =  — ™ —  =  1500  r.p.m. 
zo 

as  the  motor  speed. 

The  speed  of  the  driving  motor  must  be  strictly  constant  if  a  musical 
note  of  constant  pitch  is  to  be  heard  in  the  phones  at  the  receiving  station, 
and  as  previously  mentioned,  the  modern  shunt-wound  or  differentially 
wound  motor  satisfactorily  fulfills  this  requirement.  It  is  evident  that 
by  suitably  adjusting  the  driving  motor  speed  (by  means  of  the  motor 
field  rheostat)  a  limited  control  of  the  group  frequency  of  the  set  is  possible. 
Thus  by  driving  the  above  alternator  at  1200  r.p.m.,  the  group  frequency 
may  be  made  800  instead  of  1000.  Similarly  1800  r.p.m.  will  give  a  group 
frequency  of  1200.  There  is  no  particular  advantage  in  this,  however, 
as  the  telephones  usually  have  maximum  sensitivity  for  a  group  frequency 
of  about  1000  cycles  per  second,  and  the  operation  of  the  spark  gap  will 
be  erratic  at  other  than  rated  frequency,  as  explained  on  page  308. 

Capacity  and  Inductance  of  the  Closed  and  Open  Circuits. — The  proper 
capacity  to  be  connected  into  the  closed  circuit  will  depend  on  the  amount 


OPEN  AND  CLOSED  HIGH-FREQUENCY  CIRCUITS  335 

of  the  high-frequency  power  which  it  is  intended  to  generate,  the  charging 
voltage  to  be  employed,  and  the  group  frequency,  since 


when 

d  =  closed  circuit  capacity  in  farads; 
E  =  potential  in  volts  to  which  condenser  is  charged; 
JV  =  group  frequency  in  wave-trains  per  second. 

Thus,  if  we  assume 

TT  =  2Jkw.  =  2500  watts; 
E=  15,000  volts; 

N  =1000  (alternator  frequency  =  500) 
we  have, 

2500=  iXCi  (1.5X104)2X1000 

Ci  =  .022  microfarad. 

The  closed-circuit  inductance,  which  also  acts  as  the  primary  of  the 
oscillation  transformer,  will  be  determined  by  the  above  value  of  Ci  and 
the  maximum  wave  length  at  which  the  set  is  expected  to  radiate, 

Since  :  Xmeters  =  1885  V%Ci. 

Where 

LI  =  closed  circuit  inductance  in  microhenries; 

Ci  =  closed  circuit  capacity  in  microfarads, 

we  have,  assuming  Xmax.  =  1000  meters 

1000  =  1885  VI)  X  -022 
LI  =  12.8  microhenries. 

For  proper  operation  the  open  (antenna)  circuit  constants  L%  and  €2 
must  satisfy  the  relation 

L\C\  = 


where  L\  and  C\  are  the  same  as  indicated  above; 

€2  =  total  effective  capacity  of  antenna  circuit; 
Z/2  =  total  effective  inductance  of  antenna  circuit. 

Usually,  €2  will  be  considerably  less  than  Ci  due  to  the  difficulty  and 
expense  of  building  large  capacity  antennae  and  thus  LI  usually  exceeds 
LI  in  value.  If  we  assume  an  antenna  capacity  of  .0024  microfarad,1 
then 

022 
' 


X12.8  =  117  microhenries. 


1  Represents  approximately  an  "  L  "  antenna,  length  of  top  =  200  feet,  height  =  98 
feet,  number  of  wires  =  6. 


336  SPARK  TELEGRAPHY  [CHAP.  V 

All  of  this  inductance  would  not  be  contained  in  the  secondary  winding 
of  the  oscillation  transformer,  a  large  part  of  it  would  be  supplied  by  the 
loading  inductance,  while  a  relatively  small  portion  would  be  found  in  the 
antenna  itself.  In  the  antenna  referred  to  above,  the  inductance  would 
be,  perhaps,  20  microhenries. 

Thus,  the  closed  and  open  circuits  are  tuned  to  the  same  wave-length, 
and  if  the  coupling  between  them  has  been  properly  adjusted  (see  above), 
a  maximum  amount  of  energy  will  be  radiated  at  1000  meters  and  the 
efficiency  of  operation  will  be  a  maximum  for  the  given  conditions.  The 
procedure  to  be  followed  in  adjusting  for  a  different  wave-length  or  chang- 
ing the  energy  radiated  by  the  set  has  already  been  described. 

Elements  of  the  Receiving  Station — Visual  Detection. — The  general 
connections  and  action  of  a  receiving  set  have  already  been  discussed 
(see  page  190).  Primarily,  it  constitutes  a  circuit  which  absorbs  a  portion 
of  the  electrostatic  and  electromagnetic  energy  which  reaches  it  from  the 
transmitter,  combined  with  certain  devices  to  make  this  absorbed  energy 
produce  maximum  visible  or  audible  effects,  so  that  its  reception  may  be 
evidenced  and  intelligence  thus  transmitted. 

The  antenna  circuit  represents  the  energy  absorbing  element  of  the 
receiving  set.  The  waves  of  electromagnetic  and  electrostatic  energy 
sent  out  by  the  transmitter,  induce  an  e.m.f.  in  the  antenna  circuit,  the 
natural  frequency  of  which  is  the  same  as  that  of  the  transmitter.  If  the 
antenna  were  connected  directly  to  ground  as  indicated  in  Fig.  47 A,  the 
circuit  would  be  complete  and  a  current  would  be  caused  to  flow  as  long 
as  energy  is  radiated  by  the  transmitter.  If  a  sensitive  hot-wire  ammeter 
were  inserted  as  shown,  then  this  energy  reception  would  be  made  visible, 
and  thus  a  message  might  be  transmitted  between  the  two  stations,  if  the 
radiated  energy  is  interrupted  in  accordance  with  a  prearranged  code. 

This  arrangement  represents  the  simplest  possible  form  of  receiver, 
but  is  never  used,  due  to  the  impracticability  of  the  sensitive  ammeter 
which  would  be  required.  The  antenna  would  probably  not  be  tuned 
to  the  frequency  of  the  e.m.f.  induced  in  it,  and  the  resultant  current 
would  be  extremely  small,  requiring  a  very  sensitive  instrument  for  its 
detection. 

It  is  obvious  that  this  current  could  be  materially  increased  by  so 
adjusting  this  circuit  that  its  natural  frequency  is  made  the  same  as  the 
frequency  of  the  e.m.f.  induced  in  it,  i.e.,  the  radio  frequency  of  the  received 
signal.  This  would  be  most  easily  accomplished  by  inserting  a  variable 
inductance  in  the  circuit,  provided  the  natural  frequency  of  the  antenna 
is  above  that  of  the  incoming  energy.  (A  variable  condenser  would  be 
inserted  if  the  received  energy  has  a  frequency  above  that  of  the  antenna.) 
However,  the  current  is  very  small  even  with  the  circuit  adjusted  to 
resonance,  and  the  hot-wire  ammeter  would  of  necessity  be  of  a  very  deli- 


SCHEMES  FOR  DETECTING  SIGNALS 


337 


cate  construction,  making  it  impractical  to  use.  Such,  an  instrument 
would  possess  considerable  resistance,  which  would  still  further  limit  the 
current  flowing  when  the  circuit  is  adjusted  to  resonance.  In  addition, 
its  indications  are  inherently  sluggish,  and  would  require  such  a  slow  speed 
in  sending,  as  to  make  its  application  for  receiving  purposes  completely 
impractical.  The  addition  of  a  variable  inductance  or  capacity  for  tuning 
the  antenna  circuit  is  indicated  in  Fig.  47 B. 

Audible  Detection. — In  place  of  the  above  scheme  of  detection,  which 
may  be  termed  the  visual  method,  a  detector  is  used  which  causes  the 
incoming  energy  to  produce  audible  effects.  Thus  we  might  substitute 
a  telephone  receiver  in  the  antenna  circuit  in  place  of  the  ammeter.  The 
receiver  is  described  in  detail  below.  (See  page  341.)  Briefly,  it  consists 
of  a  soft  iron  diaphragm  actuated  by  current  flowing  through  a  winding 
placed  on  a  permanent  "U  "  magnet,  the  poles  of  which  are  placed  closely 


(A) 
FIG.  47 — Simple  schemes  for  receiving  radio  signals. 


adjacent  to  the  diaphragm.  An  alternation  of  current  of  a  certain  polarity 
thus  increases  the  pull  on  the  diaphragm,  whereas  the  reverse  alternation 
will  decrease  the  pull.  The  diaphragm  is  thus  moved  inward  and  out- 
ward, setting  up  vibrations  in  the  air  which  are  heard  as  sound  by  the 
observer. 

The  placing  of  such  a  receiver  in  the  antenna  circuit  would,  however, 
produce  no  sound  in  the  phones  even  though  high-frequency  current  were 
flowing  in  the  antenna.  This  is  due  to  the  fact  that  the  mechanical 
inertia  of  the  diaphragm  will  not  permit  it  to  follow  the  extremely  rapid 
reversals  of  the  radio  frequency  current.  This  reversal  would  occur  at 
the  rate  of  1,000,000  times  per  second  for  a  300-meter  wave  signal.  Also, 
even  though  it  were  possible  for  the  diaphragm  to  respond  to  this  current, 
no  sound  would  be  heard,  as  the  frequency  would  be  far  above  the  limit 
of  audible  frequencies  (about  20,000  cycles).  The  conditions  are  indicated 
in  the  following  curves  (Fig.  48).  The  receiver  would  also  add  thousands 
of  ohms  impedance  to  the  antenna  circuit,  so  that  only  negligible  high- 
frequency  current  could  flow. 


338 


SPARK  TELEGRAPHY 


[CHAP.  V 


Application  of  the  Rectifier. — If  we  place  in  the  antenna  circuit,  in 
addition  to  the  phones,  some  device  possessing  unilateral  conductivity, 
that  is,  a  greater  resistance  to  current  flow  in  one  direction  than  in  the 
other,  we  would  obtain  a  net  or  cumulative  effect  for  each  wave-train, 
since  the  effect  on  the  diaphragm  in  the  one  direction  would  then  exceed 
the  effect  in  the  reverse  direction.  Thus  the  diaphragm  would  be  given 
a  resultant  deflection,  springing  back  to  its  initial  position  only  after  the 
wave-train  had  passed.  Thus,  if  1000  wave-trains  strike  the  antenna  per 
second  (group  frequency  of  transmitter  =1000),  the  diaphragm  would  be 
impulsed  1000  times  per  second,  and  the  observer  would  hear  a  1000-cycle 


Diaphragm 
Movement 


Time 


FIG.  48. — Conventional  diagram  of  current  in  antenna  of  receiving  station;  even  if 
such  high-frequency  currents  could  flow  through  the  telephone  the  diaphragm  could 
not  move  so  rapidly. 

note  whenever  the  transmitter  radiated  energy.  These  conditions  are 
graphically  shown  in  Fig.  49.  The  amplitude  variation  of  the  e.m.f.  for 
this  figure  should  be  carefully  noted.  The  first  cycle  is  of  maximum  ampli- 
tude in  only  one  circuit  of  both  sending  and  receiving  stations,  namely, 
the  closed  circuit  of  the  transmitter.  In  all  other  circuits,  time  is  required 
to  build  up  the  oscillations  to  their  full  amplitude,  due  to  the  electrical 
storage  of  energy  which  takes  place  during  this  period,  just  as  in  setting  a 
mechanical  system  into  oscillation,  maximum  amplitude  is  not  obtained  on 
the  first  impulse.  (Unless  the  system  starts  with  original  distortion,  as 
e.g.,  a  pendulum  held  to  one  side  and  then  released,  which  condition  cor- 
responds to  that  existing  in  the  closed  circuit  of  the  transmitting  set.) 

The  complete  receiving  circuit  with  the  asymmetrical  resistance,  com- 
monly known  as  a  "  detector,"  is  indicated  in  Fig.  50.  (The  term 
"  detector  "  is  not  strictly  applicable,  for  it  does  not  detect,  but  enables 
the  receivers  to  detect,  or  make  evident  to  the  senses,  the  energy  that  is 
supplied  to  the  telephone  receivers.)  Due  to  the  high  resistance  of 


ACTION   OF  RECTIFIER 


339 


the  phones,  and  the  asymmetrical  character  of  the  rectifier  resistance  this 
circuit  is  not  selective,  and  it  would  be  difficult  to  receive  except  under 
the  unusual  condition  that  only  energy  from  the  sending  station  desired 


Induced 
Voltage  in 

Autenua 


Antenna 
Current 


Diaphragm 
Movement 


Time 


FIG.  49. — When  a  rectifier  is  used  the  antenna  current  is  assy  metrical;  more  flowing  in 
one  direction  than  in  the  other;  such  a  current  will  give  the  telephone  diaphragm 
one  impulse  per  wave-train. 


is  reaching  the  antenna.     Also  the  magnitude  of  the  current  flowing  even 
under  the  best  conditions  is  very  small.     For  these  reasons  it  is  desirable 
and  advantageous  to  connect  the  detecting  apparatus  in  a  separate  cir- 
cuit coupled  inductively  to  the  antenna  by  means  of  coils 
Li,  L2,  Fig.  51,  the  two  forming  what  is  known  as  the 
receiving  coupler. 

Inductively  Coupled  Receiver. — With  this  connection, 
the  primary  or  antenna  circuit  may  be  tuned  accurately  to 
the  frequency  of  the  incoming  energy,  and  since  all  high 
resistances  have  been  removed,  the  antenna  current  will 
attain  a  maximum  value  very  much  greater  than  possi- 
ble  with  the   preceding   arrangements.      Therefore  the 
e.m.f .  induced  in  the  secondary  and  the  resulting  current  Fi 
flow  will  be  maximum  and  the  signal  strongest,  although 
it  will  still  be  relatively  weak  due  to  the  high  resistances 
in  the  second  circuit,   which   diminishes   the   resultant 
current.      This   circuit   possesses  some    selectivity    due 
to  the  adjustment  of  natural  frequency  possible  in  the  low 
resistance    antenna    circuit.      To   enable  the  circuit    to  be    tuned  over 
wide    ranges    of    wave-length,     and    additional    inductance    L',    known 
as   a   "  loading  "  inductance,  is   inserted  as  shown  for  very  long  wave- 


-A  pos- 
sible scheme  for 
using  telephone 
and  rectifying 
crystal. 


340  SPARK  TELEGRAPHY  [CHAP.  V 

lengths,  while  the  condenser  Ci  may  be  cut  into  circuit  if  it  becomes 
necessary  to  tune  for  very  short  wave-lengths.  This  condenser  is  there- 
fore known  as  a  "  shortening  "  or  "  short-wave  "  condenser. 

To  increase  the  selectivity  and  sensitivity  of  the  set,  a  tuning  conden- 
ser €2  is  placed  across  the  coil  L2,  giving 
the  final  circuit  illustrated  in  Fig.  52, 
which  represents  the  arrangement  most 
generally  used. 

Neglecting  for  the  moment  the 
detector  and  phones  connected  in  shunt 
across  the  condenser,  it  is  readily  seen 
that  we  may  tune  the  secondary  circuit 
to  resonance  with  the  primary  circuit, 
and  thus  secure  a  maximum  current 

FIG.  51.-A  receiving  scheme  using  two   fl°W  in  the  circuit  L*C*'      L*  is  Sener- 
circuits,  the  secondary  being  untuned.     allY  used  for    rough    tuning,    while   a 

finer  adjustment  may  be  secured  by 

adjusting  C2.  Since  the  e.m.f.  set  up  in  the  circuit  L2C2  increases  with 
the  number  of  turns  in  L2,  it  is  desirable  to  have  this  inductance  as 
high  as  possible  without,  however,  making  the  coupling  so  close  as  to 
diminish  seriously  the  selectivity  of  the  set.  Similarly,  the  condenser 
required  for  any  wave-length  adjust- 
ment should  be  relatively  small. 
Under  these  conditions  the  radio-fre- 
quency voltage  across  the  terminals  of 
L2  and  C2  (for  a  given  amount  of 
received  energy)  will  be  a  maximum, 
and  this  radio  frequency  voltage  will, 
in  turn,  cause  a  maximum  unsym- 
metrical  current  to  flow  in  the  detector- 
telephone  circuit,  and  therefore  maxi- 
mum signal  strength  will  be  obtained.  FlG  52.— The  ordinary  receiving  circuit 
The  action  of  the  phones  and  detector  using  two  tuned  circuits,  telephone  in 
on  this  connection  is  exactly  similar  series  with  rectifier  being  shunted 
to  their  action  in  the  circuit  illustrated  across  the  tunin8  condenser  of  the 
in  Fig.  49. 

If  the  resistances  involved  in  the  primary  and  secondary  circuits  of 
the  set  are  small,  then  this  receiving  circuit  possesses  considerable  selectiv- 
ity. Undesired  signals  may  be  tuned  out  and  the  efficiency  and  operat- 
ing characteristics  of  the  set  are  very  much  better  than  those  of  the  pre- 
vious circuits  discussed. 

The  Telephone  Receiver. — The  construction  of  the  telephone 
receiver  usually  employed  for  the  reception  of  radio  signals,  known 


ACTION  OF  THE  TELEPHONE  RECEIVER 


341 


as    the    "  watch-case "  type,    is  shown   in   the    accompanying   sketch. 
(Fig.  53.) 

It  consists  essentially,  of  a  permanent  magnet  M,  with  pole  pieces  N 
and  S,  upon  which  are  wound  coils  consisting  of  many  turns  of  fine 
wire,  through  which  the  audio  frequency  pulses  of  current  pass.  A  dia- 
phragm D  is  placed  closely  adjacent  to  the  faces  of  the  pole  pieces  as 
shown.  When  no  signal  is  being  received,  this  diaphragm  is  under  a 
constant  pull  or  attraction  exerted  on  it  by  the  permanent  magnet  M. 


Case  of  aluminum  or  bakelite 


FIG.  53. — Essential  elements  of  the  ordinary  watch-case  telephone  receiver. 

This  steady  pull,  which  we  may  call  P,  is  proportional  to  the  square  of 
the  flux  flowing  through  it  and  the  permanent  magnet,  i.e., 


(9) 


where  <j>s  is  the  steady  flux  value. 

When  a  current  of    proper  polarity  flows  through  the  winding,  the 
flux  will  be  increased  proportionately  (neglecting  saturation  effects)    or 


(10) 


wherein  i  represents  current  in  the  winding. 
Therefore  the  total  flux  is: 


(11) 


and  the  total  pull  under  this  condition  becomes 


K<t>s2+2KK'4>si+KK'2i2 


(12) 


The  total  pull  thus  consists  of  three  components,  one  of  which  is  con- 
stant (K<t>s2)  and  thus  has  no  effect  on  the  diaphragm  vibrational  ampli- 
tude, while  another  is  proportional  to  the  current  variation  squared 
(KK'2i2).  This  term  represents  a  distortional  component  of  double  fre- 


342 


SPARK  TELEGRAPHY 


[CHAP.  V 


quency  and  it  is  therefore  designedly  made  relatively  small.  The  remain- 
ing component  of  pull  is  proportional  to  the  current  variation  (2KK'<J>si) 
and  this  component  is  therefore  made  as  large  as  possible,  as  the  amplitude 
of  the  diaphragm  vibrations  will  then  be  porportional  to  the  amplitude 
of  the  current  variation  (i)',  it  will  also  be  directly  proportional  to  the 
flux  due  to  the  permanent  magnet,  (<£«).  Thus,  to  make  the  vibrations 
of  the  diaphragm  a  maximum  for  a  given  current  variation,  Kfa  is 
designedly  made  large  compared  to  KK'i,  which  means  that  the  flux  (<£s) 
produced  by  the  permanent  magnet  is  much  greater  than  the  flux  pro- 
duced by  the  current  in  the  winding  (A0).  Under  these  conditions, 
distortional  effects  are  minimized  and  maximum  amplitude  of  diaphragm 
vibration  and  signal  strength  (sound)  for  a  given  signal  current  (i)  secured. 
The  d.c.  resistance  of  a  receiver  such  as  described  above  would  be 
about  2000  ohms,  as  many  as  10,000  or  more  turns  of  fine  wire  (about 
No.  40  A.  W.  G.  or  smaller)  being  employed  to  make  up  the  winding. 
The  impedance  to  an  alternating  current  will,  of  course,  be  greater  than 
this,  depending  on  the  frequency  of  the  current  and  the  effective  resistance 
of  the  circuit.  At  400  cycles  a  certain  receiver  of  this  type  had  an  impe- 
dance of  2900  ohms;  at  800  cycles  an  impedance  of  3900  ohms,  and  at 
1000  cycles  an  impedance  of  4400  ohms. 

The    Baldwin   Receiver.— Another   type    of   receiver   more    recently 
developed,  known  as  the  Baldwin  receiver,  possesses  the  advantage  that 

the  diaphragm  is  not  initially 
stressed,  and  thus  may  be  more 
responsive  and  sensitive  to  the 
pull  exerted  on  it  by  the  flux 
(A0)  caused  by  the  signal  current 
(i).  The  construction  is  indi- 
cated below  (Fig.  54). 

It  is  evident  that  when  no 
signal  is  being  received,  the  arma- 
ture being  balanced  in  its  neutral 
position  (the  flux  traversing  the 

gaps  a  and  b  in  the  same  direction  and  being  equal  in  value)  no  pull  is 
exerted  on  the  mica  diaphragm.  If  a  signal  pulsation  of  current  passes 
through  the  receiver  winding,  however,  it  produces  a  flux,  which,  combin- 
ing with  the  permanent  flux,  results  in  an  asymmetrical  distribution  of 
the  flux,  causing  a  force  to  be  exerted  on  the  armature  and  thus  on  the 
diaphragm.1 

Other  advantages  claimed  for  this  type  of  receiver  in  addition  to  the 
one  mentioned  above,  are: 


Diaphragm  of  Mica 


Telephone  Winding 


FIG.  54 — Essential  elements  of  the  Baldwin 
balanced-armature  telephone  receiver. 


1  The  student  is  referred  to  E.  I.  Bucher,  "  Practical  Wireless  Telegraphy,"  page  168, 
for  more  detailed  description. 


CRYSTAL  RECTIFIERS-  343 

(1)  The  magnetic  circuit  is  of  low  reluctances  and  thus  small  signal 
currents  will  produce  relatively  greater  fluxes  and  greater  forces. 

(2)  The  armature  is  similar  in  its  mounting  to  a  lever,  with  a  force 
acting  at  each  end.     The  diaphragm,  being  rigidly  attached  to  one  end, 
thus  has  an  increased  deflection  for  a  given  magnetizing  force,  and  thus 
the  signal  strength  is  intensified. 

It  is  to  be  noted  that  this  device  is  not  truly  balanced  (when  no  signal 
is  being  received)  in  the  case  of  detectors  where  the  initial  current  is  not 
zero,  as  in  the  vacuum  tube  and  crystal  equipped  with  polarizing  battery. 
The  pull  due  to  this  current,  however,  is  extremely  light,  compared  to 
the  heavy  pull  exerted  by  the  permanent  magnet  in  the  usual  type  of 
construction,  and  the  diaphragm  may  be  considered  as  essentially 
unstressed. 

Characteristics  of  Crystal  Rectifiers. — From  the  previously  mentioned 
function  of  the  rectifier  as  utilized  in  the  reception  of  radio  signals,  it 
will  be  seen  that  the  essential  characteristic  which  it  must  possess  is  that 
of  unilateral  conductivity.  This  means  that  the  rectifier  possesses  a 
high  conductivity  for  current  of  a  given  polarity,  and  relatively  low  con- 
ductivity for  current  of  opposite  polarity.  Due  to  this  property,  a  train 
of  high-frequency  e.m.f.  waves  impressed  on  the  circuit  containing  the 
phones  and  detector  (in  series)  will  result  in  a  net  force  being  exerted  on 
the  diaphragm,  the  resultant  deflection  producing  a  click  in  the  phones. 
With  the  detector  omitted,  the  net  effect  is  not  obtained  and  no  click 
results,  the  diaphragm  being  unable  to  follow  the  high-frequency  current 
alternations  due  to  its  mechanical  inertia.  These  effects  have  been  previ- 
ously indicated  by  the  curves  shown  in  Fig.  48  and  49. 

The  unilateral  conductivity  possessed  by  various  crystals  is  shown 
by  the  following  curves  (Figs.  55  to  58,  inclusive).  These  curves  indi- 
cate the  relatively  large  currents  obtained  when  e.m.f.  of  various  values 
and  of  a  given  polarity  are  impressed  across  the  rectifier  circuit  and  the 
comparatively  small  (practically  negligible)  currents  obtained  when  the 
e.m.f. '&  are  reversed.  These  curves  represent  the  "  d.c.  characteristic  " 
of  the  crystals  in  contradistinction  to  the  "  a.c.  characteristic "  dis- 
cussed below,  and  are  obtained  by  means  of  the  experimental  circuit  indi- 
cated in  Fig.  60  (Insert  A). 

Fig.  55  illustrates  the  characteristics  obtained  for  a  carborundum 
(silicon  carbide)  crystal.  The  curve  is  interesting  as  it  illustrates  the 
function  of  the  local  battery,  sometimes  used  in  series  with  the  detector 
and  phones,  and  known  as  a  "  polarizing  "  battery.  The  connection  of 
this  battery  in  the  detector  circuit  is  illustrated  below  (Fig.  59). 

It  is  evident  that  with  any  detector  the  greatest  asymmetrical  effect 
(and  thus  maximum  signal  strength)  will  be  obtained,  if  we  adjust  the 
crystal  to  operate  at  the  point  of  maximum  change  of  curvature.  In  the 


344 


SPARK  TELEGRAPHY 


[CHAP.  V 


Mic 

ro- 

Ar 

ips 

/ 

Car 

bor 

Line 

um 

/ 

/ 

t 

/ 

/ 

/ 

f 

10 

/ 

^ 

— 

1 

-3 

-2 

-1 

i 

^ 

*&* 

>>•" 

0 

,-*• 

^i_ 

Itrl  — 

1 

E 

case  of  the  curve  considered, 
this  does  not  occur  at  the 
zero  voltage  value  but  at 
+  1.25  volts  approximately. 
Therefore  the  local  battery 
potentiometer  would  be  ad- 
justed to  impress  an  initial 
voltage  of  +1.25  volts  on 
the  crystal.  Under  these 
conditions  the  signal  voltage 
impressed  on  the  potentiom- 
eter, detector,  and  phones 
in  series,  would  vary  the 
current  above  and  below  the 
initial  value  (indicated  by  i 
in  Fig.  55)  and  a  maximum 
asymmetrical  current  thus 
secured. 

The  "  d.c.  characteristic  " 


FIG.  55. — Characteristic  curves  of  a  carborundum 
rectifying  crystal,  using   a   fine    steel    point   for 
making  contact.    The  maximum  rectifying  action  ig  algo  indicated  on  the  figure 
occurs  when  a  polarizing  voltage  of  about  1.2 
volts  is  used. 


this  adjustment,  the  asymmet- 
rical effect  of  the  crystal  is  prac- 
tically nil,  and  the  resistance  of 
a  uniformly  high  value. 

Fig.  56  illustrates  the  charac- 
teristics taken  for  a  Cerusite 
crystal  (trade  designation),  under 
conditions  of  good  and  poor  ad- 
justment. The  asymmetrical 
conductivity  obtained  with  the 
good  rectifying  point  is  more 
pronounced  for  this  crystal  than 
for  the  carborundum  crystal  of 
Fig.  55,  and  no  polarizing  battery 
would  be  required,  as  a  sharp 
"break,"  or  high  rate  of  change  of 
curvature,  is  obtained  at  zero  volt- 
age. The  resistance  is  uniformly 
very  high  on  the  poor  rectifying 
point,  and  is  practically  constant 
in  value  for  all  e.m.f.  values.1 


for  a   poor  rectifying  point, 
which    indicates    that   with 


\ 

1 

Mk 

ro 

Ai 

ips 

/ 

Oft 

j 

[ 

/ 

/ 

no 

/ 

>er 

isit 

e 

/ 

00 

/ 

/ 

/ 

/ 

/ 

/ 

F 

3 

-5 

-: 

i 

q 

-e— 

-o- 

-& 

-e~ 

e— 

S* 

<*t" 

! 

ts- 

1 

S* 

-^ 

s* 

"•* 

Ceru- 


r.  56. — Characteristic   curves  of  a 
site  "  rectifying  crystal. 

1  Some  recent  tests  by  the  author  indicate  that  caution  must  be  observed  in  drawing 


CHARACTERISTICS  OF  CRYSTAL  RECTIFIERS 


345 


20- 


000 


18r 
Mjcro 


000 
Amps 


000 


000 


127 


000 


..eazite 


10,- 


000 


80 


00 


40 


00 


Fig.  57  illustrates  the  d.c.  characteristics  for  two  different  points 
on  a  detector  known  as  a  Lenzite  crystal,  which  show  the  same  general 
form  as  the  corresponding  curves  in  the  previous  figures.  No  polarizing 
battery  would  be  required  if  the  crystal  is  operated  on  the  good  rectifying 
point.  The  unilateral  conductivity  of  the  crystal  is  indicated  to  some 
extent  even  for  the  poor 
point,  and  some  detection 
may  be  secured  on  this  con- 
dition, if  very  strong  signals 
are  being  received. 

Fig.  58  illustrates  char- 
acteristics obtained  with  a 
combination  of  two  cystals, 
zincite  (red  oxide  of  zinc) 
and  chalcopyrite  (iron- 
copper  sulphide) ,  which 
differs  from  the  preceding 
cases  in  which  a  sharp 
metallic  point  is  placed  in 
light  contact  with  the  crys- 
tal. The  curves  indicate 
that  a  polarizing  e.m.f .  may 
be  desirable,  and  also  show 
that  considerable  rectifica- 
tion will  be  secured  even  if 
operating  on  a  poor  point. 
This  would  make  the  com- 
bination desirable  for  use 
where  adjustments  may  be 
frequent,  due  to  vibrations 

or  similar  disturbances,  which  may  be  present,  as  in  the  case  of  portable 
receiving  equipment  and  stations  on  shipboard. 

The  asymmetrical  effect  of  the  detectors  described  above,  when  an 
alternating  potential  is  impressed  across  the  circuit  in  which  they  are 
connected  is  indicated  by  the  curves  (using  a  zincite-chalcopyrite)  shown 
in  Fig.  60.  The  experimental  circuit  used  is  shown  in  Fig.  60  (Insert  B). 
Both  the  d.c.  and  a.c.  characteristics  are  indicated,  the  former  being  plotted 
between  the  d.c.  voltage  and  corresponding  current  as  heretofore,  while 
the  latter  is  plotted  between  the  effective  a.c.  voltage  and  the  d.c. 
component  of  the  rectified  alternating  current,  as  read  by  the  same  d.c. 

conclusions  from  the  d.c.  characteristics  of  the  crystal.  By  actually  connecting  the 
crystal  to  a  receiving  set,  adjusting  for  a  good  point  and  then  making  the  a.c.  and  d.c. 
tests  of  this  point  it  was  found  that  not  only  must  the  curvature  be  high  to  give  good 
detection,  but  the  a.c.  resistance  must  not  be  less  than  about  100,000  ohms. 


20 


Volts 


FIG.  57. — Characteristic  curves  of  a  "Lenzite" 
rectifying  crystal. 


346 


SPARK  TELEGRAPHY 


[CHAP.  V 


Zin 


-2 


16r 


Amps 
000 


14; 


000 


12r 


000 


-Ct  alcopy 


rit 


10r  000 


00 


4000 


-20 


ammeter  used  in  obtaining  the  "  d.c.  characteristic."     The  instantaneous 

values  of  the  current  flowing  in  the  detector  circuit  when  a  sine  wave  e.m.f. 

is  impressed,  have  been  plotted  in  Fig.  61,  wherein  the  corresponding 

voltage  values  are  also  indicated.     It  should  be  noticed  that  the  negative 

alternations  of  the  current  are  practically  negligible  in  amplitude,  while 

the  positive  alternations  are  not 
of  sine -wave  form  but  consider- 
ably more  peaked,  due  to  the 
variation  in  detector  resistance, 
which  decreases  as  the  current 
increases. 

This  current  may  be  graphi- 
cally resolved  into  its  d.c.  and 
a.c.  components  as  shown  in  the 
figure.  The  flatter  component 
will  not  affect  the  d.c.  ammeter 
the  deflection  of  which  is  pro- 
portional to  the  magnitude  of 
the  d.c.  component  only,  the 
value  of  which  it  indicates.  Thus, 
for  an  effective  a.c.  voltage  of 
1.41  volts  Fig.  60  (maximum 
value  equal  to  2  volts  as  shown 
in  Fig.  61)  the  reading  of  the 
ammeter  is  2  milliamperes,  which 
is  the  magnitude  of  the  d.c. 
component  as  indicated  in  Fig. 
61.  Thus  the  curve  obtained 

from  the    a.c.    test   indicates   the    d.c.   component   plotted    to   various 

corresponding  a.c.  voltages  as  indicated  by  the  curve  in  Fig.  60. 

The  insert  curve  in  Fig.  60  illus- 
trates the  a.c.  and  d.c.  characteristics 

to  a  magnified  scale  in  the  region  of  the 

zero  voltage  point.     It  is  interesting 

and  important  to  observe  that  this  d.c. 

characteristic     indicates    satisfactory 

rectification,  for   very   small    voltage 

values,  such  as  would  exist  across  the 

detector-phone   circuit   under  normal 

conditions,  although  the  more  extended 

curve  (main  curve  of  Fig.  60)  would 

seem  to  indicate  that  for  small  voltage 

variations,  a  polarizing  e.m.f.  of  about 

+  .25  volt  would  be  desirable.     These  data  demonstrate  the  fact  that  if  the 


Volts 


FIG.  58. — Characteristic  curves  of  a  "Perikon" 
rectifier,  utilizing  the  contact  between  zincite 
and  chalcopyrite. 


Carborundum 
detector 


FIG.  59. — Scheme  of  using  such  a  crystal 
as  carborundum  in  a  receiving  circuit. 
The  best  rectifying  action  is  obtained 
by  suitable  adjustment  of  the  poten- 
tiometer on  the  polarizing  battery. 


CHARACTERISTICS  OF  CRYSTAL  RECTIFIERS 


347 


characteristic  curves  are  to  be  considered  reliable,  and  truly  indicative 
of  what   the   rectifier  will   do   in   its   application   to  radio  signal  recep- 


100 


-80 


-70 


-50 


-40 


-30 


-20 


A.C.  T, 


/  D.C.  T 

/of  p'oint 
fork.C. 


Scale  of  Volts  for  D.C.  Test 
Effective  values  for  A.C.  Test 


Scale- 


rf-Wo 


(to  -t«  Fee-  i 


D.  C.  Test 


^  tesi 


Test 


r 


FIG.  60 — Comparison  of  d.c.  and  a.c.  characteristics  of  a  Perikon  detector.  The  a.c. 
characteristic  was  obtained  by  measuring  the  current  through  the  rectifier  with 
d.c.  ammeter  when  an  alternating  e.m.f .  was  impressed.  The  insert  shows  the  really 
important  action,  as  it  is  seldom  that  more  than  a  small  fraction  of  a  volt  is  set  up 
across  the  rectifier  when  it  is  used  in  a  receiving  circuit. 

tion,   it   is  desirable  to  investigate  them  for  low  values  of  impressed 
voltages  and  not  carry  them  out  to  voltage  values  as  large  p.s  2  volts; 


348 


SPARK  TELEGRAPHY 


[CHAP.  V 


a    magnitude    practically  never   encountered    in    normal    radio    recep- 
tion. 

Desirable  Characteristics  of  Crystal  Rectifiers. — Crystal  detectors  or 
rectifiers  should  possess  the  following  qualities: 

1.  They  should  be  mechanically  rugged  and  well  constructed.     This 
means  that  they  should  be  able  to  hold  their  adjustment  and  not  be  easily 
disturbed.     These  are  especially  desirable  characteristics  in  field  or  marine 
sets,  where  jarring  or  vibration  is  likely  to  be  present. 

2.  The  crystals  should  be  sensitive,  that  is,  should  possess  good  recti- 
fying properties,  if  their  setting  is  properly  adjusted.     Too  great  a  sen- 
sibility is  not  desirable  as  satisfactory  adjustment  is  usually  obtained  with 
difficulty.    Also  it  may  be  difficult  to  retain  the  sensitive  adjustment. 


-J-2 

Impressed  +1 

Voltage      ° 

-1 

-2 


10 

Rectified    5 
Current 

(Milliamperes) 

0 


Rectified4"6 
Current 
A.  C.  Component  o 

(Hilliainperes) 

-6 


Volts 


Total  Current 
D.  C.  Component 


A 

I      \ 


A 

I       \ 
I       \ 


A 


Time 


FIG.  61. — Analysis  of  the  current  through  a  rectifying  crystal. 

3.  The  crystal  should  be  easily  adjusted.     It  is  a  distinct  disadvantage 
if  any  marked  difficulty  is  found  in  adjusting  the  setting  for  good  reception, 
as  valuable  time  may  be  lost  in  this  way  if  a  signal  is  coming  in  and  the 
detector  not  operating  properly. 

4.  The  crystal  should  possess  self-protecting  characteristics  to  pre- 
vent itself  from  being  "  burned  out  "  and  the  setting  destroyed,  if  abnor- 
mally powerful  energy  radiations  are  received,  such  as  static  and  other 
atmospheric  disturbances. 

A  complete  explanation  for  the  asymmetrical  conductivity  of  two  dis- 
similar crystals  in  contact,  or  a  crystal  in  contact  with  a  metal  point  has 
not  yet  been  advanced.  It  may  be  due,  in  part,  to  the  thermo-electric 


CHARACTERISTICS  OF  CRYSTAL  RECTIFIERS 


349 


effects  produced  by  the  heating  of  the  function  when  the  detector  is 
carrying  current.1  The  rectifying  properties  have  also  been  considered 
as  being  due  to  electrolytic  action,  which  occurs  at  the  surface  of  the 
crystal.2  A  more  likely  explanation,  however,  is  based  on  the  "surface 
work"  for  electron  evaporation  from  the  two  crystals;  if  the  "  surface 
works"  are  different,  the  contact  point  must  offer  asymmetrical  resistance.3 

Application  of  the  Bridging  Condenser. — It  will  be  recalled  that  the 
telephone  receiver  possesses  considerable  impedance  for  a  1000-cycle  alter- 
nating current.      It  might  seem  that  it 
would  be    impossible  to    send   a   radio 
frequency  current    through    the    phone 
circuit,  and  this  would  be  the  case  were 
it  not  for  the  distributed  capacity  which  FIG.  62.— Use  of  a  "bridging"  con- 
is  associated  with  the  windings  in   the         denser  in  parallel  with  receiver, 
phone,    and    the    phone     cords.       This 

capacity  is  in  shunt  with  the  telephone  windings,  and  is  represented 
by  the  fictitious  condenser,  C",  in  Fig.  62. 

The  current  may  then  be  considered  to  divide  in  the  circuit  as  shown 
in  Fig.  63,  the  radio  frequency  component  passing  through  the  distributed 


Detector 
Current 


Phone 
Current 


Shunting 
Capacity 
Current 


Tim« 


FIG.  63. — Currents  in  the  branched  circuit  shown  in  Fig.  62. 

capacity,  which  has  a  relatively  low  impedance  to  high-frequency  current, 

while  the  audio  frequency  component  flows  through  the  phone  windings. 

Normally,  however,  the  distributed  capacity  of  the  phone  cords,  etc., 

is  only  a  few  micro-microfarads  in  value  and  is  not  large  enough  to  supply 

1 W.  H.  Eccles,  Proc.  Phys.  Soc.,  London,  Vol.  25,  p.  273,  June,  1913. 

2  R.  H.  Goddard,  Physical  Review,  Vol.  34,  1912. 

3  It  is  to  be  noted  that  any  explanation  must  be  able  to  take  care  of  the  fact  that 
certain  crystals  rectify  in  one  direction  for  low  voltages,  and  in  the  opposite  direction 
for  higher  voltages,  not  rectifying  at  all  for  some  intermediate  voltage. 


350  SPARK  TELEGRAPHY  [CHAP.  V 

a  low  impedance  by-path  for  the  high-frequency  component.  It  is  there- 
fore usual  to  connect  additional  capacity  across  the  phones,  as  shown  in 
Fig.  62,  condenser  C.  This  additional  capacity  is  known  as  a  bridging 
condenser,  and  may  have  a  value  of  approximately  5000  wf>  A  low 
impedance  path  for  the  high-frequency  component  is  thus  supplied,  thus 
permitting  a  larger  fraction  of  the  high-frequency  signal  voltage  to  act 
across  the  rectifying  crystal  and  hence  increasing  its  rectifying  efficiency. 
This,  in  turn,  increases  the  amplitude  of  the  audio-frequency  component 
flowing  through  the  phones  and  the  strength  of  the  received  signal  is  there- 
by increased. 

The  bridging  condenser  is  sometimes  considered  as  a  capacity  which 
receives  a  cumulative  charge  during  the  passage  of  a  wave-train,  due  to 
the  asymmetrical  conductivity  of  the  rectifier,  comparatively  little  cur- 
rent passing  through  the  phones.  When  the  wave-train  has  passed  this 
condenser  discharges  through  the  phones,  since  it  cannot  discharge  back 
through  the  detector,  due  to  high  resistance  in  this  circuit.  This  unidirec- 
tional discharge  passes  through  the  phone  winding  as  a  current  pulse  equiv- 
alent to  the  d.c.  component  previously  described.  Thus  one  click  is 
produced  in  the  phones  per  wave-train,  and  the  observer  hears  a  note  of 
audio  frequency  pitch  as  previously  described. 

Vacuum  Tube  Detector. — The  crystal  rectifier  is  being  rapidly  super- 
seded by  the  three-electrode  vacuum  tube  due  to  the  latter's  greater  sen- 
sitivity, reliability,  and  ease  of  adjustment.  The  action  of  the  tube  is 
discussed  in  detail  in  Chapter  VI.  to  which  the  reader  is  referred  for  a  full 
explanation  of  its  rectifying  action.  One  advantage  of  the  tube  over  the 
crystal  lies  in  the  fact  that  its  rectifying  ability  is  measured  by  the  accuracy 
of  its  design  and  construction,  while  that  of  the  crystal  is  an  inherent 
property  of  the  substance,  and  cannot  be  altered  or  improved.  With  the 
latter,  the  "  best  "  point  of  operation  is  determined  experimentally  and 
may  or  may  not  represent  the  best  performance  of  which  the  crystal 
is  capable.  On  the  other  hand,  the  tube  may  be  accurately  and  definitely 
adjusted  for  best  operation,  which  as  already  stated,  exceeds  that  of  the 
best  crystal  rectifiers.  The  more  general  use  of  the  tube  has  been  some- 
what retarded  by  its  higher  first  cost,  and  various  patent  situations  involved 
in  its  manufacture  and  distribution. 

With  the  ending  of  the  war,  however,  the  tube  is  being  more  and  more 
extensively  used  and  will  probably  be  the  only  detector  ultimately  in  use. 

Adjustment  of  Receiving  Set. — The  receiving  circuit  for  a  spark  set 
has  already  been  studied  on  page  340,  and  it  now  remains  to  discuss  the 
characteristics  of  such  a  circuit  and  the  adjustments  necessary  to  secure 
the  best  results.  Before  doing  this,  however,  we  must  define  two 
quantities,  upon  which  the  comparison  of  receiving  systems  is  based, 
i.e.:  "  audibility  "  and  "  selectivity. " 


ADJUSTMENT  OF  RECEIVING  SET  351 

"  Audibility  "  may  be  defined  as  the  ratio  of  the  audio  current  flow- 
ing through  the  telephone  receivers  to  that  which  is  necessary  to  make 
the  signals  just  audible.  To  speak  of  a  receiving  circuit  having  an  audi- 
bility of,  say,  20,  means  that  the  current  in  the  receiving  circuit  is  twenty 
times  that  which  is  just  necessary  to  produce  a  just  audible  signal. 

The  audibility  thus  defined  is  directly  proportional  to  the  current  in 
the  receiving  antenna  and,  for  weak  couplings,  say  less  than  5  per  cent, 
inversely  to  the  coupling  coefficient  between  the  receiving  antenna  cir- 
cuit and  the  receiving  closed  circuit.  Again  for  short  distances  the  receiv- 
ing antenna  current  may  be  shown  to  vary  as  follows: 

Ishshr 


where 

Ir=  receiving  antenna  current; 
7,  =  transmitting  antenna  current  ; 
h,  and  hs  =  height  of  receiving  and  transmitting  antenna,  respectively; 

R  =  effective   resistance  of  the  receiving  antenna,  including  the 

resistance  due  to  the  closed  circuit  being  coupled  to  it; 
d  =  distance  between  the  two  antennae. 

From  the  above  it  follows  that,  if  the  coupling  between  antenna  and 
closed  tuned  circuit  is  very  loose  (generally  the  case  in  practice) 

Ir 


where 

a  =  audibility;1 

k  =  coupling  coefficient  between  receiving  antenna  circuit  and  the 

receiving  closed  circuit. 

"  Selectivity  "  of  a  receiving  system  may  be  defined  as  the  ratio  of  the 
natural  wave-length  of  the  transmitting  and  receiving  antenna  circuits 
to  the  difference  between  this  wave-length  and  the  length  of  some  other 
wave  which  (of  same  field  intensity  as  signal  wave)  will  give  a  response 
just  audible.  Thus,  if: 

Xn  =  natural  wave-length  of  the  two  antenna  circuits; 

Xa  =  length  of  wave  (of  same  field  intensity  as  signal  wave)  which 

will  give  a  just  audible  response  in  the  telephone  receivers. 
$=  selectivity, 

Then:  S  =  Y^V  ..........     (15) 

An       AO 

It  will  be  seen  that  selectivity  is  a  measure  of  how  little  the  reception 

1  This  formula  is  approximate  only;  actually  the  audibility  does  not  vary  inversely 
with  R  because  the  detector  efficiency  is  involved  in  the  magnitude  of  R.  For  a  theo- 
retical discussion  of  the  best  coupling  for  detectors  of  different  types  the  reader  is  referred 
to  Chapter  XV  of  Pierce  's  "  Electric  Oscillations  and  Electric  Waves." 


352  SPARK  TELEGRAPHY  [CHAP.  V 

of  signals  from  a  certain  transmitting  station  will  be  interfered  with  by 
the  presence  of  electromagnetic  waves  of  a  different  wave-length  emanating 
from  other  stations.  Thus  if  X0  =  An,  a  condition  impossible  to  realize,  then, 


or  the  selectivity  is  infinitely  large,  and  no  interference  will  be  registered 
at  the  receiving  station. 

It  may  be  shown  that  when  the  transmitting  and  receiving  systems  are 
tuned,  selectivity  is  affected  by  the  sum  of  the  decrements  of  the  trans- 
mitting and  receiving  systems  1  and  also  by  the  audibility  of  the  receiving 
circuit  (in  so  far  as  this  is  affected  by  k),  approximately  as  shown  by  the 
following  formula: 


where,  g=a  constant; 

5t  and  Sr  =  decrements  of  transmitting  and  receiving  circuits,  respectively; 
a  =  audibility. 

Practically  no  selectivity  can  be  obtained  with  the  transmitting  and 
receiving  systems  out  of  tune. 

When  making  the  adjustments  of  a  receiving  set  the  aim  should  be 
to  obtain  the  maximum  selectivity  compatible  with  a  reasonable  audi- 
bility; but  it  must  be  borne  in  mind  that  these  two  quantities  are  inversely 
proportional  to  each  other  and  that  a  high  audibility  means  a  low  selectivity 
and  vice  versa,  as  shown  by  the  formula  above. 

We  may  now  discuss  the  characteristics  of  the  various  types  of 
receivers,  of  which  there  are,  in  general,  three: 

1st.  Those  in  which  the  detecting  circuit  is  conductively  coupled  to 
the  receiving  antenna  circuit  as  shown  in  Fig.  64. 

2d.  Those  in  which  the  detecting  circuit  is  inductively  coupled  to  the 
receiving  antenna  circuit,  as  shown  in  Fig.  65. 

3d.  Those  in  which  the  detecting  circuit  is  capacitively  connected 
to  the  receiving  antenna  circuit,  as  shown  in  Fig.  66. 

In  all  receiving  systems  the  receiving  antenna  circuit  is  supposed 
to  be  tuned  to  the  wave-length  of  the  incoming  oscillations,  so  that  the 
e.m.f.  impressed  upon  the  receiving  antenna  due  to  the  electro-magnetic 
waves  produce  the  maximum  current. 

First  Type  of  Receiver.  —  In  this  type,  since  the  energy  of  the  signals 
received  in  the  antenna  is  applied  directly  to  the  detector  circuit  without 
loss  on  any  intermediary  circuit,  it  is  plain  that  comparatively  loud  signals 
will  be  obtained,  provided,  of  course,  that  the  inductance  to  which  the 
detector  circuit  is  connected  is  of  any  reasonable  value,  so  as  to  produce 
i  See  Chapter  IV,  pp.  272-274. 


RECEIVING  CIRCUITS 


353 


a  reasonable  drop  across  the  detector  circuit;  it  has  been  shown  (Fig.  60) 
that  the  rectification  given  by  the  crystal  is  porportional  to  the  square 
of  the  impressed  voltage,  hence  if  the  inductance  used  in  the  antenna  for 
tuning  is  low,  the  drop  across  this  inductance  will  probably  be  low,  so 
that  a  poor  signal  will  be  obtained.  The  signal  given  by  the  connection 
will  probably  be  loud  and  be- 
cause of  the  very,  loudness  of 
the  signals,  the  system  must,  as 
already  pointed  out,  be  lacking 
in  selectivity.  Of  course,  the 
selectivity  may  be  improved  by 
making  the  decrements  of  the 
transmitting  and  receiving  an- 
tenna circuits  low;  see  Eq.  (16). 
Second  Type  of  Receiver.— 
This  may  be  used  either  with 


FIG.  64. — Single-circuit  receiving  system. 


1 

-4 

c 

/    j 

J 

0 

V 

K 

|H 

» 
°*i 

o 

t 

7 

/ 

or  without  a  tuning  condenser 

in  the  detector  circuit.  We  will  consider  the  two  cases  separately, 
(a)  Without  a  tuning  condenser  in  the  detector  circuit.  In  this  case  the  audi- 
bility of  the  signals  may  be  changed  by  changing  the  coupling  between 
H  and  K  (Fig.  65);  it  is  superior  to  the  first  type  because  the  selec- 
tivity may  be  greatly  increased  without  decreasing  the  audibility.  This 
is  done  by  using  a  weak  coupling  between  H  and  K,  thus  increasing  selec- 
tivity; the  signal  is  main- 
tained at  a  loud  intensity 
by  winding  K  with  many 
turns  of  wire  compared  to 
the  winding  of  H,  thus 
obtaining  perhaps  much 
greater  voltage  across  the 
terminals  of  K  than  exists 
across  H.  By  thus  using 

FIG.  65.— Two  circuit  inductively  coupled  receiving  hi&h     inductance     for     K, 
systems.  getting  larger  voltage,  the 

efficiency  of  rectification  of 

the  crystal  is  increased  sufficiently  to  permit  the  weak  coupling  required 
for  selectivity.  (fc)  With  a  tuning  condenser  in  the  detector  circuit.  An 
increase  in  selectivity  results  from  this  when,  as  is  always  the  case,  the 
detector  circuit  is  tuned  to  the  receiving  antenna  circuit,  which  is,  in  turn, 
tuned  to  the  transmitting  antenna.  For  this  case  it  has  been  found  that 
the  selectivity  is  affected  most  by  the  decrements  of  the  detector  circuit 
and  of  the  transmitting  antenna,  and  very  little  by  the  decrement  of  the 
receiving  antenna.  This  result  makes  it  possible  to  obtain  great  selec- 


354 


SPARK  TELEGRAPHY 


[CHAP.  V 


fcj                IK      r~ 

1  

^1 

!H 

—  (.000000  r— 

THci 
|£ 

p 
0 

o 

0 

o 

0 

1 

When  using  the  static 
coupling,  coils  Li  and  Lj 
are  adjusted  to  give  no 
mutual  induction 

/Ilc2     1 

^ 

tivity  even  when  the  decrement  of  the  receiving  antenna  is  high,  by  using 
a  low  decrement  detector  circuit.  On  the  other  hand,  if  the  receiving  an- 
tenna has  a  low  decrement,  then  the  use  of  a  tuned  detector  circuit  has 
but  little  advantage,  and  it  would  show  practically  no  increase  in  selec- 
tivity over  the  case  where  no  condenser  is  used  in  the  detector  circuit. 

Third  Type  of  Re- 
ceiver.— This  is  similar 
to  the*case  of  the  induc- 
tively coupled  type,  ex- 
cept, of  course,  that  the 
coupling  is  changed  by 
changing  the  two  con- 
densers Ci  and  C2,  Fig. 
66.  Increasing  the  ca- 
pacity of  these  two  con- 
densers increases  the 
FIG.  66. — Electrically,  or  capacitively,  coupled  receiving  coupling  and  hence  the 
fcystem.  audibility,  while  the  se- 

lectivity is  at  the  same 

time  reduced.  Since  the  coupling  condensers  form,  together  with  closed 
circuit,  L2  -C,  a  circuit  which  is  in  multiple  with  the  antenna  tuning 
inductance,  it  is  plain  that  the  total  equivalent  inductance  or  capacity  of 
this  multiple  circuit  must  be  changed  somewhat  by  any  change  in  the 
coupling  condensers,  thus  affecting  the  tuning  of  the  antenna  circuit,1 

Of  the  three  types  of  receivers  described  above  the  second  (inductively 
coupled    type)    is   most 

* 


widely  used,  while  the 
statically  coupled  receiv- 
ers were  largely  used  in 
the  U.  S.  Navy.  The 
first  type  is  never  used 
except  when  first  picking 
up  signals,  when  the 
operator  may,  if  the 
apparatus  will  allow  it, 
place  his  detecting  cir- 
cuit directly  across  the 
antenna  tuning  induct- 
ance; and  later  he  will  change  over  to  the  inductively  coupled  or  to  the 
statically  coupled  type,  whichever  the  case  may  be. 

We  will  now  give  the  various  steps  through  which  an  operator  should 

1  For  a  theoretical  treatment  of  the  selectivity  of  the  electrically  coupled  receiver 
see  article  by  Louis  Cohen,  ''Electrostatically  coupled  circuits,"  Proc.  I.  R.  E.,  Oct.,  1920. 


FIG.  67. — Ordinary  type  of  receiving  circuit. 


ADJUSTMENT  OF  RECEIVING   CIRCUIT  355 

pass  when  receiving  signals,  in  the  case  of  an  inductively  coupled  receiver. 
The  circuit  of  this  receiver  is  again  reproduced  in  Fig.  67  for  the  sake  of 
convenience.  To  begin  with  the  operator  has  his  set  in  the  so-called  "stand- 
by" position,  i.e.,  with  close  coupling  between  H  and  K  and  with  the 
switch  S  open,  so  as  to  make  the  detecting  circuit  aperiodic  ;  in  this  con- 
dition the  operator  manipulates  the  inductance  H  and  the  capacity 
Ci  and  picks  up  practically  all  signals  which  reach  the  antenna  with 
sufficient  intensity.  When  he  wants  to  read  a  particular  signal  he  goes 
through  the  following  manipulations:  (a)  with  S  open,1  adjust  H 
and  Ci  until  required  signal  is  loudest  and  then  the  coupling  of  H  and 
K  is  decreased  to  as  low  a  value  as  possible,  still  maintaining  a  fair  inten- 
sity of  signal  strength;  (b)  switch  S  is  closed  and  €2  is  adjusted  until 
required  signal  is  loudest,  (c)  Coupling  between  H  and  K  is  decreased 
and  at  the  same  time  H,  Ci  and  €2  are  slightly  adjusted  until,  for  any 
particular  coupling,  the  signal  is  loudest.  This  operation  is  repeated  until 
the  legitimate  signal  becomes  quite  weak,  yet  audible,  and  all  the  other 
interfering  signals  have  been  weeded  out.  When  going  through  this  last 
step  the  interfering  signals  will,  of  course,  get  weaker  and  weaker  as  the 
coupling  is  decreased  from  its  maximum  value,  but  the  audibility  may 
at  first  increase  and  then  decrease.  The  reason  for  this  latter  is  that 
the  antenna  and  the  closed  circuit  of  the  receiver  form  two  tuned  coupled 
circuits  upon  the  primary  of  which  (the  antenna)  there  is  impressed  an 
e.m.f.  of  the  same  frequency  as  the  natural  frequency  of  the  coupled  cir- 
cuits; the  curves  of  pages  103  and  104,  Chapter  I,  show  that,  under  these 
conditions,  the  current  in  the  secondary  (the  detector  circuit)  has  a  maxi- 
mum value  for  a  certain  critical  coupling  and  that  for  closer  or  weaker 
coupling  than  this  the  current  becomes  smaller.2 

In  case  the  wave-length  being  received  is  appreciably  longer  than  the 
natural  wave-length  of  the  antenna  the  shortening  condenser  Ci  will  be 
short-circuited  by  a  suitably  placed  switch,  and  the  adjustment  of  the 
antenna  circuit  tuning  will  be  accomplished  by  varying  H  only. 

Some  additional  interesting  points  regarding  the  effect  of  the  decrease 
in  the  resistance  of  the  entire  receiving  system  upon  the  audibility  and 
selectivity  may  be  deduced  by  further  considering  formulas  (13)  and  (16). 


Formula  (13)  shows  that  the  less  the  value  of  R  (resistance  of  receiving 

1  In  case  no  switch,  S,  is  provided,  condenser  C2  may  be  set  at  its  minimum  value; 
this  is  practically  equivalent  to  opening  switch  S. 

2  The  curves  given  on  pp.  103-104  were  obtained  while  an  e.m.f.  of  constant  ampli- 
tude was  impressed  on  the  primary  circuit.     In  the  circuit  of  Fig.  67  a  damped  e.m.f. 
is  impressed  as  the  primary  :    if  the  damping  is  high  these  curves  are  not  quite  applicable 
to  the  case. 


356 


SPARK  TELEGRAPHY 


[CHAP.  V 


system)  the  greater  the  audibility,  and  in  this  respect  the  effective  resist- 
ance of  the  entire  receiving  system  should  be  kept  as  low  as  possible.1 
Again  from  Formula  (16),  i.e.: 


xl 

a' 


(16) 


it  may  be  seen  that,  since  the  resistance  of  the  receiving  system  affects 
the  decrement  8r  in  direct  proportion,  any  decrease  of  R  will  decrease  dr 
and  increase  S  provided,  of  course,  that  a  is  kept  constant  by  suitably 
changing  k.  However,  since  no  matter  what  is  done  to  R  the  value  of  8t 
(transmitter  decrement)  cannot  be  changed  by  the  receiving  operator, 


FIG.  68. — Showing  arrangement  of  a  buzzer  circuit  loosely  coupled  to  the  antenna,  for 
the  testing  of  the  crystal  rectifier.  With  the  buzzer  in  operation  the  antenna 
oscillates  at  its  natural  frequency  and  so  acts  on  the  receiving  circuit  as  would  a 
signal.  Care  must  be  taken  to  prevent  induction  from  the  buzzer  circuit  getting 
into  the  K-CZ  circuit  directly  as  in  this  case  the  test  is  valueless;  the  buzzer  will 
then  be  heard  in  the  phones  even  though  the  crystal  is  short-circuited. 

it  follows  that,  when  dr  is  made  very  small,  there  is  hardly  any  gain  in 
selectivity  obtainable  by  making  it  smaller,  because,'  even  if  dr  were  zero, 
there  would  still  remain  dt  to  be  reckoned  with  in  connection  with  the 
value  of  the  selectivity.  The  conclusion  to  be  derived  from  the  above 
is  that  it  is  uneconomical  to  try  to  make  the  receiving  system  of  extremely 

1  In  addition  to  this  condition  the  resistance  introduced  into  the  circuit  by  the 
detector  and  phones  should  be  just  equal  to  the  resistance  of  the  entire  circuit,  exclusive 
of  the  detector  and  phones. 


WAVE-LENGTHS  AND  RANGES  IN  SPARK  TELEGRAPHY       357 

low  resistance  unless  the  decrement  of  the  transmitting  set  is  also  made 
correspondingly  small. 

Another  point  to  be  noted  is  that  in  most  receivers  provision  is  made 
for  adjustment  of  the  crystal  detector  so  as  to  make  sure  of  a  sensitive 
spot  thereon.  This  is  done  by  arranging  the  receiving  circuit  somewhat 
as  shown  in  Fig.  68,  where  a  buzzer  is  used  to  excite  by  impulse  (and  by 
means  of  coils  M  and  N)  the  antenna  circuit,  so  as  to  produce  therein 
currents  of  a  frequency  equal  to  the  natural  frequency  of  the  antenna  cir- 
cuit; the  currents  in  the  latter  are  transferred  by  means  of  H  —K  to  the 
detector  circuit,  and  the  detector  may  thereby  be  adjusted  for  a  sensitive 
point. 

Wave-lengths  and  Ranges  in  Spark  Telegraphy.  —  The  wave-lengths 
used  in  spark  telegraphy  vaiy  from  about  50  to  about  6000  meters.  The 
range  under  200  is  allotted  to  amateurs;  200  to  600  is  generally  used  for 
aeroplane  sets;  450  to  800  for  ship  sets,  900  to  1500  for  moderate-size 
land  stations,  and  over  1500  for  the  largest  land  stations.  The  laws  of 
the  United  States  specify  the  following  wave-lengths: 

High-power  stations  ...................  over  1600  meters. 

Navy  ................................  600  to  1600  meters. 

Ship  stations  .........................  300,  450,  600  meters. 

Amateurs  ............................  below  200  meters. 

The  power  used  is  J  to  J  kw.  for  amateur  and  aeroplane  sets,  1  to  10  kw. 
for  ship  sets,  5  to  20  kw.  for  moderate  size  land  stations  and  up  to  100  kw. 
or  more  for  the  largest  land  stations. 

The  range  covered  may  be  approximately  determined  by  means  of 
the  Austin  formula  given  below,  which  applies  to  daylight  transmission  : 

7       7         T  0.0015d 

s~ 


...... 

\Ci 

where 

7r  =  the  current  in  receiving  antenna  in  amperes; 

Is=  the  current  in  transmitting  antenna  in  amperes; 
hi  and  h?,  =  effective  heights  of  transmitting  and  receiving  antennas,  respect- 
ively, in  kilometers; 

X  =  wave  length  in  kilometers; 

d  =  distance  between  the  two  antennas  in  kilometers. 

In  the  above  formula  the  effective  resistance  of  the  entire  receiving  system 

1  See  Chapter  IX  for  further  discussion  of  transmitting  formulae.  Papers  discussing 
this  formula  are  given  by  Austin  in  Bulletin  of  Bureau  of  Standards,  Vol.  7,  No.  3,  1911, 
and  Vol.  II,  No.  1,  1914,  also  by  Libby  in  Proc.  I.  R.  E.,  Vol.  5,  No.  1,  Feb.,  1917. 
Recent  tests  by  Vallauri  throw  doubt  on  the  validity  of  this  equation,  he  having  obtained 
currents  about  ten  times  as  large  as  those  predicted  from  this  formula. 


358 


SPARK  TELEGRAPHY 


[CHAP.  V 


is  assumed  to  be  25,  ohms.  In  view  of  the  fact  that  the  distance  (d)  occurs 
as  an  exponent  it  is  difficult,  more  particularly  for  large  distances,  to  solve 
the  above  equation  directly  for  d.  The  following  may,  however,  be  done. 
Knowing  hi,  /*2,  Is  and  X,  plot  a  curve  showing  the  relation  between  d  and 
Ir.  The  value  of  d,  obtained  from  the  curve,  corresponding  to  an  Ir 
which  will  give  the  minimum  audibility  (this  depends  on  the  type  of 


, 

CURVE  SHOWING   RELATION  BETWEEN  CURRENT 
IN   RECEIVING  ANTENNA  AND  DISTANCE 
FROM   TRANSMITTING  ANTENNA 
OBTAINED  BY  MEANS  OF  AUSTIN-COHEN'S  FORMUU 

\ 

\ 

^ 

\ 

He'ignt  of  Receiving  &  of  [Transmitting  kntenna 

=  25i 

nel 

er 

i 

) 

Current 

in 

Trans'mittii 

ig  An 

tenna 

=  5  a 

np 

2re 

s 

\ 

Wave-le 

ng 

thU 

00 

me 

ters 

\ 

Curve  is 

Applica 

ble 

to 

Day-light  r. 

ra 

isr 

tiis 

ioi 

i  b 

y  " 

iea 

ns 

of 

\ 

D£ 

.inpec 

W 

av 

28 

\ 

V 

\ 

\ 

V 

\ 

\ 

V 

s 

\ 

\ 

S 

^ 

^ 

•^v 

-••^ 

—  «* 

==~- 

•*=; 

-«.•• 

**••• 

- 

"^^i 

= 

—  — 

100 


200 


300  400  500 

Distance  in  Kilometers 


600 


TOO 


800 


FIG.  69. — Calculated  value  of  current  in  the  antenna  of  the  receiving  station  as  distance 
is  varied,  the  conditions  being  as  stated  in  the  diagram. 

detector  used)  is  the  maximum  range.     An  example  has  been  worked 
out  below,  where: 

hi  =  h2  =  0.025  km. 


Is=5  amperes 
X  =  0.6  km. 


and 


.^^0.0252X5^     °-^ 
4'25X^6X^X€     ^: 


Substituting  different  values  of  d  in  this  last  equation  we  obtain  the  cor- 
responding values  of  IT  and  are,  therefore,  able  to  plot  the  curve  of  Fig.  69. 


SMALL  SPARK  TRANSMITTER 


359 


FIG.  70. — Side  view  of  a  small  spark  set  made  by  the  Wireless  Improvement  Co. 


360 


SPARK  TELEGRAPHY 


[CHAP.  V 


With  an  ordinary  crystal  detector  and  a  receiving  system  of  25  ohms  a 
current  of  7  micro-amperes  in  the  receiving  antenna  is  sufficient  to  give 
unit  audibility.  Looking  up  the  curve  we  find  that  the  distance  corre- 
sponding to  7  micro-amperes  is  610  km.'s. 

If  strays    and    interference   should    be    present  perhaps    28    micro- 


FIG.  71. — Front  view  of  the  set  shown  in  Fig.  70. 

amperes  might  be  required  in  the  receiving  antenna  in  order  to  insure 
reliable  communication,  in  which  case  the  distance  would  be  310  km.'s. 

Thus,  for  daylight  transmission,  under  poor  atmospheric  conditions, 
the  range  would  be  about  300  km.'s,  and  under  very  favorable  atmospheric 
conditions  the  range  would  be  about  600  km.'s. 

From  the  point  of  view  of  the  transmitter  in  the  problem  con- 
sidered above,  the  high-frequency  power  in  the  antenna  for  a  current  of 


ARRANGEMENT  OF  A  LARGE  SPARK  TRANSMITTER     361 


FIG.  72. — General  view  of  the  spark  transmitter  used  at  the  U.  S.  Government  station 
at  Arlington  for  broadcasting  time  signals  and  weather  reports. 


FIG.  73. — Showing  the  construction  of  the  synchronous  rotating  gap  of  the  Arlington 

transmitter. 


362 


SPARK  TELEGRAPHY 


[CHAP.  V 


5  amperes  in  the  antenna  and  assuming  the  total  resistance  of  the  antenna 
to  be  8  ohms,  would  be  given  by: 

High-frequency  power  =  8  X  52  =  200  watts. 

Assuming  efficiency  of  the  transmitting  set  from  alternator  to  antenna 
=  25  per  cent. 

200 
Alternator  output  =  -==  =  800  watts. 


RADIO    VA 


N.E.S.CO.  IOOK.W. 
TRANSMITTER 


FIG.  74. — Circuit  diagram  of  the  Arlington  transmitter.     (Proc.  I.R.E.) 
It  must  be  noted,  in  connection  with  the  above,  that  if  we  neglect  the 

O.OOlSd 

factor  e      Vx  ,  in  Eq.  (17) 


XI,  ' 


(18) 


then,  if  everything  else  be  kept  constant  the  distance  would  vary  directly 
with  the  transmitting  antenna  current  (Is) ;  but  the  power  required  from 
the  alternator  varies  with  the  square  of  the  current,  hence  to  double  the 
transmitting  distance  the  power  put  into  the  antenna  must  be  quad- 


rupled;  and,  if  the  factor  e  Vx  be  considered,  the  power  must  be  more 
than  quadrupled  to  double  the  range  of  transmission.  Hence,  the  necessity 
for  great  range  of  transmission  of  increasing  the  antenna  heights  (more 
especially  the  transmitting  antenna)  to  very  great  values. 

Arrangement  of  Apparatus  of  a  Spark  Set. — The  various  parts  required 
for  a  transmitting  set  are  generally  assembled  in  compact  form;   in  the 


TYPICAL  SPARK  SETS  363 

case  of  a  low-powered  outfit  practically  all  of  the  apparatus,  with  the  excep- 
tion of  the  hand  key  for  sending,  may  be  mounted  directly  on  a  panel.  A 
neat  design  for  a  500-watt,  quenched-spark  transmitter  is  shown  in  Figs.  70 
and  71;  the  legends  on  the  cuts  makes  them  self-explanatory.  The  larger 
land  stations  of  course  require  large  switch  boards  and  auxiliary  appa- 
ratus, in  fact  the  outfit  really  comprises  a  complete  isolated  power  plant 
equipment. 

In  Fig.  72  is  shown  the  arrangement  of  apparatus  of  the  Arlington 
spark  set,  used  for  sending  out  time  signals;  Fig.  73  gives  a  closer  view 
of  the  rotating  sychronous  spark  gap  and  Fig.  74  gives  a  complete  cir- 
cuit diagram  of  this  station. 


CHAPTER  VI 
VACUUM  TUBES  AND  THEIR  OPERATION  IN  TYPICAL  CIRCUITS  1 

Constitution  of  a  Conductor,  Possibility  of  Electron  Emission. — As 
outlined  in  Chapter  I,  a  conductor  is  made  of  atoms  (or  molecules)  with 
some  of  the  electrons  free  from  atoms,  moving  back  and  forth,  from  one 
atom  to  another.  Unless  the  conductor  is  at  absolute  zero  temperature 
its  atoms  are  constantly  in  a  state  of  agitation,  having  non-coordinated 
motions  in  all  directions.  The  free  electrons  share  the  motion  of  the  atoms, 
and  due  to  their  comparatively  small  mass  (about  1/200,000  that  of  the 
tungsten  atom)  their  average  velocity  is  very  much  greater  than  that  of 
the  atoms. 

Now  the  atoms  of  a  metal  tend  to  separate  from  each  other  at  high 
temperatures  or,  we  may  say,  the  metal  tends  to  evaporate  just  as  water 
evaporates  at  ordinary  temperatures.  We  must  imagine  the  surface  ten- 
sion of  a  metal  great  enough  to  prevent  appreciable  evaporation  at  ordinary 
temperature;  the  velocity  of  motion  of  the  atoms  is  not  sufficient  to  carry 
them  through  this  surface  tension.  With  very  high  temperatures,  how- 
ever, those  atoms  having  the  highest  velocity  break  through  the  surface 
tension  and  so  start  the  process  of  vaporization,  which  becomes  more  and 
more  rapid  as  the  temperature  rises.  To  accomplish  actually  the  vapor- 
ization of  the  ordinary  metal  requires  that  the  heating  be  done  in  vacuum, 
otherwise  oxidation  occurs  instead.  The  number  of  atoms  evaporated 
from  a  given  surface  depends  upon  the  temperature  and  the  latent  heat 
of  evaporation  of  the  metal  being  tested. 

Now  it  seems  quite  likely  that  if,  when  the  atoms  acquire  a  high  velocity, 
they  are  able  to  break  through  the  surface  tension  of  the  metal  the  electrons 
can  do  the  same  thing,  hence  we  get  the  idea  of  electrons  evaporating.2 
This  evaporation  of  the  electrons  will  take  place  at  lower  temperature 
than  that  of  the  atoms  of  the  metal  itself  because  of  the  higher  average 
velocity  of  the  electrons. 

Theoretical  Prediction  of  the  Number  of  Electrons  Emitted  from  a 
Hot  Body. — The  number  of  atoms  (or  molecules)  of  an  ordinary  liquid 

1  Since  this  material  went  to  press  there  has  been  published  an  excellent  text  on 
Vacuum  Tubes  by  H.  J.  Van  der  Bijl. — McGraw-Hill  Co. 

2  See  O.  W.  Richardson's  book  on  "  The  Emission  of  Electricity  from  Hot  Bodies." 

364 


POSSIBILITY  OF  ELECTRON  EVAPORATION  365 

which  evaporate  was  known  to  vary  with  the  latent  heat  of  evaporation 
of  the  substance  and  temperature  according  to  the  equation, 


where 

N  =  number  of  atoms  evaporating  per  second  per  sq.  cm.  of  surface; 
T  =  absolute  temperature,  ordinarily  called  degrees  Kelvin; 
a  =  latent  heat  of  evaporation  ; 
A  =  a  constant. 

Richardson  was  the  first  to  draw  an  analog  between  the  evaporation  of 
atoms  and  possible  evaporation  of  electrons  from  a  hot  metal.  Reason- 
ing from  the  above  equation  he  came  to  the  conclusion  that  the  number 
of  electrons  evaporating  per  second  (current)  could  be  expressed  by  the 
equation 


*r         ........     (1) 

in  which 

i  —  current  of  emission  per  sq.  cm.  of  hot  surface; 
T  —  absolute  temperature  of  hot  metal; 
b  =  latent  heat  of  evaporation  of  electrons  =  105,000; 
a  =  a  constant. 

As  this  predicted  current  was  due  to  the  thermal  activity  of  the  emit- 
ting surface  Richardson  suggested  the  term  thermionic  current,  a  name 
which  is  at  present  used  to  some  extent;  the  term  electron  current  is  also 
used,  but  this  is  really  not  distinctive,  because  all  currents,  arising  from 
whatsoever  cause,  are  due  to  the  flow  of  electrons. 

The  emission  of  electrons  predicted  by  Eq.  (1)  would  give  currents 
from  a  heated  tungsten  filament  about  as  shown  in  Fig.  1;  it  is  evident 
that  very  large  currents  might  be  expected  from  a  tungsten  filament  at 
temperatures  well  within  the  safe  operating  region.1  Of  course,  ordi- 
narily there  is  no  current  of  such  magnitude  due  to  emitted  electrons; 
although  the  number  of  electrons  indicated  in  Fig.  1  is  really  emitted, 
they  at  once  re-enter  the  surface  so  that  on  the  whole  there  are  no  electrons 
leaving  the  hot  surface.  As  soon  as  an  electron  leaves  the  filament  it 
(the  filament)  is  left  charged  positively  and  so  attracts  the  emitted  elec- 
tron; thus  there  are  as  many  electrons  falling  back  into  the  filament  as 
are  expelled  by  the  internal  thermal  agitation. 

JThe  melting-point  for  tungsten  is  3270°  C.;  reckoning  the  safe  operating  temper- 
ature as  that  which  gives  the  filament  2000  hours'  life,  the  safe  temperature  increases 
somewhat  with  the  diameter  of  the  filament,  being  perhaps  2200°  C.  for  a  filament 
.01  cm.  diameter  and  2300°  C.  for  one  .04  cm.  diameter. 


366 


VACUUM   TUBES  AND   THEIR  OPERATION 


[CHAP.  VI 


Suppose,  however,  that  there  is,  close  to  the  heated  filament,  a  posi- 
tively charged  metal  plate;  an  expelled  electron  will  have  two  forces 
acting  on  it,  one  tending  to  make  it  fall  back  into  the  filament,  and  the 


1000 

800 


400 


200 


20 


7 


Z 


2000 


1000 1 
""I 

600$ 


200 


2000C 


2100C 


2200°  2300°  2400° 

Temperature  (Absolute  Centigrade) 


2500C 


FIG.  1. — Theoretical  values  of  current  due  to  electron  emission  from  a  pure  tungsten 

filament. 


other  pulling  it  toward  the  positively  charged  plate.  Which  force  has 
the  preponderating  effect  will  depend,  of  course,  upon  the  value  of  the 
positive  plate  potential;  if  thic  is  made  sufficiently  high,  all  of  the  electrons 


IRREGULARITIES   IN   ELECTRON   EVAPORATION  367 

emitted  from  the  hot  surface  will  be  drawn  to  the  plate,  none  of  them 
re-entering  the  hot  emitting  surface. 

The  value  of  the  current  under  this  condition  is  called  the  saturation 
current;  this  value  of  current  measured  for  different  filament  temper- 
atures should  satisfy  Richardson's  equation  because  all  of  the  electrons 
emitted  go  over  to  the  plate. 

As  early  as  1902  Richardson  published  experimental  results  confirm- 
ing his  theory.  Many  other  experimenters  published  results  seemingly 
contradicting  the  relations  given  in  Eq.  (1),  and  for  several  years  Richard- 
son's theory  was  the  subject  of  dispute. 

It  seems  that  very  minor  changes  in  the  amount  of  gas 1  in  the  tube 
used,  or  the  condition  of  the  surface  of  the  hot  metal,  completely  nullified 
the  results  obtained,  and  such  has  been  found  to  be  the  case.  H.  A.  Wilson 
found,  e.g.,  that  the  emission  from  a  hot  platinum  filament  might  be 
reduced  to  1/250,000  of  its  normal  amount  by  first  heating  the  filament 
in  oxygen,  or  boiling  it  in  nitric  acid;  also  he  found  that  the  presence 
of  a  slight  amount  of  hydrogen  around  the  heated  filament  completely 
destroyed  the  effects  of  the  oxygen  and  nitric  acid.  On  the  other  hand 
it  is  found  that  the  electron  emission  from  tungsten  is  very  much  increased 
by  such  an  impurity  as  thorium;  if  a  small  percentage  of  thorium  is 
present  in  a  tungsten  filament  the  emission  is  many  times  as  great  as 
though  pure  tungsten  were  used. 

As  a  result  of  Wilson's  experiment  it  was  evident  that  the  condition 
of  the  hot  surface  was  of  utmost  importance  in  determining  the  emission; 
the  layer  of  oxygen-filled  platinum  on  the  surface  practically  prevented 
emission.  Yet  a  year  afterward  Wehnelt  showed  that  if  a  platinum 
filament  was  coated  with  lime  (calcium  oxide)  the  emission  of  electrons 
at  a  given  temperature  was  vastly  greater  than  from  the  platinum  itself. 

Langmuir's  experiments,  performed  with  tungsten  filaments  in  ex- 
tremely high  vacuum,  proved  without  doubt  the  truth  of  Richardson's 
prediction  and  indicated  that  the  various  experimenters  whose  tests  had 
showed  the  opposite  had  not  been  careful  enough  in  the  manipulation 
of  their  experiments  and  in  the  interpretation  of  the  results.  He  found 
that  the  higher  the  vacuum  the  more  consistently  did  experiment  and 
theory  agree,  whereas  others  had  concluded  that  gas  was  absolutely  essen- 
tial if  the  thermionic  current  was  to  be  obtained.  In  one  of  Langmuir's 
tests  he  showed  that  the  presence  of  only  .000001  mm.  pressure  of  oxygen 
was  sufficient  practically  to  stop  the  emission  of  electrons  from  a  hot  tung- 
sten filament.  It  seems  then  that  the  condition  of  the  surface  of  the  hot 
electrode  affects  the  emission  of  electrons  much  as  the  evaporation  of 
water  is  prevented  by  covering  the  surface  with  a  thin  layer  of  oil  or 
similar  substance. 

1  See  article  by  Lockrow,  Phys.  Rev.,  February,  1922,  for  effect  of  gas  on  emission. 


368 


VACUUM   TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


Distribution  of  Electrons  near  the  Surface  of  a  Hot  Metal. — In  Fig. 
2  is  shown,  in  rather  crude  fashion,  the  manner  in  which  the  electrons  are 
concentrated  near  the  surface  of  a  hot  body,  the  three  figures  being  for 

.    •    .  .      temperatures  of  per- 
'/."*  -.  '  *  V        haps  2100°,  2300°, 
"..";      .-,     '.      and  2500°  absolute 
"  .'•    •  *  »\  •  •  -"  V      temperature.        In 
{,•'"•     ' '.I     *.        (a)    but   few   elec- 
"/.!  *•/*;:..'•'      trons    are    coming 
.*  .•;„  .•  .  '.-.        Vs^V.'V  »•':,,""•. :      off  and  these  have 
' .   ]      .*«.•.      .".";:/.."/  *•'*      V^y,' vfi^rC-£;$      such  a  low  velocity 
a  £ c     "  '         that  they  are  pulled 

FIG.  2.— Conventional  diagram  to  represent  the  distribution  of  back  in*°  the  timg 
electrons  near  the  surface  of  a  hot  metal,  for  increasing  sten      before     they 
temperature.  have     moved    out 

from  the    tungsten 

perhaps  .001  cm.     In  (6)  more   electrons  are   emitted  and   their  mean 

velocity  has  increased  so  that  more  of  them  move  farther  away  from  the 

surface   before   falling  back.     In  (c)  is  shown  a  much  denser  electron 

atmosphere  near  the  surface  and  also  extending  to  considerable  distance 

from  the  tungsten 

surface.      In  one 

tungsten  filament 

tube  tested  by  the 

author      it     was 

found      that     at 

normal  operating 

temperature  only 

1/8000      of      the 

electrons   emitted 

reached  a  distance 

.15  cm.  from  the 

hot  filament,  most 

of     them     never 

going      Very       far  Velocity  of  emission,  in  108cin/sec 

(perhaps  .001  cm.)    FIG.  3.— Velocity  distribution   for  electrons   emitted  ""from  hot 

from  the  surface.  tungsten,  for  three  different  temperatures. 

In    Fig.   3    is 

shown  a  set  of  curves  corresponding  to  the  conditions  given  for  Fig.  2; 
the  area  under  each  curve  gives  the  numbers  of  electrons  emitted 
from  the  filament  and  the  form  of  the  curve  illustrates  how  the  number 
of  electrons  having  a  given  velocity  changes  as  the  temperature  is 
increased.  At  temperature  TI,  but  few  electrons  are  emitted  and  they 


y 
VELOCITY  OF  ELECTRONS  EVAPORATING  369 

have  on  the  average  a  low  velocity,  practically  none  having  a  velocity 
greater  than  V\]  at  temperature  T^  many  more  electrons  come  off  and 
on  the  average  they  have  a  higher  velocity;  the  same  effect,  but  more  of 
it,  is  shown  for  the  highest  temperature  T%. 

Some  idea  of  the  velocity  with  which  these  electrons  leave  the  surface 
of  the  tungsten  can  be  easily  obtained.  From  certain  experiments  we 
know  that  an  electron  must  fall  freely  through  a  potential  difference  of 
about  4  volts,  before  it  gains  sufficient  energy  to  break  through  the  "  sur- 
face tension  "  or  "  surface  constraint  "  of  the  metal.  If  we  use  the  rela- 
tion that,  in  any  accelerating  system, 

Potential  energy  lost  =  kinetic  energy  gained 
we  put  Ve  =  \mv2 

in  which 

V  =  potential  difference  through  which  electron   has  fallen   (e.s. 
units) ; 

e  —  charge  of  electricity  on  one  electron; 
m  =  mass  of  electron ; 

v  =  final  velocity  of  electron,  assuming  it  to  start  from  rest. 

p  p 

Transposing  we  get  v2  =  2V—  and  —  has  been  determined  many  times, 

HI/  Tfl 

its  value  being  5.3  X1017,  in  electro  static  units. 

Hence  if  an  electron  falls  through  one  volt  difference  of  potential 
(1  volt  =  ^-J-o  e.s.  unit)  the  above  relation  gives  v  approximately  5X107 
cm. /sec. 

As  the  surface  constraint  of  tungsten  is  about  4  volts  we  see  that  an 
electron,  to  break  through,  must  have  a  velocity  of  about  1X108  cm./sec. 

If  a  cold  metal  plate,  electrically  connected  to  the  filament  outside 
the  tube,  is  in  the  same  vacuum  tube  as  the  hot  filament,  and  close  to  it, 
some  of  the  high-speed  electrons  may  have  sufficient  velocity  to  carry  them 
from  the  hot  filament  to  the  cold  plate;  they  then  flow  along  in  the  cir- 
cuit connecting  the  plate  to  the  filament.  This  thermionic  plate  current 
can  exist  even  though  the  plate  is  at  the  same  potential  as  the  lowest 
potential  point  in  the  filament.  Such  an  effect  is  shown  in  Fig.  4;  the 
amount  of  the  plate  current  recorded  was  due  to  electrons  emitted  from 
the  filament  with  such  a  high  velocity  that  their  inertia  carried  them 
across  the  .2  cm.  space  separating  the  plate  from  the  filament. 

It  will  be  noticed  how  the  number  reaching  the  plate  increases  rapidly 
with  the  value  of  filament  current,  due  to  the  two  effects  mentioned 
above,  greater  emission  and  higher  velocity  of  emission.  The  total  emis- 
sion of  electrons  from  the  filament  for  various  filament  currents  \s  noted 
on  the  curve  sheet  of  Fig.  4;  above  a  filament  current  of  1.36  amperes 


370 


VACUUM    TUBES   AND   THEIR   OPERATION 


[CHAP.  VI 


this  total  emission  could  not  be  accurately  measured,  for  reasons  to  be 
taken  up  later.  The  filament  used  in  getting  the  curve  of  Fig.  4  was  only 
about  3  cm.  long  and  of  approximately  the  same  diameter  as  that  of  a 
100-watt  tungsten  lamp,  yet  it  will  be  found  by  calculation  from  the  values 
given  on  the  curve  sheet  that  at  1.3  amperes  in  the  filament  the  emission 
was  about  4X1017  electrons  per  second,  and  of  this  number  there  were 


p 

ate 

cJ 

rre 

nt- 

-PI 

ite 

CO 

line 

cte 

d 

/ 

t( 

>  negative 

en 

dc 

f  fi 

lanr 

en 

;  w 

ith 

/ 

_n}>  E 

batte1 

ry 

-C|urr 

en 

dy 

et 

> 

/ 

V 

elo 

nty  of|  eir 

ission 

/ 

1 

/ 

1 

obi 

1  e 

nih 

sio 

lat  I 

-  =  1.1 

=  4800  ink 

ro& 

mr 

en 

s 

/ 

L.2 

=  17,000 

" 

/ 

.3 

=60,000 

•• 

/ 

L.36 

=  1C 

0,0 

)0 

» 

/ 

/ 

/ 

/ 

/< 

/ 

/ 

/ 

/ 

/ 

/\ 

^ 

f 

f** 

^^* 

fc=s 

= 

•  •• 

—1 

^    —• 

•—  •  • 

— 

50 


40 


10 


1.0 


1.2  1.3 

Filament  current 


1.4 


1.5 


FIG.  4. — Electron  current  from  a  hot  filament  to  an  adjacent  cold  plate,  at  the  same 
potential  as  the  lowest  potential  of  the  filament.  Current  due  to  velocity  of 
emission  of  the  electrons. 

4X1013  which  had  sufficient  velocity  to  carry  them  away  from  the  fila- 
ment an  appreciable  fraction  of  a  centimeter. 

From  the  previous  analysis  of  electron  emission  from  a  hot  body  it 
will  be  realized  that  the  condition  close  to  the  surface  of  a  hot  filament 
resembles  very  much  the  atmosphere  surrounding  the  earth,  a  depth  of 
earth  atmosphere  of  one  kilometer  corresponding  to  a  depth  of  "  electron 
atmosphere  "  of  about  0.01  millimeter.  Just  as  the  earth's  atmosphere 
becomes  less  dense  with  increase  of  distance  from  the  surface,  does  the 


POWER  REQUIRED   FOR  ELECTRON   EMISSION 


371 


density  of  electrons  decrease  with  increase  of  distance  from  the  filament ; 
the  upper  part  of  the  earth's  atmosphere  contains  the  more  rapidly  mov- 
ing atoms  of  gas  just  as  is  the  case  of  the  high-speed  electrons  getting 
farther  away  from  the  filament  than  those  emitted  with  lower  velocity. 

Power  Required  to  Produce  Emission. — From  what  has-been  said 
it  is  evident  that  the  power  required  (for  heating  the  filament)  per  ampere 
of  emission  varies  greatly  with  the  temperature  of  the  emitting  surface; 
thus  with  a  red-hot  tungsten  filament  the  emission  is  inappreciable, 
although  the  power  required  for  maintaining  the  filament  red-hot  is 
comparatively  large. 

As  the  tungsten  approaches  a  white  heat  the  emission  increases  much 
more  rapidly  than  does  the  required  power  for  heating  the  filament.  By 
changing  the  filament  temperature  from  2100°  Kelvin  l  to  2400°  Kelvin 
the  emission  is  increased  about  23  times,  whereas  the  required  power  to 
heat  the  filament  has  increased  only  about  75  per  cent.  It  is  therefore 
advisable  to  run  the  emitting  surface  at  the  maximum  safe  temperature, 
consistent  with  reasonable  life  of  the  filament.  Dushman  2  has  given  the 
following  values  as  representative  of  reasonable  operation  of  a  tungsten 
filament,  the  life  of  the  filament  being  fixed  as  2000  hours: 


Diameter  of  Filament 
in  Cm. 

Safe  Temperature 
Degrees  Kelvin. 

Emission  in  Amperes 
per  Cm.  Lengths. 

Power  Required  for 
Heating  Filament,  in 
Watts  per  Cm. 

.0125 

2475 

.03 

3.1 

.0175 

2500 

.05 

4.6 

.0250 

2550 

.10 

7.2 

.0375 

2575 

.20 

11.3 

From  what  experimental  data  the  author  has  been  able  to  obtain  him- 
self it  seems  as  though  these  figures  are  rather  optimistic;  when  operated 
at  the  temperatures  given  in  the  above  table  it  seems  as  though  the  life 
of  the  filament  is  considerably  less  than  the  life  of  2000  hours  estimated 
by  Dushman. 

Two-electrode  Vacuum  Tube. — The  property  of  hot  bodies  in  vacuo 
permitting  passage  of  electrons  to  a  cold  electrode  in  the  same  vessel  was 
originally  called  the  Edison  effect;  it  was  noticed  in  incandescent  lamps 
as  early  as  1884.  In  1896  Fleming  gave  the  results  of  a  series  of  experi- 
ments in  thermionic  currents  through  vacuo,  but  it  is  evident  in  the  light 
of  our  present  knowledge  that  a  large  part  of  the  current  measured  by 
him  was  due  to  conduction  by  the  ionized  gas  in  the  tube  he  was  using. 
He  found  some  characteristics  which  were  really  due  to  the  electron  emis- 


1  2100°  Kelvin  =2100°  C.  absolute. 

2  See  article  by  Dushman  in  General  Electric  Review,  March,  1915. 


372  VACUUM   TUBES  AND  THEIR  OPERATION  [CHAP.  VI 

sion,  notably  the  unilateral  (one  direction  only)  conductivity  of  the  appa- 
ratus, the  non-linear  relation  between  the  plate  potential  (with  respect  to 
the  filament)  and  the  plate  current,  and  the  fact  that  a  large  separation 
of  plate  and  filament  tended  to  reduce  the  amount  of  plate  current  obtain- 
able. He  found,  however,  that  the  plate  current  was  unstable  and  that 
the  better  the  vacuum  the  less  the  plate  current  became;  both  of  these 
effects  show  that  ionized  gas  was  largely  responsible  for  carrying  the  plate 
current.  The  unilateral  conductivity  of  a  vacuum  tube  having  two  elec- 
trodes, one  hot  and  the  other  cold,  was  utilized  by  Fleming  for  the  detec- 
tion of  damped  high-frequency  waves  and  was  patented  by  him  in  1905. 
This  patent  was  a  very  important  one  in  the  field  of  radio  telegraphy;  it 
goes  by  the  name  of  the  "  Fleming  valve  "  patent.  A  cut  showing  a 


FIG.  5. — One  type  of  Fleming  valve,  used  on  early  Marconi  receiving  sets  as  detector. 

Fleming  valve  is  given  in  Fig.  5.  More  recent  devices  which  function 
because  of  the  unilateral  conductivity  between  hot  and  cold  electrodes 
in  a  vacuum  are  the  mercury  rectifier,  the  tungar  rectifier  and  the 
kenotron. 

The  mercury  rectifier  uses  a  hot  spot  on  a  pool  of  mercury  as  the  source 
of  its  electrons,  the  necessary  temperature  of  the  hot  spot  being  maintained 
by  heat  caused  by  the  plate  current  itself;  ionized  mercury  vapor  serves 
as  the  carrier  of  the  current  which  can  pass  one  way  only. 

The  "  tungar  "  rectifier  operates  in  a  manner  different  from  that  of 
the  mercury  rectifier,  in  that  a  hot  tungsten  filament  serves  as  the  source 
of  electrons,  this  filament  requiring  an  auxiliary  source  of  power  for  main- 
taining its  requisite  temperature.  The  tube  is  filled  with  an  inert  gas 


THE   TWO-ELECTRODE   TUBE 


373 


(generally  about  2  Ibs.  absolute  of  argon),  and  this  gas  is  ionized  by  the 
electrons  from  the  hot  filament;  the  carrier  of  the  plate  current  is  in  this 
case  also  ionized  gas  for  the  main  part,  the  number  of  electrons  emitted 
from  the  hot  filament  being  sufficient  to  carry  perhaps  1/500  of  the  cur- 
rent to  the  plate. 

The  kenotron  is  a  rectifying  tube  which  really  operates  as  a  thermionic 
valve;  the  tube  is  exhausted  as  thoroughly  as  possible,  so  much  so  that 
whatever  gas  may  be  present  plays  an  unimportant  role  in  the  functioning 
of  the  device.  The  plate  current  is  never  greater  than  that  actually 
emitted  by  the  hot  filament.  These  rectifying  tubes  are  made  in  large 
sizes,  sufficient  to  rectify  several  kilowatts  of  power;  the  vacuum  in  these 
is  so  high  that  no  appreciable  current  is  carried  in  the  reversed  direction 
(electrons  from  plate  to  filament)  even  if  100,000  volts  is  impressed. 

In  small  sizes  they  have 
been  used  as  voltage  regulators 
for  self -excited  generators,  the 
speed  of  which  is  variable.  By 
having  a  differential  wind- 
ing on  the  field  poles,  which  is 
supplied  with  current  through 
a  regulator  tube,  and  connect- 
ing the  filament  of  this  regula- 
tor tube  across  a  low-voltage 
winding  on  the  armature,  a 
small  generator  may  be  made 
to  maintain  practically  con- 
stant voltage  over  a  wide 
range  of  speed  variation.  The 
scheme  of  connection  is  shown 

in  Fig.  6,  and  the  reasons  for  the  tube  maintaining  such  constant  voltage 
over  such  a  wide  speed  range  will  appear  from  an  examination  of  the 
characteristics  curves  of  such  a  tube. 

Characteristic  Curves  of  a  Two-electrode  Vacuum  Tube — Value  of 
Saturation  Current. — If  the  filament  current  of  a  kenotron  is  maintained 
constant  and  plate  voltage  varied,  readings  being  taken  of  plate  voltage 
(with  respect  to  the  filament)  and  plate  current,  curves  will  be  obtained 
having  the  shape  shown  in  Fig.  7 ;  here  three  curves  are  shown  for  three 
different  filament  currents  as  noted  on  the  curve  sheet.  The  tube  from 
which  these  curves  were  obtained  is  shown  in  Fig.  8;  the  plate  is  a  cylinder 
about  .5  cm.  by  1.5  cm.  and  the  filament  is  a  helix  inside  this  cylindrical 
plate. 

Curve  1,  Fig.  7,  shows  the  variation  of  plate  current  for  a  filament  cur- 


Regulator  tube 

FIG.  6. — Use  of  a  two-electrode  tube  as  a  voltage 
regulator  for  a  variable  speed  generator. 


374 


VACUUM   TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


rent  of  1.15  amperes;   it  is  evident  that  as  the  plate  voltage  is  increased 
from  zero  the  plate  current  rises  more  rapidly  than  the  first  power  of  the 


Two  ele 


oele 

rJe  1 


trod 


acu 


1.15  ampre 


1.40 


10 


20  30 

Plate  volts 


40 


50 


10 


6     §. 

S 

4    ™ 

S 


20 


8    1 


FIG.  7. — Variation  of  plate  current  with  plate  voltage  (for  various  filament  currents) 

in  a  small  kenotron. 

voltage  until  about  10  volts  is  impressed;    for  higher  voltage  a  smaller 
increase  in  plate  current  is  obtained  and  above  30  volts  no  further  increase 


CHARACTERISTICS  OF  TWO-ELECTRODE  TUBES 


375 


in  plate  current  is  obtained,  even  if  the  plate  voltage  is  increased  to  300 
volts.  It  is  evident  that  a  plate  voltage  of  30  is  sufficiently  high  to  attract 
to  the  plate  all  the  electrons  which  the  filament  emits,  at  the  temperature 
reached  with  a  filament  current,  //,  of  1.15  amperes.  This  value  of  plate 
current,  which  is  limited  only  by  the  emitting  power  of  the  filament,  is 
called  saturation  current  of  the  tube. 

Saturation  current  evidently  will  be  determined  in  magnitude  by  the 
temperature  and  area  of  the  filament  surface;  also  for  higher  filament 
temperatures  (higher 
emission)  it  will  require 
higher  plate  voltage  to 
obtain  saturation  cur- 
rent; thus  when  //  is 
raised  to  1.25  amperes 
saturation  current  is 
increased  from  5  milli- 
amperes,  its  value  for 
//=1.15  amperes,  to 
about  IG.Smilliamperes, 
and  whereas  in  the  first 
case  30  volts  on  the 
plate  was  sufficient  to 
obtain  saturation  cur- 
rent, in  the  second  case 
even  50  volts  was  "not 
quite  sufficient  to  reach 
saturation. 

When  //  was  in- 
creased to  1.40  amperes, 
the  emission  was  so 

great  that  a  plate  voltage  of  50  was  not  nearly  enough  to  obtain 
saturation  current  and  the  value  of  saturation  current  is  going 
to  be  very  high,  judging  from  the  shape  of  the  curve.  Its  value 
was  actually  determined  in  another  test  and  found  to  be  140  milli- 
amperes. 

Considering  curve  3  of  Fig.  7,  it  is  apparent  that  for  any  plate  voltage 
shown  on  the  curve  sheet,  the  number  of  electrons  arriving  at  the  plate 
is  only  a  small  fraction  of  the  number  emitted  by  the  hot  filament;  e.g., 
with  a  plate  potential  of  20  volts  the  current  to  the  plate  was  only  10.8 
milliamperes,  whereas  the  total  emission  of  electrons  from  the  filament 
is  sufficient  to  give  a  plate  current  of  140  milliamperes.  It  is  therefore 
evident  that  to  obtain  at  the  plate  all  the  electrons  emitted  from  the  fila- 
ment a  certain  minimum  voltage  must  be  impressed  on  the  plate.  The 


FIG.  8. — Showing  the  kenotron  from  which  the  curves  of 
Fig.  7  were  obtained. 


376 


VACUUM  TUBES  AND  THEIR  OPERATION 


.  VI 


0& 
00 

o 


reason  for  this  is  given  by  an  analysis  of  the  electron  distribution  between 
the  hot  filament  and  cold  plate. 

Space  Charge. — In  Fig.  9  is  shown  in  very  elemen- 
tary fashion  the  distribution  of  electrons  between  the 
plate  and  filament;  we  will  consider  the  electric  forces 
acting  on  two  of  the  electrons  a  and  b.  Electron  a  is 
urged  to  the  plate  by  two  forces,  the  attraction  from 
the  plate  and  the  repulsion  from  all  the  electrons  between 
it  and  the  filament;  it  will  undoubtedly  go  to  the  plate. 
But  electron  6,  although  attracted  by  the  plate,  is  re- 

-p       Q  El  m       pelled  by  all  the  electrons  between  the  plate  and  itself; 

tary  representa-  whether  it  will  move  toward  the  plate  or  re-enter  the 
tion  of  the  distri-  filament  depends  upon  the  relation  between  these  two 
bution  of  elec-  forces.  It  is  evident  that  close  to  the  surface  of  the 
trons  between  filament  the  effect  of  all  the  electrons  in  the  space  be- 
the  not  filament  .  /,-,,-  ^i 

d     Id    1  te    f  ^ween  ^ne  filament  and  the  plate  (constituting  the  space 

a  kenotron.  charge)  will  practically  neutralize  any  effect  of  the  plate, 

unless  the  plate  voltage  is  high  enough  to  give  a  force  of 
attraction  greater  than  the  repulsive  force  exerted  by  the  space  charge. 

There  is  another  way  of  looking  at  the  problem;  to  bring  the  plate  to 
a  certain  potential  with  respect  to  the  filament  re- 
quires a  certain  quantity  of  electricity,  determined 
by  the  electrostatic  capacity  of  the  condenser 
formed  by  the  plate  and  filament.  Suppose  this 
quantity  of  "  positive  "  electricity  is  q,  there  will 
be  then  4-n-g  lines  of  electrostatic  force  leaving 
the  plate,  in  the  direction  of  the  filament.  These 
lines  of  force  must  end  on  q  charges  of  negative 
electricity;  but  if  the  space  charge  is  sufficiently 
large  to  furnish  the  requisite  q  the  lines  of  force 
from  the  plate  never  penetrate  to  the  fila- 
ment. 

A  .   ,  ,.  .     .  i      •      T^      -in     FIG.  10. — If    there    are 

An  attempt  to  picture  this  is  made  in  Fig.  10;  sufficient  electrons  be- 
for  the  picture  as  drawn  electron  a  experiences  no 
force  at  all  from  the  plate,  and  so  does  just  the 
same  as  it  would  if  the  plate  were  not  there,  i.e.,  goes 
back  into  the  filament.  But  if  the  plate  is  brought 
to  a  higher  positive  potential,  by  putting  more 
charge  on  it,  more  lines  of  force  will  emanate  from 
the  plate  and  so  some  may  end  on  electron  a  and 
so  attract  it  to  the  plate.  It  must  be  remembered 
that  the  above  picture  of  what  happens  is  very 
crude  and  artificial;  the  lines  of  force  really  have  no  entity  and  a  is 


tween  the  plate  and 
filament,  the  lines  of 
force  from  the  plate 
do  not  penetrate  as 
far  as  the  filament, 
thus  leaving  some 
electrons  near  the  fila- 
ment free  from  attrac- 
tion to  the  plate. 


EFFECT  OF  SPACE   CHARGE  377 

attracted,  to  some  extent,  by  the  plate  for  the  condition  shown  in  Fig.  10, 
but  the  attraction  is  negligibly  small. 

It  has  been  shown  by  Child  1  that  when  the  emission  of  the  electrons 
from  the  filament  is  much  greater  than  that  required  by  the  plate  current, 
the  plate  current  may  be  expected  to  vary  according  to  the  relation 

3/2 


in  which 

E  =  potential  of  plate  with  respect  to  filament; 
x  =  distance  between  filament  and  plate. 

When  E  is  measured  in  volts  and  x  in  centimeters  this  becomes, 

E3/2 
i  =  2.33XlO~6  —5-  amperes  per  sq.  cm.  of  plate.        .     .     (3) 

•*/ 

If  the  plate  is  cylindrical  in  form  with  the  hot  filament  placed  in  its 
axis  this  relation  becomes, 


i  =  14.65  X  10~6  X  —  -  amperes  per  cm.  length  of  cylinder,     .     (4) 


where  r  =  internal  radius  of  cylinder. 

The  diameter  of  the  filament  is  supposed  small  compared  to  the 
diameter  of  the  cylinder  in  getting  this  formula. 

If  we  have  an  equation  in  the  form  x  =  ya  we  have  also  log  x  =  a  log  y, 
so  that  if  the  data  for  the  curve  x  =  ya  are  plotted  on  logarithmic  coordinate 
paper  the  curve  should  become  a  straight  line,  the  slope  of  which  gives  the 
value  of  the  exponent  a.  Curve  3  of  Fig.  7  was  transposed  to  logarithmic 
paper  and  is  shown  in  Fig.  11  ;  it  is  seen  that  the  exponent  itself  is  variable, 
having  a  value  about  2  for  low  plate  voltages  and  rapidly  decreasing  for 
the  higher  values. 

It  could  not  be  expected  that  the  experimental  results  would  agree 
with  theory,  because  the  voltage  between  the  plate  and  filament  is  different 
in  different  parts  of  the  filament. 

This  point  must  be  borne  in  mind  in  interpreting  all  experimental  results 
on  vacuum  tubes;  practically  all  theoretical  conclusions  are  reached  from 
the  premise  of  uniform  potential  gradient  between  the  plate  and  all 
parts  of  the  surface  emitting  the  electrons.  For  the  lower  plate  voltages 
this  assumption  is  not  even  approximately  true.  The  tube  used  in  getting 
the  results  shown  in  Fig.  7  had  an  IR  drop  in  the  filament  of  6  volts  so 
that  the  potential  relations  in  the  tube  may  be  about  as  shown  in  Fig.  12. 
The  voltage  difference  is  20  at  the  negative  end  of  the  filament  and  only 

1  Physical  Review,  Vol.  32,  p.  498. 


378 


VACUUM   TUBES  AND   THEIR  OPERATION 


[CHAP.  VI 


14  at  the  positive  end,  having  values  between  14  and  20  at  the  intermedi- 
ate points. 

For  such  tubes  we  cannot  expect  to  get  theoretically  correct  results 
for  the  performance  under  any  conditions;  especially  when  the  character- 
istic varies  with  the  plate  voltage  to  a  power  higher  than  the  first  (as  the 
3/2  or  square)  the  departure  of  experiment  from  theory  must  be  expected. 


Plate  current 


rp 


two  Electrode 


ube 


Dot 


Una  y 


2x 


I  235  10  20  30        40      50    60  • 

Plate  volts 

FIG.  11. — Curve  3  of  Fig.  7  transposed  to  logarithmic  coordinates. 


The  author  built  a  tube  as  shown  in  Fig.  13  in  which  the  spiral  tungsten 
filament  A  used  for  heating  was  entirely  enclosed  in  a  tungsten  thimble 
B  •  this  thimble  constituted  the  hot  surface  from  which  the  electrons  were 
emitted.  Such  a  construction  gives  a  uniform  potential  gradient  between 
the  emitting  surface  B  and  the  cylindrical  plate  C  and  so  permits  experi- 
mentation under  the  conditions  assumed  in  theory.  With  this  construc- 
tion it  is  not  possible  to  get  the  tungsten  thimble  as  hot  as  the  filament 


EFFECT  OF  POTENTIAL  DROP  ALONG  FILAMENT 


379 


14  volts 


•17  volts 


20  volts 


I 
20  volts 


different  parts  of  the  filament; 
the  drop  at  one  end  of  the 
filament  is  14  volts  and  at 
the  other  end  is  20  volts. 


and  so  the  emission  is  rather  low,  unless  an 
oxide  coating  is  used  on  the  thimble.  Such 
a  construction  permits  the  use  of  a  high- 
voltage  filament  and,  a  much  more  impor- 
tant point,  the  electron  current  from  the  hot 
surface  is  not  directly  limited  by  the  carrying 
capacity  of  the  filament.  As  will  be  explained 
later  this  feature  becomes  important  in 
high-power  tubes ;  in  these  tubes  the  electron 
current  to  the  plate  maybe  as  high  as  12  to 
15  per  cent  of  the  filament  current,  so  that 
the  filament  current  is  12  to  15  per  cent  greater 
at  one  end  of  the  filament  than  it  is  at  the  other 
end. 

It  is  shown  in  the  next  paragraph  that 

a  tungsten   filament   does  not   give  appreci-  „ 

FIG.  12. — Variation  of  potential 

able  emission  until  it  is  very  hot,  so  that  we      drop  between  the  plate   and 
may  have  conditions  as  shown  in  Fig.  14 ;  the 
arrows  indicate  the  direction  of  electron  flow. 
With  a  plate  current  of  0.5  ampere  the  tube 
in  question  has  a  current  of  3.3  amperes  at 

one  end  and  3.8  amperes  at  the  other 
end,  as  indicated  in  the  diagram.  End 
B  of  the  filament  is  at  a  much  lower 
temperature  than  end  A ,  and  is  contrib- 
uting but  little  of  the  plate  current,  as 
the  emission  is  too  low.  End  A,  on  the 
other  hand,  is  furnishing  most  of  the 
plate  current  and  is  also  being  operated 
at  much  too  high  a  temperature.  With 
a  tube  as  shown  in  Fig.  13,  the  filament 
proper  suffers  no  loss  of  electrons,  so  has 
the  same  current  throughout  its  length. 
Variation  of  Emission  with  Filament 
Current. — Curves  Showing  Space  Charge 
Effects. — The  variation  of  emission  with 
filament  temperature  is  indicated  in 
Eq.  (1),  but  the  experimenter  generally 
has  no  means  of  measuring  the  tem- 
-Showing  one  scheme  for  get-  perature  of  the  filament;  the  curves 
ting  a  umpotential  surface  emitting  _,.  .  . 

electrons;  the  electrons  come  off  from  S1Ven  m  Fl^  15  show  how  the  emission 
the  thimble  B,  which  is  heated  by  varies  with  filament  current;  in  these 
the  filament  A.  curves  is  also  shown  the  effect  of  space 


Plate 


nipotential 
emitting  surface 


ttecy 


380 


VACUUM  TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


B 
,3.3 


3.4 


3.5 


charge  limiting  the  plate  current.  It  is  evident  that  the  filament  used 
in  this  tube  gives  practically  no  emission  with  currents  less  than  1.0 
ampere.  With  a  plate  voltage  of  100  the  plate  current  rose  rapidly  with 
increase  in  filament  current  reaching  135  milliamperes  at  a  filament 
current  of  1.40  amperes. 

When  the  plate  voltage  was  dropped  to  50  and  the  same  variation  of 
filament  current  carried  out  the  plate  current  reached  a  value  of  only  48 
milliamperes  at  7/=1.40  amperes.  With  plate  voltages  of  20  and  5  the 

maximum  plate  currents  were  10.6  milli- 
amperes and  1  milliampere  respectively. 
Now  with  If=  1.40  the  emission  is  135 
milliamperes  as  shown  in  curve  1;  with 
the  plate  at  a  positive  potential  of  5 
volts  (with  respect  to  negative  end  of 
filament)  only  1  milliampere  was  ob- 
piate  tained,  that  is,  only  1/135  of  the  elec- 
trons emitted  by  the  filament  reached 
the  plate,  the  rest  re-entering  this  fila- 
ment due  to  the  space  charge  overcoming 
the  comparatively  weak  field  from  the  plate. 
Speaking  in  terms  of  the  idea  de- 
picted in  Fig.  10  we  can  say  that  the 
lines  of  force  from  the  plate  penetrated 
but  a  short  way  into  the  electron  atmos- 
1+  o.5\mpej»  phere;  the  great  mass  of  the  emitted 
FIG.  14.— The  emission  of  electrons  electrons  which,  it  must  be  remembered, 
from  various  parts  of  the  same  fila-  stay  very  close  to  the  filament,  never 
ment  differs  very  much;  because  feel  the  tractive  effect  of  the  positive 
of  the  current  to  the  plate,  the  plate>  Thoge  few  having  exceptionally 
filament  current  (hence  filament  ,.  ,  ,  -.  .,  ,  •*  ,1  . 

,   high    outward    velocity    (due    to    their 
temperature)   is    much  greater  at 

one  end  of  the  filament  than  at  velocity   of    emission    and    suitable    col- 
the  other.  lisions   with  the  other  electrons  in  the 

electron    atmosphere)    reach    the    outer 
regions  of  the  atmosphere  and  so  get  attracted  to  the  plate. 

Even  for  the  lower  values  of  filament  current  (Fig.  15)  the  four  values 
of  plate  voltage  do  not  give  the  same  plate  current  as  might  be  expected. 
This  is  due  to  the  fact  that  the  IR  drop  in  the  filament  is  appreciable; 
in  the  special  tube  pictured  in  Fig.  13  all  curves  coincide  in  the  lower  parts. 
In  comparing  the  curves  of  Fig.  15  with  those  of  Fig.  7  it  is  to  be 
noticed  that  although  they  have  the  same  general  shape  they  have  entirely 
different  meanings.  In  Fig.  7  the  flat  parts  of  the  curves  indicate  that 
saturation  current  has  been  obtained  and  in  the  lower  curved  portions 
the  space  charge  is  limiting  the  current;  in  Fig.  15  the  lower  curved  por- 


3.8  amperes 


EFFECT  OF  FILAMENT  TEMPERATURE  ON  ELECTRON  EMISSION      381 


tions  indicate  that  saturation  current  is  flow- 
ing and  the  upper  flat  parts  indicate  that 
space  charge  is  limiting  the  plate  current. 

The  Three-electrode  Tube.1 — The  three- 
electrode  tube  differs  from  the  two-electrode 
tube  just  analyzed  in  that  a  third  electrode 
(called  the  grid,  because  of  its  ordinary  form) 
is  employed  to  control  the  plate  current.  In 
its  normal  form  the  grid  is  a  metal  mesh  of 
some  kind  interposed  between  the  plate  and 
filament;  the  electrons  passing  from  the  fila- 
ment to  the  plate  have  to  go  through  the 
holes  in  the  grid  mesh  and  their  passage  to 
the  plate  is  controlled  to  any  desired  extent 
by  the  potential  of  the  grid  with  respect  to 
the  filament.  In  this  form  of  tube  therefore 
the  plate  current  is  controlled  by  three  factors, 
the  filament  current,  the  grid  potential  and 
the  plate  potential. 

The  control  electrode,  or  grid,  in  the  ordi- 
nary form  of  tube  as  invented  by  Deforest,  is 
inside  the  tube,  directly  in  the  path  of  the 
electrons  traveling  from  filament  to  plate.  It 
is  possible,  however,  to  use  a  control  electrode 
outside  the  tube,  although  it  seems  as  though 
this  kind  of  control  offers  more  difficulties 

1  Eccles  has  suggested  the  name  "  triode  "  for  the 
three-electrode  tube  functioning  by  grid  control  of  an 
electron  stream. 


70 


50' 


PLATE 


CURRENT 


VS  FILAMENT  CURRENT 


Cur 


PI 


ite 


volt 


50 


100 


Two 


lectrode  tube 


10 


6     8   0.9    2     4     6     8    1.0    2     4      6     8    1.1    2     4     6     8   1.2    2     4      6     8    1.3    2     4      6 

Elament  current 

FIG.  15. — Variation  of  plate  current  in  a  kenotron  as  filament  current  is  varied;    for 
any  one  curve  the  plate  voltage  was  held  constant. 


382 


VACUUM   TUBES  AND   THEIR   OPERATION 


[CHAP.  VI 


than  the  internal  grid.  In  one  type  of  outside  grid  tube  tried  by  the 
author  the  control  worked  for  a  few  seconds  and  then  the  accumulation 
of  electrons  on  the  inside  walls  of  the  tube  made  it  stop  functioning. 
The  inner  walls  of  the  glass  must  be  made  partially  conducting  to 
prevent  this  accumulation  of  charge. 

The  inside  control  electrode  need  not  be  placed  between  the  filament 
and  plate;  it  will  work  to  some  extent  even  if  it  is  on  the  side  of  the  fila- 
ment opposite  to  that  on  which  the  plate  is  situated.  Its  action  in  such 

a  tube  is  not  as  efficient  in  controlling  the 
plate  current  as  in  the  normal  placement; 
in  the  analyses  to  follow  it  will  be  sup- 
posed that  the  grid  is  inside  the  tube  be- 
tween the  filament  and  plate  and  the 
curves  given  to  illustrate  the  text  will  be 
records  obtained  from  such  tubes. 

Potential  Distribution  in  the  Three- 
electrode  Tube. — The  three-electrode  tube 
functions  because  of  the  effect  of  the  grid 
on  the  potential  distribution  between  the 
filament  and  plate;  it  is  therefore  neces- 
sary to  have  a  clear  idea  of  this  potential. 
In  Fig.  16  is  shown  by  the  dotted  line 
(a)  this  potential  distribution  between 
two  metal  plates,  one  marked  F  to  repre- 
sent the  filament,  the  other  marked  P  to 
represent  the  plate. 


FIG.  16. — Two  metal  plates,  one  Et 


The  filament  is  sup- 


volts  higher  potential  than  the  Posed  at  zero  potential  and  the  plate  at 
other,  have  a  uniform  potential  positive  potential  Ep.  With  a  uniform 
gradient  between  them,  the  po-  field  distribution  as  shown  in  the  upper 
tential  being  about  as  shown  by  part  of  the  figure  the  potential  between 
dotted  line  a;  if  plate  discovered  }  d  ^  off  uniforml 

with  an  electron  atmosphere  the   r 

potential  is  changed  to  the  form  In  the  actual  tube  such  a  uniform  po- 
shown  by  line  6.  tential  gradient  does  not  obtain ;  owing 

to  the  comparatively  small  surface  of  the 

filament  the  potential  falls  more  rapidly  near  the   filament  than  near 
the  plate. 

If  we  now  suppose  an  electron  atmosphere  to  cover  the  surface  of  F 
the  potential  distribution  is  changed  to  some  such  form  as  indicated  by 
the  full  line  (b)  in  Fig.  16.  The  potential  gradient  becomes  much 
lower  in  the  vicinity  of  F  because  most  of  the  field  of  P  ends  on  electrons 
in  the  vicinity  of  F  and  so  never  reaches  F;  in  fact  if  the  emission  is  much 
greater  than  the  plate  current  (practically  always  the  case  with  three- 
electrode  tubes  in  normal  operation)  the  potential  gradient  very  close 


THE  THREE-ELECTRODE   TUBE 


383 


to  the  surface  of  Ft  due  to  the  positively  charged  plate  P  is  essentially 
zero.  In  Fig.  17  is  represented  a  filament  F,  plate  P,  and  grid  G  (shown 
in  cross-section  by  the  small  circles)  in  the  lower  part  of  the  figure  is  shown 
by  the  line  marked  (a)  the  potential  distribution  between  P  and  F  with- 
out any  action  from  G,  the  curved  form  of  this  line  is  caused  by  the  "electron 
atmosphere  around  F.  It  must  be  remembered  that  most  of  the  electrons 
emitted  are  very  close  to  F  and  re-enter  F  without  having  moved  very 
far  toward  G.  The  potential  gradient  in  which  the  great  majority  of 
the  electrons  lie  (close  to  F)  is  very 
small,  hence  they  experience  but 
little  tractive  effort  from  P. 

If  now  G  is  made  positive  the 
potential  distribution  is  changed  to 
the  line  marked  b  in  Fig.  17.  The 
potential  gradient  between  G  and 
F  has  been  much  increased  so  that 
many  of  the  electrons  which  pre- 
viously fell  back  into  the  filament 
will  now  move  toward  G.  Refer- 
ring to  the  upper  part  of  Fig.  17, 
electron  a,  which,  without  positive 
grid,  would  have  fallen  back  into 
the  filament,  now  moves  toward  G, 
and  so  is  found  in  some  such  posi- 
tion as  a'.  In  this  position  it  ex- 
periences two  attractions,  one  from 
G  and  one  from  P.  Because  of  the 
relatively  higher 
larger  surface  of 
electrons  which  arrive  at  this  posi- 
tion will  move  to  the  plate,  instead 
of  going  to  G  as  might  be  supposed. 
There  may  arrive  at  position  a',  however,  an  electron  which  has 
some  velocity  in  the  direction  of  G;  the  result  of  this  velocity 
and  the  two  attractions  from  G  and  P  may  result  in  its  going  to  G 
instead  of  P.  Other  electrons  moving  from  F  toward  G  may  find 
themselves  in  such  a  position  (with  respect  to  the  grid  wires)  as 
shown  by  b';  these  electrons  will  almost  surely  go  to  the  grid  instead 
of  to  the  plate. 

We  may  therefore  conclude  that  the  interposition  of  a  positively 
charged  grid  between  the  filament  and  plate  will  partially  neutralize  the 
effect  of  the  space  charge;  more  of  the  electrons  emitted  from  the  filament 
will  move  away  from  it,  some  of  them  going  to  the  grid  and  some  going 


potential     and    FIG.  17. — In  a  three-electrode  tube  the  po- 
P    most   of   the        tential  distribution  between  the  filament 
arid  plate  may  be  as  shown  by  either  b,  a, 
or  c,  according  to  the  potential  of  the 
grid. 


384  VACUUM   TUBES  AND   THEIR  OPERATION  [CHAP.  VI 

to  the  plate.  A  positive  grid  then  increases  the  plate  current,  plate  poten- 
tial remaining  fixed. 

A  negatively  charged  grid  will  result  in  a  potential  distribution  some- 
what as  shown  by  curve  c  of  Fig.  17;  if  the  grid  is  as  negative  as  shown 
by  the  curve  the  plate  current  will  be  reduced  to  practically  zero,  because 
none  of  the  electrons  (except  a  very  few  which  are  emitted  with  exception- 
ally high  velocity)  can  move  against  the  negative  potential  gradient 
between  F  and  G.  It  must  be  noticed  of  course  that  the  potential  curve 
on  such  a  line  as  indicated  by  M  —N  (Fig.  17)  will  be  different  from  that 
on  such  a  line  as  Mr  —TV';  the  grid  potential  will  not  be  so  effective  on 
the  line  Mf  —N'  as  on  a  line  lying  closer  to  one  of  the  grid  wires. 

It  will  be  appreciated  at  once  that  this  effect  of  the  grid  in  controlling 
the  flow  of  electrons  to  the  plate  will  depend  on  various  features  of  con- 
struction, of  the  tube.1  The  grid  will  exercise  the  most  control  when  its 
wires  are  very  fine  and  close  together,  and  when  it  completely  surrounds 
the  filament.  Unless  the  grid  is  considerably  larger  (in  length  and  breadth) 
than  the  space  occupied  by  the  filament  many  of  the  electrons  will  go  from 
the  filament  around  the  grid  and  thus  arrive  at  the  plate  without  having 
been  subjected  completely  to  the  controlling  action  of  the  grid. 

This  idea  is  illustrated  in  Fig.  17.A;  the  construction  shown  in  a  will 
permit  the  grid  to  exert  a  much  greater  control  over  the  electron  stream 
than  will  the  construction  shown  in  6. 

1  The  question  of  the  shielding  action  of  a  grid  is  taken  up  in  Maxwell's  "  Electricity 
and  Magnetism,"  Vol.  1;  the  case  worked  out  is  for  a  flat  plate  and  flat  filament,  of 
infinite  extent.  In  an  article  in  Proc.  I.R.E.,  Vol.  8,  No.l,  J.  M.  Miller  shows  how 
closely  Maxwell's  theory  applies  to  the  construction  of  an  ordinary  tube. 

In  an  article  published  in  Vol.  15,  No.  4,  of  The  Physical  Review,  R.  W.  King  shows 
how  the  value  of  the  controlling  effect  of  the  grid  depends  upon  the  parameters  of  the 
tube.  The  theoretical  voltage  amplification  factor  of  the  tube  /J.Q  (see  p.  417  for  sig- 
nificance of  this  constant)  is  shown  to  be  expressible  as 

2-jran 


eTT — 

2-rrrn 


in  which 


a  =  distance  between  grid  and  plate; 
n=  number  of  grid  wires  per  cm.; 
r=  radius  of  the  grid  wire. 

In  the  derivation  of  the  above  formula  the  grid,  hot  filament  surface,  and  plate  have  all 
been  assumed  as  infinite  parallel  planes;  although  actual  tubes  depart  very  far  from 
this  requirement  experimentally  determined  values  of  no  for  several  tubes  of  widely 
different  construction  check  with  the  calculated  value  quite  well. 

The  interesting  point  in  both  Miller's  and  King's  analyses  is  that  the  distance  between 
the  grid  and  filament  plays  no  part  in  determining  the  value  of  ^o;  the  closenes?  of  thf 
grid  to  the  plate  is  apparently  the  controlling  factor. 


HYDRAULIC   MODEL  OF  THREE-ELECTRODE  TUBE 


385 


9          o 

V 


It  is  possible  to  build  a  hydraulic  model  of  a  three-electrode  tube  which 
illustrates  very  well  the  general  ideas  involved  in  the  tube  action.  A 
jar  (Fig.  18)  (such  as  glass 
storage-battery  container)  has 
placed  in  the  lower  part  a 
pipe  A,  closed  at  its  two  ends, 
which  is  full  of  small  holes 
on  its  lower  side  and  is  con- 
nected to  an  air  supply  of  very 
low  pressure.  A  rubber  sheet 
(such  as  the  rubber  used  by 
dentists)  is  fastened  to  the 
side  of  this  pipe  A  and  also  to 
a  rod  C  in  the  upper  part  of 
the  jar,  horizontal  and  parallel  FlG-  17A.— The  construction  shown  in  a  will  give 

to  A.     To   make   the  model      ^ef  !d  G  mu\h  ^ater  cont*  «*™  than 

that  shown  in  o;   the  more  completely  the  grid 

simple    only   one-half    of    the       encloses  the  filament  and  the  finer  its  structure 
three-electrode  tube  is  repre-       the  greater  will  be  its  controlling  action, 
sented;  a  metal  sheet  E  fast- 
ened to  A  makes  all  the  air  bubbles  which  escape  move  to  the  left  (in  Fig. 
18)  and  so  run  up  on  the  under  side  of  the  rubber  sheet  and  escape  past 
C.      This  stream  of  bubbles  represents  the  electron  stream  from  a  fila- 


FIG.  18. — Hydraulic  model  of  the  three-electrode  tube. 


386 


VACUUM   TUBES   AND   THEIR  OPERATION 


[CHAP.  VI 


nient,  A  being  the   filament  and   C  the    plate,  (.'  being    at    higher   level 

than  A,  as  must 
be  the  potential 
of  the  plate  with 
respect  to  that 
of  the  filament. 
A  stick  D  has 
several  parallel 
wooden  pinsf  ast- 
ened  to  it  and 
the  lower  ends 
of  these  pins  are 
fastened  (by 
tacks)  to  the  rub- 
ber sheet  close 
to  pipe  A,  as 
shown.  When 
D  is  moved  up 
and  down,  the 

FIG.  19.— Hydraulic  model  of  the  three-electrode  tube.  lower  ends  of  its 

pins  lift  up  and 

down  those  parts  of  the  rubber  sheets  to  which  they  are  attached ;  in 
Fig.  19  is  shown  a  sketch  of  the  rubber  sheet  with  the  bar  D  lifted,  and 
in  Fig.  20  is  shown 
the  form  of  the 
rubber  sheet  when 
the  bar  D  is  de- 
pressed. If  the 
pressure  of  the  air 
in  the  pipe  A  is 
properly  adjusted 
the  flow  of  air 
bubbles  up  the  un- 
der side  of  the  rub- 
ber sheet  resembles 
(more  closely  than 
any  analogy  the 
author  has  seen) 
the  flow  of  elec- 
trons in  a  three- 
electrode  tube. 


FIG.  20. — Hydraulic  model  of  the  three-electrode  tube. 


The  action  of  the  bar  D  with  its  attached  pins,  producing  small  hills 
and  valleys  in  the  rubber  sheet,  illustrates  well  the  action  of  the  grid. 


USE  OF  THE   THREE-ELECTRODE   TUBE  387 

The  depression  of  the  pins,  making  it  more  difficult  for  the  air  to  pass  up 
along  the  sheet,  illustrates  a  negative  grid,  and  when  the  pins  are  lifted  up 
the  increased  flow  of  air  corresponds  to  the  increased  plate  current  with 
positive  grid.1 

The  effect  of  the  space  charge  is  not  simulated  very  well  by  the  model; 
the  accumulation  of  air  between  the  "  grid  "  (row  of  pins,  d,  d,  d)  acts  to 
prevent  other  bubbles  of  air  coming  through  the  small  holes  in  the  "  fila- 
ment "  (pipe  A)  but  this  action  is  not  strictly  analogous  to  the  mutual 
repulsion  of  the  electrons  in  the  actual  space  charge  effect. 

Fields  of  Use  of  Three-electrode  Tube. — Detector,  Amplifier,  Gener- 
ator or  Converter. — The  three-electrode  tube  was  first  used  as  a  detector 
of  radio  signals  from  spark  stations;  it  was  much  more  sensitive  than  its 
competitors,  the  magnetic  detector,  Fleming  valve,  etc.,  and  so  rapidly 
displaced  these  as  a  detector.  In  its  original  form  as  manufactured  by 
Deforest  a  potential  of  about  30  volts  was  used  on  the  plate;  the  normal 
plate  current  was  a  few  hundred  microamperes.  Although  these  original 
tubes  were  rather  erratic  in  their  behavior,  and  not  uniform  in  their 
characteristics  (one  tube  not  being  like  another)  by  careful  adjustment 
of  filament  current  and  plate  voltage,  they  were  nearly  as  good  detectors 
as  the  later  types. 

As  the  grid  potential  of  a  three-electrode  tube  controls  the  plate  cur- 
rent (the  power  for  which  is  supplied  by  a  local  battery)  it  is  evidently 
applicable  as  a  relay,  the  signal  voltage  controlling  the  delivery  from  the 
local  power  supply.  When  properly  adjusted  the  grid  circuit  takes  an 
extremely  small  power  to  operate,  so  that  compared  to  the  amount  of 
power  used  in  the  grid  circuit  the  amount  controlled  in  the  plate  circuit 
may  be  thousands  of  times  as  great. 

If  the  grid  circuit  is  adjusted  to  take  no  power  itself  the  power  ampli- 
fication is  infinite;  it  must  be  remembered,  however,  that  to  operate  the 
grid  circuit  certain  coils,  condensers,  and  resistances  are  required;  taking 
the  losses  in  these  necessary  associated  circuits  into  account  the  power 
amplification  is  not  infinite,  but  it  is  very  large  even  then.  Thus  a  certain 
tube  used  in  telephone  circuits  as  an  amplifying  repeater  has  a  power 
amplification  of  about  one  thousand  times. 

If  an  alternating  potential  difference  is  impressed  on  the  grid  of  a  tube 
the  plate  current  periodically  increases  and  decreases.  This  pulsating  cur- 
rent in  the  plate  circuit  may  be  made  to  produce  fluctuations  in  the  grid 
potential  by  means  of  a  suitable  transformer,  the  primary  of  which  is  con- 
nected in  the  plate  circuit  and  the  secondary  connected  between  the  fila- 

1  By  having  the  pins,  d,  d,  etc.,  in  the  form  of  tubes  open  at  their  lower  ends  and 
having  corresponding  holes  in  the  rubber  sheet,  some  of  the  air  bubbles  will  run  up  these 
tubes  when  handle  D  is  lifted,  thus  imitating  the  action  of  the  positive  grid  attracting 
some  of  the  electrons,  causing  grid  current. 


388  VACUUM  TUBES  AND  THEIR  OPERATION  [CHAP.  VI 

ment  and  grid.  If  a  suitable  condenser  is  connected  across  either  the 
primary  or  secondary  winding  to  give  a  natural  period  to  the  circuit,  the 
fluctuations  in  the  plate  current  will  be  maintained  by  their  action  on 
the  grid  potential. 

With  this  arrangement  then  the  plate  current  fluctuates  between  cer- 
tain maximum  and  minimum  values,  the  voltage  of  the  grid  alternates, 
and  in  the  condenser  (no  matter  which  circuit  it  is  connected  with)  an 
alternating  current  flows.  The  device  thus  becomes  a  generator  of  alter- 
nating-current power;  it  might  perhaps  be  more  properly  called  a  con- 
verter for  changing  continuous-current  power  into  alternating-current 
power.  The  frequency  of  the  alternating  current  is  fixed  by  the  L  and 
C  of  the  oscillatory  circuit,  and  the  amount  of  power  available  depends 
on  the  average  value  of  the  plate  current  and  the  voltage  of  the  battery 
or  generator  supplying  the  current. 

Small-power  tubes,  using  a  plate  potential  of  300  volts  and  plate  cur- 
rent of  40  milliamperes,  giving  about  4  watts  of  high-frequency  power, 
were  used  extensively  by  the  armies  for  radio  signaling.  Some  of  the 
larger  power  tubes,  used  for  higher-power  sets,  can  generate  200  watts 
or  more  per  tube;  the  generator  furnishing  the  plate  current  impresses 
about  1500  volts  on  the  plate  and  the  electron  current  is  about  0.3  ampere. 

Various  Types  of  Tubes. — According  to  the  purposes  for  which  they 
are  to  be  used  several  different  types  of  tubes  have  been  evolved.  Tubes 
designed  for  detecting  high-frequency  currents  need  to  have  a  power  out- 
put of  only  a  very  small  fraction  of  a  watt;  they  are  generally  fitted  with 
small  filaments,  because  but  little  emission  is  required  and  the  voltage 
used  in  the  plate  circuit  is  low.  Typical  tubes  use  a  filament  current  of 
1.0  ampere  at  4  volts  and  use  a  plate  battery  of  20  volts.  Tubes  used  for 
amplifiers  are  more  generally  higher  plate  voltage,  perhaps  100  or  150  volts; 
the  size  of  filament  is  about  the  same  as  used  for  a  detector  tube.  Tubes 
used  for  generating  power  are  designed  for  higher  plate  voltage,  from 
300  to  2500  volts;  as  the  amount  of  power  available  depends  upon  the 
value  of  plate  current  and  this  in  turn  upon  the  emission,  the  filament  is 
much  larger  than  in  the  amplifier  and  detector  tubes.  A  4-watt  tube 
(output)  might  require  a  filament  current  of  1.5  amperes  at  10  volts;  a 
200- watt  tube  might  require  3.7  amperes  at  20  volts.  Later  a  tabulated 
list  of  ratings  for  various  tubes  will  be  given. 

The  grids  used  vary  from  a  very  fine  mesh  of  the  finest  tungsten  wire 
obtainable  (wound  40  per  cm.)  to  a  lattice  work  of  comparatively  coarse 
wire  spaced  about  3  per  cm.  The  grid  may  be  flat  or  cylindrical  according 
to  the  form  of  tube. 

The  plates  used  are  of  various  forms;  they  vary  from  a  short  zig-zag 
shaped  tungsten  wire  perhaps  5  cm.  long,  or  a  small  thimble  about  0.5 
cm.  in  diameter  and  0.5  cm.  long  to  two  heavy  plates  about  5  cm,  square. 


VARIOUS  FORMS  OF  THREE-ELECTRODE  TUBES  389 

The  material  used  for  the  grids  and  plates  is  generally  nickel  or  tungsten, 
or  molybdenum;  the  tubes  designed  for  generating  much  power  are  likely 
to  have  all  metal  parts,  filament,  grid,  and  plate  of  tungsten. 

In  Fig.  21  are  shown  some  of  the  more  common  tubes;  A  and  B  are 
power  tubes  of  50-  and  250- watt  ratings,  respectively;  C  and  D  ape  small- 
power  tubes  designed  for  an  alternating-current  output  of  about  4  watts, 
E,  F  and  G  serve  as  either  detectors  or  amplifiers;  H  is  a  Deforest  audion 
of  the  original  type,  I  is  a  cylindrical  tube  made  for  amateur  use;  J  is 
a  modern  Marconi  tube;  K  and  L  are  two  amplifying  bulbs,  the  latter 
having  extremely  fine  grid  and  very  small  plate  (a  nearly  invisible  zig- 
zag wire) ;  M  is  a  special  power  tube  with  grid  brought  out  at  tip  of  the 


FIG.  21. — Various  types  of  tubes  used  in  getting  the  experimental  data  given  in  this 

chapter. 

bulb.  The  former  tubes  are  all  of  American  manufacture;  at  N  is  shown 
an  English  power  tube,  at  0  a  special  French  amplifier  bulb  and  at  P  a 
small  English  detector  and  amplifier  tube.  At  Q  is  shown  a  special  type 
of  tube  called  a  dynatron,  explained  on  page  534. 

In  most  of  the  smaller  tubes  the  glass  bulb  is  fitted  with  a  brass  collar 
by  which  they  are  held  in  a  suitable  socket;  the  socket  is  equipped  with 
four  flexible  contacts  which  press  against  four  pins  projecting  from  the 
base  of  the  bulb.  These  four  pins  connect  to  the  filament,  grid,  and  plate. 

Limits  of  Operation  of  a  Tube. — There  are  in  general  two  limiting 
factors  in  the  use  of  a  vacuum  tube — overheating  and  consequent  collapse 
of  the 'parts  or  of  the  bulb  itself,  and  ionization  of  the  residual  gas  in 
the  tube.  It  is  impossible  to  completely  evacuate  a  tube  so  that  some 


390  VACUUM   TUBES  AND  THEIR  OPERATION  [CHAP.  VI 

gas  is  always  present;  if  too  high  a  plate  potential  is  impressed  or  too 
high  a  filament  current  (with  fairly  high  plate  voltage)  is  used  this  resid- 
ual gas  will  ionize  and  thereby  change  the  operating  characteristics  of 
the  tube  by  an  amount  depending  upon  the  amount  of  gas  present. 

With  a  tungsten  filament  tube  the  evacuation  process  is  carried  out 
more  thoroughly  than  v/ith  the  oxide  coated  filament  so  that  destructive 
ionization  is  not  likely.  The  limit  of  the  tungsten  tubes  (aside  from  the 
prescribed  limit  for  filament  current)  is  the  safe  heating  of  the  plate  and 
grid,  generally  the  plate,  because  the  grid  circuit  is  so  adjusted  that  the 
grid  takes  but  little  current.  This  heating  is  due  to  the  power,  used  in 
accelerating  the  electrons  as  they  move  from  the  filament  to  the  plate, 
being  given  up  when  the  electrons  are  stopped  by  hitting  the  plate;  the 
phenomenon  is  called  electron  bombardment.  The  amount  of  power  so 
used  on  the  plate  is  equal  to  the  product  of  the  plate  voltage  and  the  plate 
current;  if  this  product  varies  cyclically  (as  it  actually  does  when  the  tube 
is  being  used  for  power  converter),  its  average  value  must  be  taken  in 
calculating  the  amount  of  power  used  in  bombarding  the  plate.1 

The  safe  power  to  be  useof  in  bombarding  the  gird  is  much  less  than 
that  for  the  plate,  for  two  reasons;  the  surface  of  the  grid  is  generally 
much  smaller  than  that  of  the  plate,  and  the  possibility  of  heat  radiation 
from  the  grid  is  less  than  that  of  the  plate. 

The  large  tube  shown  at  B,  Fig.  21,  has  a  rating,  for  example,  of  250 
watts  plate  and  25  watts  grid.  Thus  a  plate  current  of  0.25  ampere 
(steady  value)  would  be  permissible  with  a  plate  voltage  of  1000  volts, 
and  with  this  amount  of  power  used  in  the  tube  the  plate  becomes  quite 
a  bright-red  color.  The  two  tubes  shown  at  C  and  D  have  a  safe  plate 
capacity  of  12  watts;  with  a  plate  voltage  of  300  (their  rated  value)  the 
average  plate  current  should  not  exceed  40  milliamperes. 

The  other  tubes  shown  at  E,  F,  G,  H  and  7,  etc.,  are  never  so  operated 
that  heating  is  the  limiting  factor;  they  are  designed  to  be  used  in  certain 
circuits,  and  if  the  filament  current  or  plate  voltage  are  far  from  their 
rated  values  it  is  likely  that  the  tubes  will  not  function  efficiently. 

Effect  of  Gas  in  a  Vacuum  Tube. — Ionization. — The  modern  vacuum 
tube  is  a  true  electron  relay;  it  functions  entirely  by  means  of  the  stream 
of  electrons  emitted  from  the  filament,  and  these  electrons  in  rnotion 
constitute  the  only  current  in  the  tube.  This  ideal  is  not  quite  realized 
by  any  vacuum  tube,  but  it  is  so  nearly  approached  that  whatever  other 
current  may  exist  is  so  small  as  to  make  its  effect  negligible  when  consider- 
ing the  action  of  the  tube. 

The  earlier  types  of  vacuum  tubes  (Fleming  valves  and  Deforest 
audions)  were  not  at  all  well  evacuated  in  the  light  of  modern  practice; 

1 A  bombardment  equivalent  to  10  watts  per  sq.  cm.  of  plate  will  bring  its  temperature 
to  about  1300°  C.;  such  a  temperature  gives  the  plates  a  fairly  bright  red  color. 


ACTION  OF  GAS  IN  A  VACUUM  TUBE  301 

there  was  a  deal  of  gas  left  in  the  bulb  at  the  completion  of  the  evacuation 
process  and  this  gas  made  the  tubes  very  erratic  and  undependable  in 
their  behavior.1  Not  only  would  various  bulbs,  supposedly  similar,  have 
very  different  characteristics,  but  any  one  bulb  would  not  act  consistently, 
and  many  tricks  had  to  be  employed  to  make  the  bulbs  perform"  to  the 
best  advantage. 

An  exact  study  of  the  effect  of  %as  in  a  vacuum  tube  cannot  be  given 
here;  only  those  points  which  bear  directly  on  the  operation  of  the  tube 
in  radio  practice  will  be  outlined.  The  student  is  referred  to  some  such 
book  as  Thomson's  "  Conduction  of  Electricity  through  Gases  "  for  a 
deeper  analysis  than  will  be  attempted  here. 

A  cold  electrode  in  a  vacuum  tube,  unless  subjected  to  considerable 
electron  bombardment,  will  not  give  off  electrons  in  appreciable  quan- 
tities; thus  in  a  two-electrode  tube  if  the  plate  is  made  negative  with 
respect  to  the  filament  no  current  will  flow,  because  if  the  plate  is  made 
negative  any  current  which  flows  from  plate  to  filament  must  be  caused 
by  electrons  leaving  the  cold  plate.  Experiment  demonstrates  the  truth 
of  this  statement ;  if  other  possible  carriers  of  current  are  eliminated  (such 
as  actual  leaks  inside  or  outside  the  tube,  or  gas  inside  the  tube)  the  amount 
of  current  which  will  flow  is  too  small  to  be  measured.  We  may  safely 
conclude  that  when  a  cold  electrode  (either  grid  or  plate)  of  a  tube  shows 
current  in  such  direction  as  to  indicate  electrons  flowing  from  it,  inside 
the  tube,  the  tube  has  in  it  gas  which  is  serving  as  a  conductor  of  current.2 
This  statement  neglects  the  possibility  of  secondary  emission  of  electrons 
due  to  excessive  bombardment  by  electrons  coming  from  the  filament; 
this  effect  will  be  treated  in  a  later  paragraph. 

Ordinarily  a  gas  is  a  good  insulator  and  will  not  carry  current,  but 
when  under  rather  low  pressure  it  may  be  made  to  carry  very  large  cur- 
rent if  by  some  means  it  becomes  ionized.  By  this  term  is  meant  the 
breaking  up  of  the  normal  gas  atom  into  two  parts,  a  free  electron  and 
positively  charged  nucleus;  this  breaking  up  of  a  gas  atom  corresponds 
to  the  "  break-down  "  of  any  ordinary  insulator  when  it  is  subjected  to 
too  high  a  potential  gradient. 

In  a  Geissler  tube  the  gas  becomes  ionized  (showing  the  well-known 
blue  glow)  only  when  rather  high  potentials  are  used,  generally  several 
thousand  volts.  Now  in  the  vacuum  tube  used  for  radio  such  high  voltage 

1  It  is  quite  evident,  however,  that  Fleming  appreciated  the  necessity  of  a  high 
vacuum  to  make  the  tubes  constant  in  behavior;  the  superiority  of  present  evacuation 
is  due  not  so  much  to  any  conception  of  its  importance,  perhaps,  as  to  the  better  pumps 
now  available. 

2  It  must  be  remembered  that  even  with  the  highest  vacuum  obtainable  there  is 
still  a  tremendous  number  of  gas  molecules  in  the  evacuated  space;   it  is  likely  that 
in  highest  vacuum  tubes  used  to-day  (10~8  mm.  of  mercury)  there  are  of  the  order  of 
iO8  gas  molecules  per  cubic  centimeter. 


392  VACUUM  TUBES  AND  THEIR  OPERATION  [CHAP.  VI 

is  practically  never  used;  ionization  of  the  gas  in  the  tube  may  occur  with 
voltages  as  low  as  thirty  or  forty.  This  is  due  to  the  fact  that  the  hot 
filament  furnishes  the  electrons  which  by  their  motion  (caused  by  the 
positive  plate  potential)  serve  to  start  the  ionization  of  the  gas  atoms. 
In  a  Geissler  tube  no  such  means  is  at  hand  for  starting  the  ionization, 
hence  the  comparatively  high  voltage  required  to  show  the  effect. 

The  role  played  by  the  electrons  emitted  from  the  filament  in  pro- 
ducing ionization  is  easily  shown  by  a  simple  test.  If  a  tube  which  is 
known  to  be  faulty  is  subjected  to  normal  plate  potential  with  cold  fila- 
ment, no  plate  current  will  flow  and  the  tube  will  show  no  signs  of  ioniza- 
tion. Now  if  the  filament  current  is  gradually  increased  emission  of 
electrons  will  commence  and  a  slight  plate  current  will  flow;  at  a  certain 
filament  temperature,  depending  upon  how  much  gas  there  is  in  the  tube, 
the  familiar  blue  haze  will  appear  in  the  bulb,  accompanied  generally  by 
a  very  large  increase  in  the  plate  current,  thus  showing  that  the  filament 
must  be  emitting  a  certain  minimum  number  of  electrons  before  appreci- 
able ionization  of  the  gas  occurs. 

If  but  a  small  amount  of  gas  is  present  the  pale  blue  glow  may  be  so 
weak  as  to  be  invisible,  but  the  presence  of  appreciable  quantity  of  gas 
is  generally  shown  by  erratic  changes  in  the  plate  current. 

Some  oxide-coated  power  tubes  show  a  bright  fluorescence  on  the 
plate  when  being  used,  generally  in  the  form  of  a  pattern  of  the  grid. 
It  is  easy  to  mistake  this  effect  for  ionization  because  of  the  blue  color 
from  the  fluorescing  plate;  if  the  plate  is  hidden  from  the  eye  (by  the  hand 
or  a  piece  of  cardboard)  it  will  be  seen  that  there  is  no  blue  glow  in  the 
space  inside  the  tube.  The  intensity  of  the  effect  of  fluorescence  depends 
upon  the  condition  of  the  surface  of  the  plate,  which  is  generally  covered 
with  more  or  less  oxide. 

Danger  to  a  Tube  from  Ionization. — When  a  tube  ionizes  the  con- 
sequences resulting  depend  upon  the  type  of  tube  being  used  and  upon 
how  quickly  the  condition  is  removed.  In  the  case  of  a  detecting  tube, 
or  amplifying  tube,  the  state  of  ionization  will  generally  stop  the  function- 
ing of  the  tube,  its  characteristics  being  entirely  different  when  the  tube 
is  filled  with  a  semi-conductor  (the  ionized  gas)  than  those  of  a  normal 
electron  tube.  If  either  the  plate  voltage  or  filament  current  is  reduced 
the  ionization  will  disappear  and  the  tube  may  operate  as  well  (or  possibly 
better)  than  it  did  before  ionizing. 

In  the  case  of  a  power  tube  the  situation  is  different;  unless  either 
the  filament  current  or  plate  potential  is  immediately  reduced  the  tube 
may  be  completely  spoiled.  Ionization  practically  never  occurs  in  a  tung- 
sten tube  because  of  the  high  degree  of  vacuum  ordinarily  used;  the  oxide 
filament  tube  is  much  more  likely  to  suffer  from  it.  In  these  tubes  there 
is  always  a  lot  of  gas  in  the  metal  parts  of  the  tube,  filament,  grid,  and 


METHOD  OF  EVACUATING  TUBES  393 

plate;  now  when  ionization  starts  the  electrons  of  the  ionized  gas  travel 
to  the  plate,  it  being  positive,  but  the  positive  nuclei  travel  to  the  filament 
and  subject  it  to  a  bombardment. 

This  bombardment  results  in  extra  heating  of  the  filament,  generally 
in  one  spot,  which  extra  heating  tends  to  aggravate  itself  and  bum  the 
filament  out  at  this  point.  The  hotter  the  filament  the  greater  the  electron 
emission,  and  also  gas  is  likely  to  be  emitted  from  the  filament  at  this 
hot  spot;  where  the  gas  and  electron  emission  both  increase  the  ionization 
increases,  increasing  the  bombardment  of  the  filament  at  this  spot,  and 
thus  by  the  cumulative  action  burning  it  out.  At  the  time  the  filament 
burns  out  it  releases  a  lot  of  gas  which,  becoming  ionized,  may  permit 
the  passage  of  such  a  large  current  from  the  plate  as  to  result  in  a  miniature 
"  explosion  "  inside  the  tube,  completely  wrecking  the  parts  and  break- 
ing the  bulb. 

When  a  power  bulb  with  oxide  filament  once  ionizes  it  is  practically 
valueless  l  until  re-exhausted;  the  ionization  itself  will  probably  result  in 
the  emission  of  extra  gas  from  the  bombarded  parts,  so  that  the  tube  has 
more  gas  in  it  after  ionization  than  before. 

Evacuation  of  a  Vacuum  Tube. — Because  of  the  deleterious  effects  of 
gas  the  electron  tube  must  be  very  carefully  freed  from  any  appreciable 
quantity  of  it.  With  modern  pumps  the  getting  out  of  the  gas  from  the 
space  inside  the  bulb  is  very  simple  and  rapid  but  this  is  not  sufficient. 
Metals,  oxides,  and  glass  absorb  a  deal  of  gas  which  gradually  comes  out; 
so  that  a  tube  pumped  "  clean  "  will  soon  show  gas  because  of  its  emission 
from  the  parts  of  the  tube.  This  emission  is  very  slow  at  ordinary  temper- 
atures, so  that  a  tube  might  be  pumped  a  long  time  without  getting  suffi- 
cient gas  from  the  parts  to  prevent  further  emission.  If,  however,  the 
glass  and  metal  parts  are  heated,  the  gas  is  expelled  from  them  very 
rapidly,  and  this  is  the  scheme  used  in  evacuating  tubes;  the  whole  tube 
is  subjected  to  a  "  baking  "  process  while  connected  to  the  pumps. 

This  heating  should  be  carried  much  higher  than  any  temperature  at 
which  the  tube  may  operate;  thus  if  in  practice  the  plates  and  filament 
operate  at  dull-red  heat  they  should  be  run  for  several  minutes  at  a  bright- 
red  heat  during  evacuation.  This  overheating  of  the  parts  is  regularly 
done  with  tungsten  tubes  but  it  cannot  be  carried  out  to  the  same  degree 
with  the  oxide-coated  filaments.  The  coated  filament  is  easily  spoiled 
if  subjected  to  too  high  a  temperature,  and  this  limits  the  possibility  of 
complete  evacuation.  For  this  reason,  as  previously  mentioned,  the  oxide- 
coated  power  tubes  are  much  more  subject  to  destructive  ionization  during 
operation  than  are  the  tungsten  tubes. 

1  It  may  be  used,  however,  for  generating  a  small  amount  of  power,  providing  the 
plate  voltage  is  kept  sufficiently  low;  thus  a  300- volt  tube  which  ^has  ionized  badly  may 
sometimes  be  used  by  reducing  the  plate  voltage  to  perhaps  250. 


394 


VACUUM   TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


Detection  of  Gas  in  a  Three-electrode  Tube.— In  Fig.  22  is  shown  a 
set  of  curves  from  a  detector  tube,  illustrating  the  effect  of  filament  tem- 
perature on  the  tendency  of  the  tube  to  ionize.  With  .40  ampere  and 


20 


30 


41) 


80 


90 


100 


110 


120 


50  60  70 

Plate  voltage 

FIG.  22. — Plate  current  of  a  tube  containing  gas,  showing  effect  of  ionization. 

.45  ampere  in  the  filament  the  tube  would  not  ionize  (at  least  not  to  such 
an  extent  as  to  show  itself);  with  .50  ampere  ionization  started  with 
the  plate  voltage  at  40  and  the  current  at  once  jumped  to  ten  times 
its  value.  This  increase  was  due  to  two  distinct  actions;  first,  the  pres- 


DETECTION   OF  GAS  IN  A  TUBE 


395 


ence  of  the  ionized  gas  reduced  the  limiting  action  of  the  space  charge  to 
practically  zero,  thus  permitting  the  plate  current  to  increase  at  once  to 
the  value  fixed  by  the  emission  from  the  filament;  second,  the  ionized 


rmte  current  in  raicroamperes 

1  I 

1   12 

0 

1  f 

I  I  i 

D 

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10 

0 

I/ 

fl 

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i 

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( 

I 

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1  / 

/ 

1  / 

1  1/ 

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^*-* 

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• 

c 

•—    — 

I  —  -^ 

I 

7 

c 

1 

.^      ^ 

_—  —% 

L.     — 

—    " 

..      i- 

==! 

-     - 

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Audion  use 

d  as  valve. 

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Filament  c 

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arrent  =|.45  amp 

~/W$- 

Curves 

tak 

;n  one  minute  a 

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ig  take 

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ffl 

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jl 

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A 

10           20           30 

40           50           60 

70           80           90           100         110          120 

Plate  voltage 

FIG.  23. — Disappearance  of  gas  from  a  tube;  curves  were  taken  in  the  order  1-2-3; 
ionization  showed  on  the  first  curve,  to  a  lesser  extent  in  the  second  and  not  at  all 
in  the  third. 

gas  acts  as  a  conductor,  giving  a  current  in  addition  to  that  afforded  by  the 
emission  from  the  filament.  With  higher  filament  currents  the  ioniza- 
tion set  in  at  lower  voltages  as  indicated  on  the  curve  sheet. 


396 


VACUUM   TUBES  AND   THEIR  OPERATION  [CHAP.  VI 


In  Fig.  23  are  shown  three  curves  from  the  same  tube,  one  taken  after 
the  other.  Curve  1  was  taken  first ;  ionization  set  in  with  a  plate  potential 
of  40  volts,  causing  a  large  increase  in  plate  current,  which  value  was 
maintained  for  one  minute.  The  plate  voltage  was  then  reduced  to  zero 
and  again  increased,  and  with  same  filament  current  as  before;  ioniza- 
tion set  in  at  60  volts,  indicating  that  during  the  maintenance  of  the  ioniza- 
tion current  previously,  some  of  the  gas  had  been  occluded  in  the  glass 
walls  of  the  tube  or  elsewhere.  This  idea  is  substantiated  by  the  fact  that 
when  ionization  did  set  in  (somewhat  above  60  volts)  the  current  jumped 


Hysteresis"  \ 


p  of  audior 


as^a 


Ltejconne 


togeth 


ent  'current  =p  .350  anips, 


Time  of  cycle  r  3  mins 


10   15   20   25   30  35  40 


45   50   55   60 
Volts  on  plate 


65      70      75 


90      95     100 


FIG.  24. — In  this  tube  the  effect  of  the  gas  present  was  to  so  alter  the  emitting 
properties  of  the  filament  that  the  saturation  current  was  appreciably  different 
with  increasing  and  decreasing  plate  voltages,  showing  probably  change  in 
emissivity  of  the  filament. 

to  only  1000  microamperes,  whereas  previously  it  had  gone  to  1200  micro- 
amperes. In  a  short  time  the  ionization  ceased,  as  indicated  by  dis- 
appearance of  the  blue  haze  and  decrease  in  plate  current  to  an  even 
lower  value  at  56  volts  than  it  had  at  60  volts  before  ionizing.  Upon 
again  increasing  the  voltage  the  current  followed  the  values  shown. 
Upon  dropping  the  plate  voltage  once  more  to  zero  and  going  through 
the  same  range  as  before  the  plate  current  varied  as  shown  by  curve  3, 
no  ionization  at  all  occurred.  This  action  is  quite  typical  of  tungsten 
filament  tubes;  they  tend  to  clean  themselves  of  any  gas  present  in  the  bulb. 
In  Fig.  24  is  shown  a  peculiarity  of  a  tube  having  a  small  amount  of 


DETECTION   OF  GAS  IN  A  TUBE 


397 


gas  present;  a  kind  of  "  hysteresis  "  cycle  occurs,  the  current  not  going 
through  the  same  values  for  decreasing  plate  voltage  as  for  increasing 
plate  voltage.  At  voltages  higher  than  fifteen  this  tube  showed  a  drooping 
current-voltage  curve,  which  means  that  its  a.c.  resistance  (for  limited 
values  of  impressed  alternating  e.m.f.)  is  negative;  as  long  as  it  held  this 


100 


-6-4—2          0        —  2 
Grid  potential 


+4       +6       +8        +10      +12     +14      +16 


FIG.  25. — A  small  amount  of  gas  in  a  three-electrode  tube  may  produce  more  or  less 
regular  "humps"  in  the  plate  current  curve. 

characteristic,  this  tube  might  be  used  as  a  two-electrode  tube  for  pro- 
ducing oscillations,  its  operation  being  the  same  as  that  of  a  Dudell  sing- 
ing arc. 

The  normal  variation  between  plate  current   and  grid  voltage  in  a 
three-electrode  tube  gives  smooth  curves,  but  if  gas  is  present  abnormal 


398 


VACUUM   TUBES  AND  THEIR  OPERATION  [CHAP.  VI 


shapes  may  be  obtained.     Fig.  25  shows  an  effect  of  this  kind  and  for  each 
of  the  plate  voltages  used  a  "  hump  "  occurs  in  the  plate  current  curve. 


7 


Z 


[Tungsten  tube 


(V'T.  11) 


late  potential 


20  volts 


3 


Grid  potential 

FIG.  25 A. — Showing  the  effect  of  a  small  amount  of   gas  in   producing  a  well-defined 
"hump"  in  the  plate  current  curve. 

The  position  of  this  hump  shifts  to  different  grid  voltage  for  the  different 
plate  voltages  used  in  the  test. 


DETECTION  OF  GAS  IN   A   TUBE 


399 


In  Fig.  25A  is  shown  a  more  striking  example  of  this  same  peculiarity. 
The  curve  is  for  a  well-pumped  modern  tube  using  tungsten  filament; 
it  is  undoubtedly  due  to  the  presence  of  mercury 
vapor  in  the  tube.  If  a  mercury  vapor  pump  is 
used  for  evacuation,  some  of  the  mercury  vapor 
will  be  left  in  the  tube  unless  a  proper  freezing 
trap  is  used.  If  a  tube  showing  this  effect  is 
used  for  a  detector  of  radio  signals  it  is  remark- 
ably sensitive  if  adjusted  to  just  the  right  grid 
potential  by  a  suitable  potentiometer.1 

If  a  tube  is  completely  freed  from  gas  the 
current  to  the  grid  will  not  reverse  when  the 
potential  of  the  grid  is  made  negative.  Even  in 
a  very  well  pumped  tube,  however,  there  is  a 
slight  reversed  current  to  the  grid  when  the  grid 
is  negative,  caused  by  the  positive  ions  of  gas  in 
the  tube.  This  grid  current  depends  upon  the 
gas  present  being  ionized  by  the  electron  flow 
to  the  plate  and  is  zero  if  the  electron  flow  is 
zero.  The  more  plate  current  there  is  the  more  is 
the  gas  ionized  and  hence  the  greater  is  the  grid 
current. 

The  effect  is  shown  in  Fig.  26,  which  shows 
the  grid  current  in  a  well  pumped  tungsten  tube ; 


I   I   I    I 


11 


J_i 


GRID  CUKHENT  IN  WELL   EVACUATED  TUNGSTEN  TUBE 
WITH  TWO  DIFFERENT  PLATE  POTENTIALS 


12 


10  8  6  4  2  —   0   -f- 

Grid  potential  (to  negative  end  of  filaments)  in  volts 


FIG.  26. — Even  in  the  very  high  vacuum  tubes  the  grid  shows  a  reversed  current  when 
its  potential  is  negative;  these  curves  are  for  a  type  P  pliotron  having  a  high  degree 
of  evacuation. 

it  is  seen  that  for  plate  voltage  of  100  the  reversed  grid  current  is 
much  less  than  it  is  for  a  plate  voltage  of  200;  this  is  due  to  the  lower 
plate  current  at  the  lower  plate  voltage  producing  less  intense  ionization 

1  It  must  be  remembered  that  when  the  grid  is  subjected  to  very  high  frequency  varia- 
tion* in  its  potential  it  is  quite  likely  that  the  plate  current  does  not  vary  in  the  manner 
indicated  by  the  curve  obtained  in  direct  current  test,  such  as  that  given  in  Fig.  25.4 . 


400  VACUUM  TUBES  AND  THEIR  OPERATION  [CHAP.  VI 

of  the  gas  present.  As  the  grid  potential  was  increased  (in  the  negative  direc- 
tion) the  grid  current  decreased  instead  of  increasing  as  might  be  expected. 
This  is  due  to  the  decrease  of  plate  current  with  the  lower  grid  potentials. 

A  tube  having  considerable  gas  in  it  may  be  made  extremely  sensitive 
as  a  detector  if  adjusted  with  a  plate  or  grid  voltage  nearly  sufficient  to 
produce  ionization;  the  slight  increase  in  grid  potential  due  to  the  incom- 
ing signal  may  then  cause  ionization  to  occur  with  a  resultant  great  increase 
in  the  plate  current.  Such  tubes  are  not  reliable  enough  to  be  of  any 
great  practical  importance,  however;  the  modern  high-vacuum  tube  if 
properly  connected  in  cascade  with  the  others,  may  produce  the  same 
amount  of  amplification  and  at  the  same  time  have  the  necessary  reli- 
ability of  action. 

Tungsten  Filaments  and  Oxide-coated  Filament. — As  noted  in  the 
first  paragraph  of  this  chapter,  a  pure  metal  such  as  tungsten  must  operate 
at  a  very  high  temperature  before  an  appreciable  emission  of  electrons 
takes  place;  to  get  the  amount  of  emission  required  for  a  power  tube 
the  tungsten  must  be  at  a  dazzling  white  heat.  In  first  operating  tubes 
of  this  type  the  experimenter  will  get  an  incorrect  idea  of  their  behavior 
unless  meters  are  used,  and  the  filament  is  run  right  up  to  its  rated  current. 

Tubes  using  a  Wehnelt  cathode,  or  oxide-coated  filament,  on  the  other 
hand,  must  not  be  operated  at  a  high  temperature  or  they  will  be  spoiled. 
These  filaments  are  made  of  thin  platinum  strip,  coated  l  with  a  mixture 
of  various  oxides  (barium,  strontium,  and  calcium)  together  with  a  suit- 
able cement;  in  order  to  make  the  oxide  coating  adhere  more  tenaciously 
the  platinum  strip  is  generally  twisted  about  itself.  These  filaments 
should  never  be  operated  at  a  temperature  higher  than  that  required  to 
give  a  bright  cherry-red  color;  the  detector  and  amplifier  bulbs  generally 
operate  satisfactorily  at  a  much  lower  temperature  than  this. 

To  get  the  same  emission  from  a  tungsten  filament  as  from  an  oxide- 
coated  filament  requires  about  twice  the  amount  of  power;  where  the  cost 
or  difficulty  of  obtaining  power  is  of  prime  importance,  therefore,  the 
oxide-coated  tube  is  superior.  For  detector  and  amplifier  tubes  used  in 
army  field  work  for  "  standby  "  service,  being  in  continued  use,  this  ques- 
tion of  power  supply  is  of  more  importance  almost  than  any  other;  the 
power  for  heating  the  filaments  must  be  transported  generally  in  the 
form  of  portable  storage  batteries  and  that  tube  requiring  the  fewest 
renewals  of  batteries  is  the  best,  even  though  some  of  its  other  character- 
istics may  not  be  as  good. 

Power  tubes,  on  the  other  hand,  use  a  considerable  amount  of  power 
in  their  plate  circuits,  as  much  or  more  than  that  used  for  heating  the 
filament  so  that  the  filament  power  does  not  have  the  same  relative  impor- 
tance as  it  does  for  the  detector  and  amplifier  bulbs  in  which  the  filament 

1  Generally  1  to  2  milligrams  per  sq.  cm.  of  surface. 


CHARACTERISTIC  CURVES  OF  THREE-ELECTRODE  TUBES      401 

requires  perhaps  3  watts  for  heating,  whereas  the  plate  circuit  requires 
but  .01  watt.  So  far  as  power  consumption  of  the  tube  is  concerned, 
therefore,  the  lower  filament  power  of  the  oxide  tube  does  not  offer  such 
great  advantage,  in  fact,  it  seems  to  the  author  that  the  oxide  filament  is 
not  the  equal  of  the  tungsten  filament  for  power  tubes.  The  vacuum 
attained  in  oxide  filament  tubes  is  never  as  good,  or  as  permanent,  as  that 
commonly  used  with  tungsten  filaments,  and  this  fact  leads  to  their  very 
frequent  failure.  The  gas  present  ionizes  and  this  ionization  (if  there 
is  appreciable  gas  present)  completely  spoils  their  operation  as  generators. 
It  sometimes  happens  that  a  tube  ionizes,  due  to  excessive  potential 
gradients,  and  when  the  high  plate  voltage  is  removed,  the  tube  acts  as 
well  as  before,  but,  on  the  other  hand,  the  result  of  the  ionization  frequently 
results  in  a  burnt-out  filament  and  completely  spoiled  tube. 

With  a  tungsten  tube,  on  the  other  hand,  even  if  ionization  occurs, 
the  effect  will  soon  disappear  if  the  plate  voltage  is  held  up  to  its  normal 
value;  the  effect  of  the  exceedingly  hot  tungsten  filament  is  to  use  up, 
in  some  way  or  other,  the  gas  causing  the  ionization.  In  such  a  tube 
the  vacuum  is  likely  to  improve  the  more  the  tube  is  used. 

Characteristic  Curves  for  Three-electrode  Tubes. — The  so-called 
"  static  "  characteristic  curves  of  a  three-electrode  tube  show  how  the  plate 
current  and  grid  current  vary  as  the  grid  potential  is  varied  over  a  sufficient 
range  to  cause  this  plate  current  to  vary  from  its  maximum  operating 
value  to  zero,  the  plate  potential  being  constant  while  the  series  of  points 
for  the  curve  is  being  obtained.  The  same  curves  are  taken  for  several 
values  of  plate  potential. 

Another  set  of  curves  is  sometimes  used  showing  the  variation  of 
plate  and  grid  currents  as  the  plate  potential  is  varied  from  zero  to  its 
maximum  safe  value,  the  grid  potential  remaining  constant,  a  series  of 
such  curves  is  obtained  for  various  grid  potentials. 

Another,  and  probably  more  useful,  set  of  curves  show  how  the  plate 
and  grid  currents  vary  as  the  grid  potential  is  varied,  the  plate  potential 
varying,  during  the  process  of  getting  the  curve,  in  the  same  way  it  does 
when  the  tube  is  actually  used  in  a  detecting  or  generating  circuit.  When 
being  used  the  three-electrode  tube  always  has  an  impedance  of  some  kind 
in  series  with  the  plate  circuit.  The  value  of  the  voltage  used  in  the 
plate  circuit  is  constant,  not  varying  as  the  grid  potential  is  varied,  by 
signal  or  otherwise;  it  is  therefore  evident  that  as  the  grid  potential 
varies,  thus  varying  the  current  in  the  plate  circuit,  the  plate  potential 
must  vary  because  it  is  equal  to  the  plate  circuit  voltage  minus  the  drop 
in  the  series  impedance,  and  this  drop  varies  with  the  grid  potential. 

This  last  set  of  curves  is  the  one  which  most  readily  permits  the  pre- 
diction of  the  behavior  of  the  tube.  A  resistance  should  be  put  in  the 
plate  circuit  equal  to  that  which  is  used  when  the  tube  is  actually  operating; 


402 


VACUUM   TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


a  plate  circuit  voltage  should  be  used  such  that  when  the  grid  is  set  at 
the  same  potential  as  its  average  potential  under  operating  conditions 
the  plate  current  is  the  same  as  its  average  operating  value.  The  plate- 
circuit  voltage  is  frequently  called  the  "  B  "  battery  voltage. 

It  has  become  customary  in  speaking  of  grid  potential  to  refer  the  grid 
to  the  negative  end  of  the  filament;  unless  otherwise  stated  all  the  curves 
shown  in  this  text  are  so  given.  In  case  the  characteristics  are  desired 
when  the  grid  is  connected  to  the  positive  end  of  the  filament  it  is  only 


Plate  current  microamperes 

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Grid  potential 

FIG.  27. — An  old  Deforest  audion,  after  being  well  evacuated  and  baked,  showed  just 
as  regular  characteristics  as  the  modern  tube. 


necessary  to  move  the  "  zero  grid  potential  "  along,  on  the  curve  sheets 
as  given,  by  an  amount  equal  to  the  IR  drop  in  the  filament. 

In  Fig.  27  is  shown  a  set  of  plate-current  curves  from  an  old  Deforest 
audion,  after  it  had  been  re-evacuated  to  take  off  all  possible  gas.  The 
plate  circuit  had  no  added  resistance  except  that  of  the  B  battery,  which 
was  so  low  that  the  variation  in  plate  current  did  not  appreciably  affect 
the  plate  potential.  On  the  curve  sheet  is  shown  the  locus  of  the  "  free 
grid  potential,"  i.e.,  the  potential  at  which  the  grid  set  itself  when  its 


CHARACTERISTIC   CURVES   FROM   TYPICAL  TUBES  403 

external  terminal  was  completely  insulated.     This  point  will  be  taken  up 
more  in  detail  later. 

For  the  tube  used  in  getting  the  curves  of  Fig.  27  it  will  be  noticed 
that  the  grid  voltage  was  more  effective  (in  controlling  the  plate  current) 
than  the  plate  voltage  in  the  ratio  of  about  two  to  one.  Thus  to 
get  1  milliampere  of  plate  current  it  is  necessary  to  use  either  (EP  =  2Q, 
#,=  13),  (#P  =  30,  #,  =  5.6),  (#P  =  40,  Eg=l),  (#P  =  50,  #,=  -3.4),* 
EP  =  QO,  Eg=  -7.2)or(#p  =  70,  #,=  -12).  Using  the  two  extreme  values, 
we  see  that  a  decrease  in  plate  potential  of  (70 -20)  =50  volts  is  neu- 
tralized (in  so  far  as  it  affects  plate  current)  if  the  grid  potential  is 
increased  from  -12  volts  to  +13  volts,  or  a  change  of  25  volts. 

In  Fig.  28  is  shown  a  set  of  curves  from  a  tube  designed  for  amplifying 
purposes;  free  grid  potentials  in  this  tube  follow  about  the  same  changes 
as  for  the  tube  used  in  Fig.  27.  The  much  greater  control  of  the  grid 
of  the  tube  is  seen  from  the  values  of  plate  voltage  and  grid  voltage  for 
a  current  of  .001  ampere.  This  is  obtained  with  either  (Ep=  160,  Eg=  .2), 
or  (#p  =  70,  #,  =  2.6)  so  that  an  increase  in  grid  potential  of  2.4  volts 
offsets  a  decrease  in  plate  potential  of  90  volts;  the  effectiveness  of  the 
grid  is  thus  thirty-eight  times  as  great  as  that  of  the  plate. 

In  Fig.  29  is  shown  a  set  of  curves  for  a  tube  having  the  plate  and  grid 
very  close  to  the  filament,  the  grid  being  comparatively  coarse  compared 
to  that  of  the  tube  of  Fig.  28.  In  Fig.  29  the  grid  potentials  are  referred 
to  the  positive  end  of  the  filament;  as  the  filament  IR  drop  was  about  3 
volts  it  is  seen  that  if  the  grid  were  connected  to  the  negative  end  of  the 
filament  the  grid  current  would  be  practically  zero.  This  tube  is  generally 
used  as  a  detector  with  the  grid  normally  somewhat  positive. 

It  will  be  noticed  that  the  grid  current  (for  a  given  grid  potential) 
decreases  as  the  plate  potential  is  increased.  When  the  grid  and  plate  are 
positive  by  about  the  same  amount  (curves  D  and  Df  with  grid  3  volts 
positive)  each  takes  about  the  same  thermionic  current;  the  greater  area 
of  the  plate  compensates  for  the  greater  proximity  of  the  grid  and  filament. 

Fig.  30  shows  the  effect  of  filament  current  on  the  static  characteristics 
of  a  large  power  tube  (G.  E.  pliotron  type  P-10,  the  10  signifying  the 
number  of  grid  wires  per  inch).  The  grid  currents  with  negative  grid 
potentials  are  too  small  to  be  plotted  on  the  curve  sheet.  The  filament 
currents  were  measured  at  that  end  carrying  the  smaller  current. 

As  was  pointed  out  in  Fig.  14,  the  current  in  a  filament  varies  through- 
out its  length  when  it  is  delivering  electrons  to  the  plate,  the  amount  of 
variation  depending  directly  on  the  value  of  the  plate  current.  In  Fig. 
31  is  shown  a  set  of  curves  to  illustrate  this  point;  a  constant  voltage 
of  32  was  impressed  on  the  filament,  the  grid  was  held  at  a  positive  poten- 
tial of  +100  volts  and  the  plate  voltage  varied  from  zero  to  200  volts. 
This  set  of  curves  serves  not  only  to  show  the  peculiar  changes  in  filament 


404 


VACUUM  TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


current,  but  also  how,  as  the  plate  voltage  increases,  the  grid  current  is 
reduced.  The  sum  of  the  grid  current  and  plate  current  gives,  for  all 
values  of  plate  voltage,  the  difference  between  the  two  filament  currents. 
The  resistance  of  the  filament  of  a  vacuum  tube  under  such  conditions  is 


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Grid  potential 

FIG.  28. — Plate  current  curves  for  a  tube  intended  as  a  voltage  amplifier. 


not  a  simple  function  of  volts  and  amperes;   it  involves  all  the  theory 
of  a  long,  leaky,  telegraph  line. 

The  safe  filament  current  for  these  large  power  tubes  is  always  rated 
in  terms  of  the  maximum  current,  that  is,  the  end  of  the  filament  where 


CHARACTERISTIC  CURVES  FROM  TYPICAL  TUBES 


405 


-i  o  i 

Grid  potential 


FIG.  29. — Characteristic  curves  for  an  ordinary  detector  tube,  for  a  wide  range  of  plate 
voltages.  For  the  lowest  plate  voltage  the  grid  current  and  plate  current  are  about 
equal. 


406 


VACUUM   TUBES  AND   THEIR  OPERATION 


[CHAP.  VI 


S8J8dnmu;ra  ui  ^uoaano 


soaadray 


CHARACTERISTIC   CURVES   FROM    TYPICAL  CURVES 


407 


the  plate  current  and  battery  heating  current  combine  to  give  a  current 
greater  than  normal  battery  current. 

In  Fig.  32  are  shown  curves  for  the  same  tube  as  used  for  Fig.  30;  the 
filament  current  (larger  value)  was  held  at  3.60  amperes  and  various 


Variation  of  filame 


;  Filament 


grid  potential  con 


ne, 


With 

lj=l 


;=;3.40an 


z 


t  curren 


nstant  a 


and 


peres 


t  at-r 


-jr 


vo  ts 


with 


32  vo 


plate 


ts  and 


3.7 


3.G 


3.5 


3.4 


3.3 


3.2 


3.1 


20 


40 


6U 


40 


60 


80        200 


80        100        20 
Plate  voltage 

FIG.  31. — Showing  the  effect  of  the  plate  voltage  upon  the  filament  current  of  a  power 
tube,  the  voltage  impressed  on  the  filament  being  constant.  The  change  in  grid 
current  produced  by  increasing  plate  potential  is  also  shown. 

voltages  were  impressed  on  the  plate.  With  low  plate  voltage  it  is  seen 
that  when  the  grid  becomes  positive  the  plate  current  undergoes  a  rapid 
decrease.  This  combination  of  high  positive  grid  voltage  and  low  plate 
voltage  occurs  when  the  tube  is  used  for  generating  power  and  results 


408 


VACUUM   TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


in  peculiar-shaped  plate  current  instead  of  a  sinusoidal  variation  as  is 
generally  assumed. 

In  Fig.  33  are  shown  the  characteristic  curves  for  a  G.  E.  P-20  (20  grid 
wires  per  inch)  pliotron  obtained  by  holding  the  grid  potential  constant 


0.3 


140      120       100       80 


20          0          20 
Grid  potential 


100      120       140 


FIG.  32. — Static  characteristics  of  a  Type  P  pliotron  for  various  plate  voltages,  filament 

current  being  constant. 

while  varying  the  plate  voltage.  For  all  these  curves  the  grid  currents 
were  only  a  few  microamperes.  In  this  tube  it  is  evident  that  1  volt 
on  the  grid  has  the  same  effect  on  plate  current  as  11  volts  on  the  plate. 

In  Fig.  34  are  shown  similar  curves  for  a  P-10  pliotron,  values  having 
been  obtained  for  low  plate  voltage  and  high  positive  grid  voltages  and  in 


CHARACTERISTIC  CURVES   FROM   TYPICAL  TUBES  409 


on  plate  =250 


vali 


PI 


^ilameht  i 


stant 


ot 


on 


at 


P- 


ur 


.65  amps. 


20 


=J 

am 


^ 


r 


=  0 


EC 


E, 


-10 


90 


100       200       300       400        500        600       700       800       900       1000     1100      1200 
Plate  voltage 

FIG.  33. — Static  characteristics  of  a  Type  P  tube  for  various  fixed  grid  potentials  and 
variable  plate  voltage.  The  curve  in  the  upper  part  of  the  diagram  shows  the 
limit  of  operation  of  the  tube. 


410 


VACUUM   TUBES  AND   THEIR  OPERATION 


[CHAP.  VI 


Fig.  35  are  shown  some  typical  curves  for  a  finer-mesh  grid  (P-30).  In 
this  tube  the  grid  voltage  is  twenty-two  times  as  effective  as  the  plate 
voltage  in  determining  plate  current.  It  will  be  noticed  how  quickly 

the  grid  current  rises  as  the 
plate  potential  decreases  be- 
yond a  certain  limit. 

Potential  of  the  Free  Grid 
of  a  Three-electrode  Tube. — 
When  the  grid  of  a  vacuum 
tube  is  entirely  disconnected 
from  other  circuits  it  is  said 
to  be  "  free/'  meaning  that  it 
is  free  to  assume  any  potential 
circumstances  may  demand. 
Actually  a  grid  is  never  really 
free,  because  there  is  always 
some  leakage  from  the  grid  to 
the  plate  and  filament  even  in 
tubes  with  extremely  high 
vacuum.  If  the  value  of  this 
leak  resistance  is  perhaps  50 
megohms  the  grid  may  be  reck- 
oned as  free,  although  in  many 
tubes  a  much  greater  resistance 
exists  and  the  grids  are  corre- 
spondingly more  "  free." 

It  is  almost  an  axiom  in 
vacuum-tube  operation  that  a 
grid  should  never  be  left  free. 
Consistent  operation  of  the 
tube  is  almost  impossible  unless 

the  resistance  between  the  grid 
FIG.  34.— Similar  to  the  curves  of  Fig.  33,  this  ,  .      . \  -  .., 

tube  having  a  grid  with  coarser  mesh.  and  filament  1S  of  defimte  value> 

and  sufficiently  low;    it  seldom 

exceeds  one  megohm  in  ordinary  detecting  or  amplifying  sets. 

In  Fig.  36  is  shown  a  connection  in  which  a  free  grid  is  used;  tube  1 
is  repeating  into  tube  2,  the  fluctuations  of  plate  voltage  of  1  being 
impressed  on  the  grid  of  2.  The  grid  of  2  cannot  be  connected  directly 
to  the  plate  of  1  because  this  plate  is  at  comparatively  high  positive 
potential,  due  to  its  B  battery.  By  putting  an  insulating  condenser  C 
between  the  plate  of  1  and  grid  of  2  the  fluctuations  of  plate  voltage  repeat 
through  the  condenser  into  the  grid,  but  the  grid  is  insulated  from  the 
high  positive  continuous  e.m.f.  of  the  plate  of  1. 


0  100  200  300  400  500  600  700  800 
PJate  voltage 


CHARACTERISTIC  CURVES  FROM   TYPICAL  TUBES 


411 


Now  such  a  grid  is  free;  the  insulation  of  condenser  C  will  be  hun- 
dreds of  megohms,  so  that  the  grid  is  free  to  assume  any  potential  what- 
ever. Because  of  the  irregular  action  of  a  tube  so  connected  a  high  resist- 


Type  P  -30 


•yf 


=  3.65  amps. 


~J$ 


\ 


0  200  400  600  800  1000 

Plate  volts 

FIG.  35. — Similar  to  the  curves  of  Fig.  33,  this  tube  having  a  grid  with  finer  mesh. 

ance  leak  of  one  megohm  or  less  (as  indicated  by  the  dotted  line  connec- 
tion) is  always  used,  to  keep  the  grid,  normally,  at  a  suitable  potential. 
Some  of  the  effects  produced  by  a  free  grid  will  be  indicated  by  the 


412 


VACUUM   TUBES  AND   THEIR  OPERATION 


[CHAP.  VI 


accompanying  curves.     In  Fig.  37  is  shown  how  the  potential  of  a  free 
grid  may  be  expected  to  change  as  the  plate  voltage  is  increased  from 


Tube   1 


FIG.  36. — A  circuit  illustrating  the  meaning  of  the  term  "free  grid,"  the  grid  of  the 
second  tube  is  electrically  free  to  assume  any  potential  that  circumstances  may 
demand. 


pect  to 


Potential 


of 


grid,  Mtt 


ve  enc 


of  filament. 


Measiirec 


by  static  voltme 


Cur 


Current 


=.350  a 


nperes 


-2.0 
9 

81 


g 
S     7 

I     6 


3 


N: 


£     7 

•!i     6 

-u 

I     5 

a  4 

•d 

§    3 
2 

1 
0 


x 


-2- 


40 


50 


10  20  30 

Volts  from  plate  to  negative  end  of  filament 

FIG.  37. — Variations  in  free  grid  potential  for  various  plate  voltages  and  filament  cur- 
rents; measurements  by  a  highly  insulated  sensitive  static  voltmeter. 

zero,  for  various  filament  temperatures.     The  higher  the  plate  voltage 
the  closer  the  grid  potential  approaches  zero  potential,  i.e.,  that  of  the 


FREE  GRID  POTENTIAL  413 

negative  end  of  the  filament.  With  zero  plate  voltage  the  grid  goes  neg- 
ative as  much  as  2  volts,  due  undoubtedly  to  the  accumulation  of  electrons 
which  have  left  the  filament  with  enough  initial  velocity  to  carry  them 
as  far  as  the  grid. 

In  Fig.  38  are  shown  the  free  grid  potentials  of  ten  different  tubes 
all  of  them  having  some  gas  (although  not  enough  to  produce  visible 
ionization  with  the  plate  potentials  used).  In  getting  these  curves  the 
filament  current  was  brought  to  its  normal  value  with  plate  at  the  desired 
voltage,  the  grid  being  connected  to  the  negative  end  of  the  filament. 
The  grid  was  then  disconnected  from  everything  and  the  plate  current 
noted;  by  then  connecting  the  grid  to  a  suitable  potentiometer  and  vary- 
ing its  potential  the  same  value  of  plate  current  was  obtained.  A  volt- 
meter connected  across  the  potentiometer  served  to  show  this  grid  poten- 
tial which,  as  it  gave  the  same  plate  current,  must  be  that  of  the  free  grid. 

The  potential  of  the  free  grid  depends  entirely  on  the  order  in  which 
the  successive  adjustments  are  carried  out,  thus  if  the  grid  is  left  free, 
filament  current  brought  to  normal  and  then  plate  potential  brought  to 
normal  an  entirely  different  value  for  free  grid  potential  may  be  obtained 
than  would  be  if  the  plate  were  first  put  at  its  proper  potential  and  then 
the  filament  current  brought  to  normal. 

In  Fig.  39  is  shown  the  curve  obtained  (with  free  grid)  by  holding 
the  plate  at  150  volts,  increasing  the  filament  current  from  a  low  value 
to  a  high  value  and  then  decreasing  the  filament  current  through  the  same 
range.  A  peculiar  loop  is  obtained  explained  by  the  fact  that  as  the  plate 
potential  was  applied  before  there  was  a  liberal  supply  of  electrons  in  the 
vicinity  of  the  grid  the  grid  went  positive.  This  positive  grid  gave  com- 
paratively large  values  of  plate  current  from  A  up  to  the  point  B  on  the 
curve  sheet;  here  the  grid  suddenly  lost  most  of  its  positive  charge  due 
to  bombardment  by  many  electrons,  and  became  nearly  zero  in  potential 
with  a  consequent  decrease  in  the  plate  current.  From  C  to  D  and  back 
to  C  the  grid  had  nearly  the  same  potential  for  increasing  as  for  decreasing 
filament  current,  but  from  C  to  E  the  grid  potential  was  much  lower  than 
it  was  for  the  corresponding  values  of  filament  current,  when  increasing 
values  were  being  taken.  At  E  the  grid  suddenly  increases  its  potential 
a  small  amount  and  for  the  remainder  of  the  cycle  it  has  about  the  same 
potential  as  it  had  for  increasing  filament  current;  other  tubes  showed 
exactly  the  same  effect. 

In  Fig.  40  are  shown  the  potentials  of  the  free  grid  of  a  telephone 
amplifying  tube.  For  low  values  of  filament  current  the  free  grid  assumes 
a  potential  about  half  that  of  the  plate,  then  as  the  filament  current  is 
increased  the  grid  potential  decreases  gradually  until  a  critical  value  of 
filament  current  is  reached.  At  this  critical  filament  current  (i.e.,  critical 
supply  of  electrons)  the  grid  potential  suddenly  falls  to  a  comparatively 


414 


VACUUM   TUBES  AND   THEIR  OPERATION 


[CHAP.  VI 


a 

5 

!! 


O  "-     n3 
—  O     ^ 


o  o 

Kg 


.23 


w  c 

3 '« 


OJ        1 

6  ',!!, 


S        S 


?     ^ 

« 


f   a 


*-S     cS 

*     «,| 


IS 


!'t 


•43 


•fl  S 

+-•  & 


8 


7    I 


FREE   GRID   POTENTIAL 


415 


low  value,  which  value  decreases  somewhat  as  the  filament  current  is 
still  further  increased.  It  will  be  noticed  that  for  this  tube  the  free  grid 
is  always  positive,  whereas  for  the  ten  tubes  tested  for  Fig.  38  most  of 
the  grid  potentials  were  negative. 

Relations  between  Currents  and  Potentials  in  a  Three-electrode 
Tube. — From  experimental  results  already  presented  it  is  evident  that 
the  grid  current  and  plate  current  of  a  three-electrode  tube  vary  with 
either  filament  current,  plate  voltage,  or  grid  voltage.  It  is  also  evident 
that  the  grid  current  is  negligibly  small  compared  to  the  plate  current, 
and  that  the  plate  current  is  not  affected  directly  by  the  grid  current 


Plato  curieiit  (milliamperes) 

tO**01000tCl**G>OOOtO*-<3500OtO.U010oOfO«&.0>00 

fB 

PL 

ite 

vojlts 

— 

150 

I 

Te 

lep 

hoJ 

ic  i 

ep 

eat 

er 

tub 

e 

/ 

J 

1 

1 

2 

^ 

D 

/ 

&* 

*f 

X 

A 

^ 

^\ 

/ 

s 

*£* 

7 

x 

7 

/ 

r 

/ 

X 

— 

X 

/ 

/ 

/> 

' 

. 

X 

^ 

X 

^ 

x 

J 

^. 

^* 

^" 

F 

A 

T^- 

*~* 

H*^ 

—  ' 

^ 

•z*' 

.80                       .90                       1.00                      1.10                     1.20                 1.30                      1,40 
Filament  curasnt 

FIG.  39. — A  peculiar  cycle  obtainable  from  a  tube  having  a  free  grid;  as  the  filament 
current  was  increased  and  then  decreased  the  plate  current  went  around  the  loop  as 
indicated  by  the  arrow  heads;  plate  potential  was  kept  constant. 


except  under  unusual  conditions,  as,  e.g.,  curve  A  of  Fig.  32.  Unless 
we  are  specifically  interested  in  the  losses  in  the  grid  circuit  the  grid  current 
may  be  neglected.  Furthermore,  unless  the  conditions  are  such  that 
saturation  current  is  reached  (plate  current  using  all  the  electrons  emitted 
from  the  filament)  the  filament  current  does  not  affect  the  plate  current 
to  a  great  extent.  We  shall  therefore  examine  in  this  section,  the  rela- 
tions between  plate  current  and  grid  and  plate  potentials,  neglecting 
grid  currents  and  the  effect  of  too  small  a  filament  current. 


416 


VACUUM   TUBES  AND  THEIR  OPERATION  [CHAP.  VI 


=150 


\ 


100 


75 


.8     2     4.     6     8     .9     2     4      6      8    1.0    2     4      6      8    1.1    2     i      6     8   1.2    2     4      6      8   1.3    2     1     6 


FIG.  40. — Showing  the  peculiar  variations  in  free  grid  potential  as  filament  current  was 
increased;  for  this  special  tube  the  free  grid  assumed  positive  potential  under 
all  conditions. 


EQUATION  OF  PLATE  CURRENT 


417 


We  have  seen  that  the  plate  current  depends  upon  both  plate  voltage 
and  grid  voltage,  to  some  power  higher  than  the  first,  and  that  the  grid 
potential  is  much  more  effective  in  controlling  the  current  than  is  the 
plate  potential.  We  may  therefore  write, 


(5) 


where 


Ip  =  plate  current  in  amperes; 
A  =a  constant  depending  upon  type  of  tube; 
Ep=  potential  of  plate  to  negative  end  of  filament; 
Eg  =  potential  of  grid  to  negative  end  of  filament; 
juo=  relative  effectiveness  factor  of  Ett\ 
x  =  an  unknown  exponent,  possibly  variable. 


Langmuir  has  given  this  equation  with  the  value  of  #  as  1.5;  Van  der 
Bijl  has  given  the  equation  with  the  value  of  x  as  2.0,  having  also  an 
added  quantity  inside  the  parenthesis,  a  small  constant  in  which  are  taker 
care  of  such  factors  as  velocity  of  emission  of  electrons,  contact  difference 
of  potential  of  the  electrodes,  etc. 

The  quantity  juo  is  the  theoretical  voltage  amplifying  power  of  the 
tube;  it  is  ordinarily  taken  as  a  constant,  its  value  depending  solely  upon 
the  geometry  of  the  tube.  Many  tests  show  this  to  be  true  for  the  ordinary 
use  of  the  tube;  it  may  be  that  with  very  low  plate  voltage  and  high  grid 
voltage  MO  changes  some- 
what, but  in  the  ordinary 
working  range  of  Eg  and 
Ep  it  is  practically  con- 
stant. As  previously  stated, 
it  varies  in  different  types 
of  tubes  from  2  to  200  or 
more. 

When  many  determina- 
tions of  MO  are  to  be  made, 
it  is  worth  while  to  arrange 
some  apparatus  as  shown 
in  Fig.  41,  a  scheme  due  to 
J.  M.  Miller.  The  resist- 
ance R2  is  preferably  10 
ohms  and  Ri  is  a  decade 

resistance  box  having  units,  10-ohm,  100-ohm,  and  1000-ohm  units;  the 
1000-ohm  units  are  used  very  seldom,  but  few  tubes  having  high  enough 
values  of  MO  to  require  them. 

An  ammeter  A\  serves  to  read  the  filament  current,  and  milliam- 
meter  A2  serves  for  plate  current.  This  meter  should  have  two  or  three 


MAA- 
JJ, 

f               1 
H,J 

vww     Rl 
H'ww 

^AAAA/V  — 

\     ; 

FIG.  41. — An  arrangement  of  apparatus  for  rapidly 
determining  the  voltage  amplification  factor  of  a 
tube. 


418  VACUUM  TUBES  AND  THEIR  OPERATION  [CHAP.  VI 

scales,  so  that  for  various  types  of  tubes  to  be  tested  the  plate  current 
will  give  indications  well  up  on  the  scale.  The  filament  battery  should 
be  perhaps  6  volts  and  Et,  and  Ec  should  have  voltages  suitable  for  the 
tubes  to  be  tested. 

With  S  open  Eb,  Ec,  and  7/  are  put  at  their  proper  values  and  the 
reading  of  At  is  noted.  Then  S  is  closed,  permitting  current  7  to  flow 
around  the  circuit  E,  RI,  Tfe,  E,  the  reading  of  A%  will  in  general  change; 
by  properly  adjusting  R\,  however,  it  will  be  found  that  the  reading  of 
A2  (which  is  the  plate  current)  does  not  change  when  switch  S  is  closed. 
The  ratio  of  R\  to  R%  for  this  adjustment  gives  //o. 

By  examination  of  Fig.  41  it  will  be  seen  that  depressing  key  S  raises 
the  voltage  impressed  on  the  plate  by  an  amount  IRi,  and  depresses  the 
voltage  of  the  grid  by  an  amount  IR%.  From  inspection  of  Eq.  (5)  it 
is  evident  that  if  IP  does  not  change  when  S  is  closed, 


where  AEP  and  AEg  are  the  changes  in  Ep  and  E0  due  to  closing  switch  S. 
We  therefore  have  the  relation 


or 


With  this  scheme  it  is  possible  to  investigate  the  dependence  of  /*o  on  Eff, 
Ep,  and  7/  very  quickly. 

The  value  of  RI  should  not  be  so  high  that  the  drop  through  it,  due 
to  the  plate  current,  is  an  appreciable  fraction  of  EJ,,  otherwise  the  plate 
potential  will  not  be  Eb,  but  something  less,  and  must  be  calculated. 

The  value  of  the  exponent  x  should  theoretically  be  a  constant,  but 
in  the  actual  tube  it  is  constant  only  for  a  limited  range  of  voltages.  The 
voltage  between  the  plate  and  filament  is  different  for  the  different  parts 
of  the  filament,  and  the  velocity  of  emission  of  the  electrons  may  not  be 
negligible  when  the  plate  and  grid  voltages  are  low. 

If  the  grid  is  held  at  zero  voltage  the  relation  between  Ip  and  Ep  is 
IP  =  AEPX.  The  determination  of  the  exponent  x  is  most  easily  carried 
out  by  plotting  the  various  values  of  Ip  and  Ep  on  logarithmic  cross- 
section  paper;  if  x  is  a  constant  the  graph  is  a  straight  line  with  slope 
equal  to  x.  If  'the  graph  is  not  a  straight  line  the  value  of  x  varies,  but 
it  may  be  determined  for  any  value  of  Ep  by  measuring  the  slope  of  the 
graph. 

Figs.  42  and  43  give  the  variations  between  plate  current  and  plate 
voltage  for  two  amplifying  and  detecting  bulbs  designed  for  40  volts  on 
the  plate  and  an  IR  drop  in  the  filament  of  about  3.5  volts.  The  two 


FORM    OF  PLATE-CURRENT   CURVE 


419 


urves  were  transposed  to  logaril 
n  Fig.  44,  the  straight  dotted  line 
iave  if  the  plate  current  varied 
rith    the    square    of    the    plate 
oltage.      From  the  logarithmic 
raphs    the   values    of    x    were 
leasured     and     transferred    to 
"igs.  42    and    43    to   give    the 
urves  of  x  there  shown. 
In  Fig.  45  is  shown  the  log- 
rithmic  graph  for  a  high  power 
liotron,  the  rated  plate  voltage 
eing    1000-2000    volts;     it    is 
een  that  for  high  plate  voltages 
le  plate  current  varies  as  the 
quare    of    the    plate    voltage, 
"or  the  lower  plate  voltages  the 
R  drop  in  the  filament  (about 
0  volts)    and   the    velocity    of 
mission  of   the   electrons   tend 
o  give  an  exponent  other  than 
;  however,  if  the  grid  is  held 

;hmic  paper,  giving  the  graphs  shown 
shows  the  slope  the  two  curves  would 

900 

/ 

/ 

Plate  current  10~6  amperes 

/ 

/ 

/ 

/ 

/ 

/' 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

7 

/ 

/ 

/ 

/ 

/ 

f 

Ty 

36  1 

r.T. 

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/ 

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Ti 

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202468     10     2468     20     2468     30     2468     40     24 

Plate  volts 

FIG.  42. — Variation  of  plate  current  in  a  tungsten  filament  tube  as  EP  is  varied  and 
grid  potential  held  constant;  values  of  the  exponent  of  Eq.  (5),  p.  417. 


420 


VACUUM   TUBES  AND  THEIR  OPERATION  [CHAP.  VI 


at  —10  volts,   the  plate  current  follows   the  square    law  very   closely 
throughout  the  range  of  the  graph.     A  greater  negative  potential  makes 


1000 
900 
800 
700 
600 

400 

300 
1  200 
100 

7 

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ritt 

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ap< 

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be 

lov 

r 

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lilame 

nt 

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89  10   123456789  20   123456789  30   12345678 

Plate  volts 

FIG.  43. — Curves  similar  to  those  of  Fig.  42,  the  tube  used  having  an  oxide-coated 

filament. 

the  plate  current  vary  with  higher  power  of  plate  voltage  for  the  lower 

values  of  plate  potential;  this  is  to  be  expected  from  inspection  of  Eq.  (5). 

Different  tubes  of  the  same  type  will  not  follow  exactly  the  same  law 

of  plate  current  variation,  due  probably  to  small  differences  in  the  struc- 


FORM  OF  PLATE-CURRENT  CURVE 


421 


ture.  In  Fig.  46  are  shown  the  results  of  tests  on  twenty-four  tubes  all 
having  the  same  rating;  twelve  had  oxide  coated  filaments  with  a  filament 
IR  drop  of  2.6  volts  and  the  other  twelve  had  tungsten  filaments  with 
an  IR  drop  of  3.6  volts.  The  curves  for  the  individual  tubes  ran  in  gen- 
eral, parallel  to  the  boundaries  of  the  cross-sectioned  areas,  as  indicated 
on  this  curve  sheet 


J 

IUUU 

800 

dj 

9 

/ 

/ 

/ 

£  §  §  1  J  11 

Plate  current  in  10  amperes 

/I 

Curve  A  -  VT 
Curve  B-VT 

11-  If  =  1 
1-I/=1 

.10  E 
.10  E 

:J=I 

i 

/ 

J 

/      1 

, 

S 

- 

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L                     2           "34             6        8      10                  ,  20  .         30      40 
Plate  volts 

FIG.  44. — The  curves  of  Figs.  42  and  43  transposed  to  logarithmic  coordinates;  this 
graph  shows  that  the  exponent  for  Eq.  (5)  is  neither  1.5  nor  2,  but  is  a  variable  for 
both  tubes. 


Resistance  of  the  Circuits  of  a  Three-electrode  Tube  and  its  Vari- 
ations.— There  are  three  circuits  to  be  considered  in  getting  the  character- 
istics of  three-electrode  tubes,  the  filament,  the  grid  to  filament  circuit, 
and  the  plate  to  filament  circuit.  The  grid  to  filament  is  called  the  input 
circuit  of  the  tube,  and  the  plate  to  filament  is  called  the  output  circuit 
of  the  tube. 


422 


VACUUM   TUBES  AND   THEIR  OPERATION 


[CHAP.  VI 


111  the  ordinary  small  detecting  and  amplifying  tube  the  filament 
current  is  practically  independent  of  any  changes  in  the  grid  and  plate 
circuits.  In  large  power  tubes,  however,  this  is  not  so,  the  resistance 
of  the  filament  varying  a  good  deal  as  either  the  grid  or  plate  potential 
is  varied,  this  variation  being  shown  by  impressing  constant  voltage  on 
the  filament  and  then  impressing  various  potentials  on  the  grid  and  plate. 


TYPE 


PLIOTRON 


Curve  1    Eg 
Curve  2    Eg 


=  0 

=  - 10  volts 


.40 
.30 

.20 

.10 


Curve  3    Eg 
All  curves 


=  -20  volts 
f  =  3.65  ampe 


/ 


.04 


.02 


01 


100 


200 


400 


600 


800  1000 
Plate  voltage 


2000 


FIG.  45. — Logarithmic  plot  of  the  plate  current  curve  for  a  high-voltage  power  tube; 
with  a  certain  constant  negative  grid  potential  the  plate  current  of  this  tube  varies 
with  the  square  of  the  plate  voltage. 

The  accompanying  changes  in  grid  and  plate  current  cause  a  non-uniform 
current  to  flow  through  the  conductor,  under  which  condition  the  filament 
has  a  different  resistance  than  it  has  when  the  current  is  the  same  every- 
where through  its  length. 

The  resistances  of  the  input    and  output  circuits  vary  throughout 
extreme  ranges,  and  they  are  different  for  alternating  current  than  for 


FORM   OF  PLATE   CURRENT  CURVE 


423 


continuous  current;  we  shall  first  consider  the  output  circuit.  The  ratio 
of  plate  voltage  to  plate  current  is  generally  called  the  output  impedance. 
As  there  can  be  no  appreciable  lag  in  the  motion  of  the  electrons  behind 
the  impressed  electric  field,  it  might  seem  more  appropriate  to  speak  of 
output  resistance  instead  of  output  impedance.  But  it  is  to  be  remembered 
that  the  plate  current  is  influenced  by  the  grid  as  well  as  by  the  plate, 


i  2  4          6      8    10 

Plate  voltage 

FIG.  46. — Logarithmic  plots  of  24  typical  detector  tubes,  12  with  tungsten  filaments 
and  12  with  oxide-coated  filaments.  The  curves  for  the  individual  tubes  lay  inside 
the  areas  as  noted. 

and  it  may  well  be  that  variation  of  plate  current  is  not  in  phase  with 
the  variation  of  plate  potential.  From  this  viewpoint  the  plate  filament 
circuit  has  impedance,  not  merely  resistance. 

If,  however,  we  maintain  the  grid  at  zero  potential  (or  any  other  fixed 
potential)  the  plate  current  will  vary  with  plate  voltage  only  and  we  may 
speak  of  plate  circuit  resistance.  With  constant  grid  potential  and  vary- 


424 


VACUUM  TUBES  AND   THEIR  OPERATION 


[CHAP.  VI 


ing  plate  potential  the  values  of  plate  current  determine  this  resistance 
of  the  plate  circuit,  R0p,  for  continuous  currents.  Such  a  curve  for  a  tungs- 
ten filament  detecting  tube  is  shown  in  Fig.  47;  on  the  same  curve  sheet 
is  shown  a  curve  of  MO  for  this  tube,  from  which  it  may  be  seen  that  the 

value  of  no  is  practically  constant, 
except  for  very  low  plate  voltages. 
The  value  of  ROP  continually  increases 
as  Ep  is  diminished. 

The  value  of  the  alternating  cur- 
rent resistance,  RP,  is  determined  by 


the  ratio  of 


-r      the  grid  voltage  be- 


ing maintained  constant;   if  we  keep 
i    the   grid   at   zero   voltage   we   may 


v>"2    write 

.? 


aEpx 


or 


dE, 


r 
dTp~~axEpx-1  =    v 

But   the   continuous    ciirrent   resist- 
ance is 

7?    -E»-      l 
**'    T,  ~^T~l 

From  these  we  get  the  relation, 

P  _Rop 

Hp-  ... 


(7) 


FIG.  47. — Curves  of  /*0  and  Rop  of  a  small          Jn  pjg.  48  are  shown  the  curves 
tungsten  filament  tube;  the  value  of  Rop   of  Rp  and  R^  for  an  oxide-filament 

is  obtained  by  finding  the  quotient  of  »•*  •  .1  •    ,     •     v 

amplifying  tube;    the  points  mdicat- 
Ev  by  Ip  m  a  continuous-current  test. 

ed  by  circles  on  the  RP  curve  were 

obtained  by  the  alternating  current  measurement  and  those  indicated 
by  crosses  were  obtained  by  dividing  the  points  on  the  ROP  curve  by  the 
proper  value  of  x.  On  the  same  curve  sheet  is  shown  the  value  of  MO 
for  this  tube;  it  is  nearly  constant  in  the  working  range  of  the  tube  (EP 
between  20  and  40  volts)  and  falls  off  with  the  lower  plate  voltages, 
whereas  the  curve  of  Fig.  47  showed  an  increasing  MO  with  lower  plate 
voltages. 

The  value  of  RP  is  found  experimentally  by  the  scheme  outlined  in 
Fig.  49,  originated  by  J.  M.  Miller;  the  same  arrangement  serves  to 
measure  MO  by  alternating-current  test  providing  the  phone  resistance 
is  negligible  compared  to  the  tube  resistance.  Fig.  50  shows  a  curve  of 
Mo  obtained  by  the  method;  it  shows  MO  to  be  independent  of  filament 


RESISTANCE  OF  PLATE   CIRCUIT 


425 


8    20     2     4 
Plate  voltage 


40 


FIG.  48. — Curves  of  /*o>  Rp,  and  Rop,  of  an  oxide-coated  detector  tube;  the  curve  of 
Rp  can  be  obtained  by  dividing  values  of  Rop  by  the  corresponding  value  of  x  of 
Eq.  (5) .  Such  values  are  indicated  on  curve  of  RP  by  X .  Sometimes  the  curve 
of  /m>  shows  a  decided  "  hump  "  for  certain  plate  voltage. 


426 


VACUUM  TUBES  AND  THEIR  OPERATION 


[ClIAP.  VI 


current.     With  *S2  open  the  ratio  of  n  to  r2  is  varied  until  no  signal  is 
heard  in  the  telephone  and  we  then  have 


(8) 


In  measuring  Rp,  n  and  ro  are  fixed  at  some  convenient  value  (say 
equal  to  each  other),  and  with  82  closed  R  is  varied  until  no  signal  is  heard 
in  the  phone.  With  this  adjustment  we  have 


(9) 


Flowing  through  the  potentiometer  there  is  a  current  i,  which  gives 

a  drop  between  grid  and  fila- 
ment =  7>i  =  Eg.  If  the  alter- 
nating voltage  Eg  is  impressed 
on  the  grid  of  a  vacuum  tube 
it  will  produce  an  alternating 
current  in  the  plate  circuit, 
I P.  Of  course  the  actual  plate- 
circuit  current  is  not  alter- 
nating, it  is  pulsating;  this 

pulsating  current  may  be    re- 
FIG.  49.— An  arrangement  of  apparatus  for  con-   solved   into    &    gteady     current 
veniently  measuring  the  ju0  of  a  tube  as  well  as    T  ,. 

the  alternating  current  resistance  of  the  output    7<"    and     an     alternating     cur- 
circuit,  rent   Ip.      The   current    IOP   is 

produced  by  the  steady  values 

of  Eg  and  Ep  and  the  alternating  current  Ip  is  caused  by  the  variations 
in  Eg. 

The  magnitude  of  this  current  Ip  can  be  calculated  by  remembering 
that  a  voltage  Eg  in  the  grid  circuit  is  equivalent  to  a  voltage  ^Eg  in 
the  plate  circuit.  This  voltage,  noEg,  will  cause  an  alternating  current 


to  flow  in  the  plate  circuit  which  is  equal  to 


Rp-\-R 


through  the  resistance  R  must  give  a  drop  equal  to 


This  current  flowing 


and  if  there  is 


RP+R 
no  signal  heard  this  drop  must  equal  that  across  r2  (which  is  equal  to 

Eg—j  when  a  balance  is  obtained.     We  therefore  have, 

R 


Solving  this  equation  for  Rv  we  get  the  relation  given  in  Eq.  (9)  above. 


MEASUREMENT  OF   AMPLIFICATION   CONSTANT 


427 


In  case  the  resistance  R  does  not  permit  a  balance  to  be  obtained,  it 
being  too  small,  the  ratio  of  —  can  be  suitably  altered. 

The  relation  between  IP  and  Eg  is  not  a  linear  one  and  it  is  therefore 
evident  that  RP  must  vary  throughout  the  cycle  of  change  in  Ett.  The 
value  of  RP  is  therefore  represented  correctly  only  by  a  constant  (the 


1.0  1.10 

Value  of  filament  current 


1.20 


1.30 


1.40 


pIG  50. — Value  of  ^o  of  a  small  amplifying  tube,  obtained  by  the  scheme  outlined  in 
Fig.  49;  this  shows  no  to  be  nearly  independent  of  the  filament  current. 

value  of  which  we  call  RP)  and  a  series  of  harmonic  terms;  these  harmonic 
terms  become  more  pronounced  as  Eg  is  varied  through  wider  ranges. 

In  the  measurement  of  RP  by  the  method  outlined  above  it  will  be 
found  that  complete  silence  cannot  be  obtained  at  the  balance  point;  the 
note  heard  in  the  telephone  is  complex  and  only  the  fundamental  note 
can  be  balanced.  A  balance  will  generally  be  most  easily  obtained  if 
comparatively  low  values  of  Eg  are  used,  say  not  more  than  0.1  volt; 
moreover  it  will  be  found  that  the  value  obtained  for  RP  varies  with  Eg 
becoming  greater  for  high  values,  as  explained  on  p.  499. 

The   resistance   of   the   input   circuit  (grid  filament)  for  continuous 


428 


VACUUM   TUBES  AND   THEIR  OPERATION  [CHAP.  VI 


current  is  practically  infinite  for  all  values  of  negative  voltage;  the  cur- 
rent taken  by  the  grid  of  the  average  tube  when  the  grid  is  at  lower  poten- 
tial than  any  part  of  the  filament  is  of  the  order  of  one  microampere  or 
less.  With  a  positive  grid  the  current  to  the  grid  varies  approximately 
as  the  square  of  the  grid  potential.  When  the  grid  and  plate  are  at  the 
same  positive  potential,  the  two  currents  are  of  the  same  order  of  magni- 
tude (see  Figs.  35,  32,  and  29),  so  that  the  grid-filament  resistance  Rg 


FIG.  51. — A  suitable  bridge  arrangement  for  making  high-frequency  measurements; 
with  the  two  lower  arms  open  the  condensers  Ca  and  C&  serve  to  balance  out  spurious 
capacities  in  arms  Ri  and  Rz. 

is  about  the  same  as  the  plate-filament  resistance  Rp.  It  goes  through 
the  same  kind  of  changes  with  respect  to  filament  current,  grid  voltage,  etc., 
as  does  Rp.  It  is  to  be  noted  from  the  curve  sheets,  however,  that  whereas 
an  increase  of  Eg  decreases  Rp  an  increase  in  Ep  causes  an  increase  in  Rg. 

To  measure  the  alternating  current  input  resistance,1  a  scheme  such 
as  that  illustrated  in  Fig.  49  is  not  directly  applicable;  for  any  ordinary 
scheme  of  measurement  a  transformer  will  be  required  to  decrease  the 
grid  circuit  resistance  to  a  value  readily  measured. 

The  author  has  used  a  bridge  for  measuring  the  characteristics  of  the 
input  circuit  of  various  tubes,  the  measurement  being  made  at  50,000 

1  See  page  443  for  the  effect  of  this  input  resistance  on  the  tuning  of  the  receiver 
circuit. 


RESISTANCE   OF  INPUT  CIRCUIT 


429 


cycles.  The  scheme  used  is  illustrated  in  Fig.  51;  the  same  setting  of 
the  bridge  permitted  the  measurement  of  both  capacity  and  resistance 
of  the  tube  input  circuit.  The  50,000-cycle  power  was  supplied  to  the 
bridge  by  wire  A,  the  other  side  being  grounded.  The  condensers  Ca 
and  Ct,  are  adjusted  to  balance  the  bridge  when  the  (3)  and  (4)  arms  are 
open,  to  neutralize  any  spurious  capacity  in  the  bridge  ratio  arms  and 
are  left  set  after  once  being  balanced  (unless  ratio  is  changed).  Suitable 
high-resistance  leaks  are  shunted  across  Ci  and  €2,  these  resistances  being 
free  from  appreciable  distributed  capacity.  Certain  precautions  have 
to  be  observed  in  using  such  a  bridge  as  noted  in  an  article  by  the  author 
in  the  Proc.  I.R.E.1 


/ 

/ 

Ti 

TO 

V.T 

.1 

) 

c 

oncl 

act 

met 

vs 

If 

/ 

EC 

=-.o 

5Efl 

=0.2 

EP 

=18 

j 

I 

1 

1 

7 

7 

/ 

/ 

/ 

./ 

1 

/ 

„ 

^ 

.3  .4  .5  .6  .7  .8  .9  1.0          1.1          1.2 

Filament  Current 

FIG.  52. — Variation  of  input  circuit  conductance  with  filament  current. 

With  suitable  values  of  €2  and  #4  the  bridge  is  balanced  with  S  open, 
the  values  of  C2  and  R*  being  recorded.  When  S  is  closed  the  balance 
is  destroyed,  due  to  the  capacity  and  conductance  of  the  tube  input  cir- 
cuit; by  properly  decreasing  C2  and  increasing  R±  the  balance  may  be 
again  obtained.  The  total  capacity  and  conductance  in  the  (4)  arm 
must  now  be  the  same  as  when  S  was  open,  so  that  the  capacity  of  the 
input  circuit  is  at  once  obtained  as  the  difference  in  the  two  settings  of 
€2',  from  the  two  values  of  R±  the  conductance  of  the  input  circuit  can 
be  readily  calculated. 

1  "  Some  notes  on  vacuum  tubes,"  Proc.  I.R.E.,  Vol.  8,  No.  3,  June,  1920. 


430 


VACUUM   TUBES   AND   THEIR  OPERATION 


[CHAP.  VI 


In  Figs.  52-55  are  shown  the  variation  in  the  input  circuit  of  a  small 
detecting  tube  rated  at  1.1  amperes  filament  current  and  20-40  volts  in 
the  plate.  Unless  the  tube  is  defective  the  conductance  is  practically 
zero  until  about  0.8  ampere  is  used  for  heating  the  filament.  It  then 
rises  rapidly  until  with  normal  filament  current  the  conductance  is  about 
12  micromhos,  showing  an  input  resistance  of  about  80,000  ohms.  The 
values  of  Ep  and  E0  used  are  noted  on  the  curve  sheet. 

In  Fig.  53  is  shown  the  variation  of  the  input  conductance  as  plate 
voltage  was  varied;  this  decrease  in  conductance  with  increasing  plate 


M  rfJ"  cs  <x  Q  tt>_  4*  a  cc  g 
Coaduetauce  in  10  mho 

TV 

f)O 

V. 

Cc 

nduc 

an 

ce 

vs  PMte 

volts 

\ 

=  1, 

0 

E(T 

;  — 

35 

E«T 

0.2 

\j 

\ 

Sq 

^ 

S 

X 

N 

^*^ 

V, 

X 

•^ 

X 

v 

\ 

^ 

"v. 

\, 

v^ 

^ 

^•5 

fc 

\ 

L 

•^ 

-^. 

-•*-, 

--€ 

^ 

—  ^ 

•  —  , 

0                    5                   10152025303540 
Plate  volts 

FIG.  53. — Variation  of  input  circuit  conductance  with  plate  voltage. 

potential  could  have  been  predicted  from  inspection  of  curves  such  as 
given  in  Fig.  29.  In  Fig.  54  is  shown  the  variation  in  input  conductance 
as  the  grid  is  made  more  negative,  and  in  Fig.  55  is  shown  the  effect  of 
the  magnitude  of  the  alternating  voltage  impressed  on  the  grid  for  testing. 
It  is  evident  from  the  four  curves  given  above  (which  are  all  for  the 
same  tube)  that  if  the  input  resistance  of  a  tube  is  to  be  kept  high  the  grid 
must  at  all  times  be  negative  (with  respect  to  the  negative  end  of  the 
filament).  For  the  tube  the  characteristics  of  which  are  given  above, 
the  grid  should  normally  be  negative  about  0.5  volt  more  than  the  maxi- 
mum value  of  the  voltage  to  be  impressed  on  the  input  circuit.  The 


RESISTANCE   OF   INPUT   CIRCUIT 


431 


resistance  of  the  input  circuit,  as  one  component  of  the  impedance  of  the 
input  circuit,  is  of  great  importance  if  the  tube  is  to  be  used  as  detector 


Type 


1.10 


V.T 


0.2 


18 


1.0 


.9 


.8 


.2 


.1 


.7  .6  .5  A  .3 

Value  of  Ec  (negative) 

FIG.  54. — Variation  of  input  circuit  conductance  with  grid  potential. 


Type  V  T.  1 


1.10 


=-.05    E0=20 


.1 


.2 


.8 


1.0 


3  .4  .5  .6  .7 

Value  of  E0(etfective) 

FIG.  55.  —  Variation  of  input  circuit  conductance  with  amplitude  of  voltage  impressed 

on  the  input  circuit. 

or  amplifier;  if  the  tube  is  to  be  used  as  detector  the  input  circuit  resist- 
ance may  very  seriously  affect  the  selectivity  of  the  receiving  circuit, 
because  of  its  damping  effect  on  the  signal. 


432 


VACUUM   TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


Capacity  of  the  Input  Circuit  of  a  Three-electrode  Tube. — It  would 
seem  as  though  the  capacity  (electrostatic)  of  a  vacuum  tube  is  so  small 
as  to  be  negligible,  but  such  is  far  from  the  truth;  the  internal  capacity 
of  a  tube  may  have  very  great  effect  on  its  operation,  especially  at  high 
frequencies.  There  are  three  capacities  to  be  considered,  filament  to 
grid,  grid  to  plate,  and  grid  to  plate  and  filament  when  connected  together. 
Part  of  the  internal  capacity  is  in  the  actual  working  parts  of  the  tube, 
(filament,  grid,  and  plate)  but  a  lot  of  it  is  in  the  "  lead  in  "  wires,  where 
they  come  close  together  in  the  seal.  The  base  into  which  the  tube  fits 
also  has  an  appreciable  capacity. 

In  the  accompanying  table  are  shown  the  values  of  capacities  for  several 
types  of  tubes  at  present  used,  the  tubes  having  the  following  ratings : 


No. 

Filament 
Current. 

Plate 
Voltage 

Plate 
Current. 

Type  of 
Filament. 

Intended 
Service. 

1 

1.1 

20-40 

6X10~4 

Oxide 

Detector    and 

Amplifier 

2 

1.1 

20-40 

4X10~4 

Tungsten 

Detector   and 

Amplifier 

3 

1.30 

130 

7X1Q-4 

Oxide 

Amplifier 

4 

1.75 

350 

5X10-2 

Tungsten 

Power 

5 

1.35 

300 

4X10-2 

Oxide 

Power 

6 

6.5 

500 

15X10-2 

Tungsten 

Power 

7 

3.6 

1000 

25X10-2 

Tungsten 

Power 

The  capacity  of  these  tubes  was  measured  in  the  bridge  shown  in  Fig. 
51,  at  50  kilocycles  and  the  results  were  as  follows,  the  capacities  being 
in  10-12  farads: 


No.  1. 

No.  2. 

No.  3. 

No.  4. 

No.  5. 

No.  6. 

No.  7. 

Grid  to  filament,  plate  free  

10.4 

6.4 

6.8 

5.6 

7.6 

8.0 

55.6 

Grid  to  plate,  filament  free  

14.4 

4.4 

7.6 

3.0 

8.4 

8.0 

22.0 

Grid  to  plate  and  filament  these 

being  connected  together 

17  0 

7  2 

12  4 

7  2 

11.2 

10.2 

69.6 

It  will  be  noticed  that  the  capacity  of  grid  to  plate  and  filament  is 
not  equal  to  the  sum  of  the  other  two  capacities;  this  is  due  to  the  "  over- 
lapping "  of  the  fields  of  the  grid-filament  condenser  and  the  grid-plate 
condenser.  In  Fig.  56  is  shown  a  possible  arrangement  of  the  "  seal -in  " 
wires;  the  capacity  from  G,  to  P  and  F  in  parallel,  involves,  besides  the 
capacity  inside  the  tube,  the  capacity  of  the  wires,  a,  6,  c,  and  d.  Such 
an  arrangement  will  not  give  a  capacity  from  d  to  a,  6,  and  c,  equal  to  the 
sum  of  the  capacity  from  d  to  c  and  6,  and  that  from  d  to  a. 


CAPACITY  OF  INPUT  CIRCUIT 


433 


GAAAAA/WV 


\ 


Now  when  a  tube  is  being  used,  for  whatever  purpose,  the  plate  and 
filament  are  connected  together  through  the  B  battery  and  whatever 
external  impedance  is  introduced  in  the  plate  circuit,  and  the  input  cir- 
cuit is  from  grid  to  filament;  it  is  therefore  evident  that  the  capacity 
of  the  input  circuit  is  that  between  the  grid  as  one  plate  of  the  condenser 
and  the  plate  and  fila- 
ment connected  together 
as  the  other  plate  of  the 
condenser. 

From  the  values  given 
in  the   above   table   the 
input     circuit      capacity   FIG.  56. — Possible  arrangement  of  the  wires  of  a  three- 
of   the    average    tube    is  electrode  tube  where  they  go  through  the  press. 

small  enough  to  be  neg- 
lected, and  it  very  frequently  has  been,  judging  from  the  values  of  capac- 
ities used  in  certain  amplifying  sets.  But  the  values  of  capacity  of  the 
input  circuit  previously  given  are  what  the  author  has  called  the 
"  geometrical  capacity  "  of  the  input  circuit;  the  actual  capacity  is  very 
different  from  the  values  given, 

In  practically  all  circuits  involving  the  use  of  a  vacuum  tube  it  is 
required  to  have  an  impedance  of  some  sort  in  the  plate  circuit;    this 

impedance  may  be  a  resist- 
ance, a  choke  coil,  or  the 
primary  winding  of  a  trans- 
former, and  the  value  Of  this 
impedance  is  generally  of  the 
same  magnitude  as  the  a.c. 
resistance  of  the  plate  circuit 
of  the  tube,  RP,  or  somewhat 
greater. 

When  such  an  impedance 
is  used  in  series  with  the  B 
FIG.  57.— Forms  of  plate  current  and  plate  potential   battery  the  voltage    on   the 
when  a  sine  wave  of  voltage  is  impressed  between      ^     ^     varies    when     the 
the  grid  and  filament.     When  the  resistance  in  the   p  . 

plate  circuit  is  very  high  the  fluctuation  in  plate  Sri(l  voltage  Effis  varied  and 
potential  is  nearly  ^  times  as  great  as  the  volt-  the  amount  of  fluctuation  in 
age  impressed  on  the  grid.  Ep  is  generally  much  greater 

than  Eg.      If  an  impedance 

is  used  in  the  plate  circuit,  which  is  very  high  compared  to  the  tube 
resistance,  the  fluctuation  of  EP  is  nearly  equal  to  fjioE0.  It  is  always 
somewhat  less  than  this  value,  and  we  put  it  equal  to  nEff  where  ju  lies 
between  zero  and  /JLQ,  depending  on  the  plate  circuit  impedance. 

Let  us  suppose  a  resistance,  R,  used  in  the  plate  circuit;    it  is  at  once 


•i,  -*-P 


434  VACUUM  TUBES  AND  THEIR  OPERATION  [CHAP.   VI 

evident  that  as  Eg  increases,  increasing  thereby  /„,  Ep  must  fall  because 
of  the  increased  value  of  IpR.  The  forms  of  Egj  Ip  and  E,,  are  then  as 
shown  in  Fig.  57;  when  the  grid  voltage  rises  (with  respect  to  the  fila- 
ment) the  plate  voltage  falls,  and  the  actual  plate  voltage  is  represented 
by(Eop-ipR)  =(E0p—^E0  sin  pt},  where  E^sin  pt  is  the  voltage  impressed 
between  the  grid  and  filament,  ip  is  the  instantaneous  value  of  Ip  sin  pt,  the 
resulting  fluctuation  in  plate  current,  and  Eop  is  the  value  of  the  plate 
voltage  when  Ea  is  zero. 

We  have  then  to  consider  the  charging  current  taken  by  the  grid 

F when  acted  upon  by  an  alter- 

c  EO  1    nating  voltage    E0t  the   con- 

G/WWVXVWVW^ -T* denser    CG~F   beinS     charged 

CQ  (0*i)e  @  by  voltage    E0  and  the    con- 

p i lAAAMAAAAAA/     denser  CG-P  in  parallel,  being 

R  charged  to    a   voltage  (/*+!) 

FIG.  58.— The  circuit  impressing  the  voltage  Eg  to  ^>  as  shown  in  Fig.  58.  The 
the  input  circuit  must  furnish  enough  current  to  factor  (/x-f-l)  occurs  because 
charge  the  condenser  CG-F  to  a  voltage^ and  when  the  grid  voltage  rises 
the  condenser  CO-P  to  a  voltage  (M+l)  E9.  with  regpect  to  the  filament, 

an  amount  Eff,  the  plate  volt- 
age falls,  with  respect  to  the  filament,  by  an  amount  ^E0;  it  therefore  falls 
with  respect  to  the  grid,  an  amount  (^-\-\}Eg. 

The  amount  of  charging  current,  therefore,  which  must  be  furnished 
by  the  input  circuit  is  given  by 


from  which  the  effective  capacity  of  the  input  circuit  is  found  to  be 

(10) 


Thus  the  effective  capacity  of  the  input  circuit  is  not  only  much  greater 
than  the  geometrical  capacity,  but  it  varies  with  any  factors  which  affect 
Hj  the  voltage  amplification  factor  of  the  tube  and  circuit. 

Due  to  the  mutual  capacity  of  the  grid-filament  condenser  and  grid- 
plate  condenser,  and  also  to  the  fact  that  the  two  voltages  Ep  and  Eg 
are  not  exactly  180°  apart,  the  capacity  of  the  input  circuit  of  a  tube 
will  actually  be  somewhat  less  than  that  predicted  from  Eq.  (10). 

This  mutual  capacity  of  the  two  condensers  brings  in  another  very 
interesting  phenomenon:  the  field  of  the  grid-plate  condenser  may  so 
react  on  the  grid-filament  condenser  as  to  give  a  voltage  in  this  condenser 
in  phase  with  the  impressed  e.m.f.  of  this  condenser  (i.e.,  the  e.m.f. 
impressed  on  the  input  circuit)  so  as  to  give  the  input  circuit  a  negative 
conductance.  Such  an  effect  would  result  in  the  plate  circuit  reacting 


CAPACITY   OF  INPUT  CIRCUIT 


435 


on  the  input  circuit  to  augment  any  voltage  impressed  on  the  input  cir- 
cuit. 

Using  the  bridge  scheme  illustrated  in  Fig.  51,  the  capacities  and  con- 
ductances of  the  input  circuits  of  several  of  the  tubes  tabulated  on  p.  432 
were  measured  at  50,000  cycles.  In  Fig.  59  are  shown  the  capacity  and 


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1  1 

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10 


20 


30  40  850 

Plate  circuit  resistance  in  10  ohms 


70 


FIG.  59. — Capacity  and  conductance  of  tube  VT  1  as  the  resistance  in  the  plate  circuit 
is  varied;  the  /j.  of  the  tube  is  shown  also,  so  that  the  dependence  of  capacity  upon 
/x  may  be  noted. 

conductance  of  tube  No.  1  with  normal  conditions  of  plate  voltage,  filament 
current,  etc.,  as  the  external  plate  circuit  resistance  was  varied;  on  the 
same  curve  sheet  is  shown  the  value  of  the  voltage  amplification  factor 
of  the  tube  for  the  various  plate  circuit  resistances.  It  is  seen  that  the 
capacity  of  the  grid  to-ground  circuit  (same  as  input  circuit,  because 


436 


VACUUM   TUBES  AND   THEIR  OPERATION 


[CHAP.  VI 


the  filament  is  generally  grounded)  increases  from  17/uM/  (micro-micro- 
farads) to  71  MM/  as  the  plate  circuit  resistance  was  increased  from  zero 
to  80  kilohms. 


80 
70 
60 

to 

'3 

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K[\  "T 

^-^ 

^-  —  • 

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<X 

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/* 

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40  50 

Plate  circuit  reactance  in  10  ohms 


60 


70 


80 


FIG.  60. — Capacity  and  conductance  of  the  input  circuit  of  detector  tube  VT  1,  as  the 
plate  circuit  reactance  is  varied.  Note  that  the  input  conductance  is  positive 
throughout  a  certain  range  of  the  reactance. 


As  the  capacity  CG-F  of  this  tube  was  10.4,  and  the  capacity  CG-P 
was  14.4  wf,  and  the  value  of  /z  is  4.65  for  #=80  kilohms,  it  might  be 
expected  that  the  input  capacity  would  be  equal  to  (10.4+ (4.65+ 1)14.4) 


CAPACITY   AND   CONDUCTANCE   OF   THE   INPUT   CIRCUIT      437 


=  91.6  MM/-     The  discrepancy  between  the  measured  and  predicted  values 
is  undoubtedly  due,  in  part,  to  the  mutual  capacity  of  CG-F  and  CG-p. 

The  conductance  of  the  input  circuit  was  positive  for  all  values  of  plate 
circuit  resistance  and  gradually  increased  as  R  was  increased. 

In  Fig.  60  are  shown  the  capacity  and  conductance  for  the  same  tube, 
the  plate  circuit  impedance  being  an  inductance  with  a  reactance-resist- 
ance ratio  between  25  and  50.  In  this  case  the  increase  in  capacity  is 
greater  than  when  an  equal  amount  of  resistance  was  used  in  the  plate 
circuit.  Thus,  with  a  reactance  in  the  plate  circuit  of  50  kilohms  the 
input  circuit  has  a  capacity  of  82  MM/,  whereas  a  resistance  of  50  kilohms 
gave  an  input  capacity  of  only  65  MM/-  This  difference  in  behavior  of 
reactance  and  resistance  is  due  to  the  fact  that  the  M  of  the  circuit  is 
greater  in  one  case  than  in  the  other,  as  will  be  explained  later. 

That  any  capacity  present  between  the  grid  and  plate,  and  which 
is  not  in  the  field  of  the  grid-filament  condenser,  is  increased  by  the  factor 
(M+!)  was  proved  by  actually  connecting  a  capacity  of  20  MM/  across 
the  plate-grid  terminals  of  the  tube  and  noting  the  increase  in  the  effective 
capacity  of  the  input  circuit,  the  M  of  the  circuit  being  4.2.  The  capacity, 
of  the  input  circuit  increased  by  102  MM/>  whereas  calculation  would 
make  it  increase  by  (4.2+1)  X20;  or  104  MM/- 

The  conductance  of  the  input  circuit  of  the  tube  was  negative  through- 
out a  certain  range  of  plate  circuit  reactance,  thus  indicating  transfer 
of  power  from  the  plate  circuit 
back  to  the  grid  circuit,  with  no 
other  coupling  between  the  grid 
and  plate  circuits  than  what  ex- 
isted in  the  tube  itself.  This 
curve  shows  that  the  three  elec- 
trode tube  is  not  inherently  a 
"  one-way  repeater/'  as  has  been 
commonly  supposed;  the  output 
circuit  does  control  the  input 
circuit  to  an  appreciable  extent,  FIG.  61. -In  such  a  circuit  as  this,  with  effi- 


cient  coils  used  in  both  circuits,  with  suit- 
able values  of  the  capacities  the  tube  will 
maintain  itself  in  an  oscillatory  state,  due 
to  the  negative  conductance  as  shown  in 
Fig.  60. 


sufficient  in  fact  to  maintain  the 
tube  in  operation  as  a  generator 
of  alternating-current  power  when 
it  is  connected  to  the  proper  cir- 
cuit. If  the  grid  circuit  and  plate 

circuit  are  each  tuned  to  the  same  frequency,  as  indicated  in  Fig.  61, 
the  tuning  condensers  are  sufficiently  small  (and  the  coils  fairly  efficient), 
the  coupling  of  the  two  circuits  inside  the  tube  may  be  sufficient  to 
maintain  the  tube  in  the  oscillating  state,  alternating  currents  flowing 
in  circuits  L&i  and  L\C\. 


438 


VACUUM  TUBES  AND  THEIR  OPERATION  [CHAP.  VI 


In  Figs.  62-66  are  shown  the  characteristic  curves  of  some  of  the 
other  tubes  tested.  It  is  seen  that  the  same  general  shape  holds  for  all 
three  electrode  tubes,  the  difference  being  one  of  degree  only.  The 
capacity  of  the  grid-ground  circuit  of  the  ordinary  tube,  when  it  is  oper- 
ating with  the  normal  amount  of  resistance  (or  reactance)  in  the  plate 
circuit,  is  from  five  to  ten  times  as  much  as  the  geometrical  capacity  of 


| 

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100 

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140 
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10 


30        40 


50        60        TO        80        90       100      110       120       130      140       150 
Plate  circuit  resistance  in  10 ;1  ohms 


FIG.  62. — Variation  in  conductance  and  capacity  of  the  input  circuit  of  a  telephone 
repeater  tube  as  plate  circuit  resistance  is  varied. 

the  circuit,  and  the  amount  of  this  increase  is  controlled  principally  by 
the  capacity  between  the  grid  and  plate. 

As  has  been  pointed  out  the  characteristics  of  the  input  circuit  of  a 
tube  depend  upon  the  relative  phases  of  the  input  voltage  and  the  voltage 
variation  between  the  plate  and  filament.  As  this  phase  relation  will 
evidently  depend  upon  the  kind  and  amount  of  reactance  in  the  external 


CAPACITY  AND  CONDUCTANCE   OF  INPUT  CIRCUIT 


439 


portion  of  the  plate  circuit  we  may  expect  the  input  characteristics  to 
vary  with  the  input  frequency  because  this  will  determine  the  reactance, 
other  things  being  constant.  This  effect  has  been  investigated  theoretic- 


130 
120 
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10                   20                  30                  40                  50                   60 

Plate  circuit  reactance  in  10  ohms 

FIG.  03. — Curves  similar  to  those  of  Fig.  62,  the  plate  circuit  having  a  variable  react- 
ance instead  of  resistance. 

ally  by  Ballantine,1  who  shows  that  for  resistive  plate  circuit  the  effective 
input  capacity  decreases  with  an  increase  in  frequency  and  the  input 
conductance  increases  with  an  increase  in  frequency.  For  reactive  plate 
circuit  the  effect  of  frequency  may  be  to  either  decrease  or  increase  the 
1  Stuart  Ballantine,  "The  Thermionic  Amplifier,"  Physical  Review,  Vol.  XV,  No.  5. 


440 


VACUUM  TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


input  circuit  constants,  depending    upon  the  amount  of  the  reactance 
used. 

Operation  of  Three-electrode  Tube  as  Detector  of  Damped-wave 
Signals.  Grid  Condenser.  Leak  Resistance.  Normal  Grid  Poten- 
tial.— Any  detector  of  high-frequency  currents  must  in  some  way  cause 
low-frequency  pulsations  of  current  through  the  telephones  when  the 


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12        13        14        15        16 


Resistance  in  plate  circuit  in  10  ohms. 

FIG.  64. — Variation  in  conductance  and  capacity  of  the  input  circuit  of  a  small  power 
tube  (VT-2)  as  plate  circuit  resistance  is  varied. 

device  itself  is  actuated  by  high-frequency  currents.  The  frequency  of 
the  low-frequency  pulsations  is  fixed  by  the  number  of  damped-wave 
trains  arriving  at  the  antenna  per  second  in  case  of  reception  of  a  signal 
from  a  spark  station,  and  is  fixed  by  local  conditions  when  receiving  from 
a  continuous  wave  station.  The  case  we  shall  consider  in  this  section 
is  for  spark  signals  only;  damped-wave  trains  of  the  form  shown  in  Fig. 
67  are  to  be  detected  by  the  three-electrode  tube.  The  time  between 


THREE  ELECTRODE  TUBE  AS  DETECTOR  OF  DAMPED  WAVES       441 


wave  trains  A  may  be  from  .005  to  .0005  second;  the  duration  of  a  wave 
train  B  may  be  from  .00001  to  .001  second,  and  the  time  of  one  cycle, 
C,  may  be  from  .0000001  to  .00003  second. 

The  function  of  the  detector  is  to  produce  in  the  telephone,  fluctuation 
of  current,  of  frequency  fixed  by  the  time  A,  as  large  as  possible  with  a 
given  amplitude  of  signal  voltage.  The  scheme  of  connections  used  when 


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Elate  circuit'reactance  in  103  ohms 


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FIG.  65. — Curves  similar  to  those  of  Fig.  64,  the  plate  circuit  having  a  variable  reactance 

instead  of  resistance. 

no  condenser  is  inserted  in  series  with  the  grid  of  the  tube  is  shown  in 
Fig.  68;  the  ground  terminal  of  the  input  circuit  is  generally  connected 
to  the  negative  end  of  the  filament  or  to  some  point  in  the  circuit  at  a 
lower  potential  than  the  negative  end  of  the  filament.  This  is  possible 
by  either  of  the  two  schemes  sketched  in  Fig.  69;  in  (a)  a  resistance  R 
is  inserted  in  the  negative  filament  wire  and  the  potential  of  point  A  is 


442 


VACUUM  TUBES  AND   THEIR  OPERATION 


[CHAP.  VI 


thus  lower  in  potential  than  the  negative  end  of  the  filament  by  an  amount 
IfR,  generally  one  volt  or  less,  whereas  in  (6)  a  battery  C  is  inserted  in 
series  with  the  input  circuit  to  properly  lower  the  grid  potential.  In 
case  a  careful  adjustment  of  this  potential  is  desired  (generally  not  neces- 


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4          5          6          7          8          9         10        11 
Plate  circuit  reactance  in  10 3  ohms 


12       13 


FIG.  66. — Variation  of  conductance  and  capacity  of  the  input  circuit  of  a  large  power 
tube  as  plate  circuit  reactance  is  varied. 


sary)  the  grid  may  be  connected  to  battery  C  through  a  suitable  potenti- 
ometer connection. 

The  reason  for  maintaining  the  grid  at  a  negative  potential  is  evident 
in  looking  at  the  input  circuit  conductance  curves  previously  given;  sup- 
pose the  conductance  of  the  grid  circuit  is  10~5  mhos,  and  the  signal  being 


THREE-ELECTRODE  TUBE  AS  DETECTOR 


443 


received  is  600  meters,  the  tuning  condenser  C\  (Fig.  68)  being  set  at 
200  fji/jf.     A  conductance  of  10~5  mhos  is  equivalent  to  a  shunt  resistance 


i     A    /\    yy    / 

v  v  vv^ 


.  A  A  /\  / 

U    V    V    v/ 


Receiving 
circuit 


detector,  without  use  of  a  con- 
denser in  series  with  the  grid. 


I 

FIG.  67. — Conventional  representation  of  part  of  a  damped  wave  signal. 

of  105  ohms  around  condenser  Ci,  and  this  is  approximately  equivalent 
(by  Eq.  (31)  Chapter  II)  to  a  resistance  of  25.4  ohms  in  series  with  Ci. 
But  such  a  large  resistance  would  materi- 
ally interfere  with  the  selectivity  of  the 
receiving  circuit,  in  fact  would  make  it 
practically  useless  if  there  was  much  in- 
terference; the  resistance  of  the  receiving 
circuit  itself  would  be  only  a  few  ohms, 
perhaps  five. 

The  characteristics  of  the  tube  being 
as  shown  in  Fig.  70,  the  normal  grid  po- 
tential being  Eoa,  the  question  is  how 

much  will  the  telephone  current  (Fig.  68)   FlQ    68._Connection  scheme  for 
change  during  the  time    one   of  the  wave       using  a  three-electrode  tube  as 
trains   of  Fig.    67  is  actuating  the  grid. 
By  actually  plotting  the  values  of  plate 
current  for  each  grid  potential  we  get  the 

curve  of  plate  current  shown  by  ip  in   Fig.  70,  while  the   grid  potential 
is  undergoing   the   changes   indicated  by  the  curve  ett.     The  increase  in 

the   average  value   of   the   plate  cur- 
rent is   indicated  by  the  dotted  line 
in  Fig.  70,  and  this  average  increase, 
during    the    time    the   grid   is   being 
excited   by    a    wave    train,    is   what 
determines   the  response  of  the  tele- 
phone diaphragm.     Such  a  use  of  the 
static    characteristic    of    the  tube  is 
permissible  only  if  the  receiving  circuit 
FIG.  69.— Two  schemes  for  maintaining  is  S(>  arranged  that,  as    the    signal  is 
the  average  potential  lower  than  the  received,  the  plate  potential  does  not 
lowest  potential  point  of  the  filament,   appreciably  vary;   this  condition  im- 
plies an  external  plate  circuit  of  im- 
pedance which,  compared  to   the   internal   plate  resistance,  is   negligible 
for  the  frequency  of  the  signal. 


444 


VACUUM  TUBES  AND  THEIR  OPERATION 


[CHAP.  V! 


The  author  arranged  a  tube  circuit  so  that  its  input  voltage  and  plate 
current  could  be  recorded  on  an  oscillogram,  when  a  damped  sine  wave 
of  about  100  cycles  (having  the  general  form  of  an  actual  wave  train  from 
a  highly  damped  spark  station)  was  impressed  on  the  input  circuit;  some 
of  the  films  obtained  are  presented  herewith.  In  Fig.  71  are  shown  the 
input  voltage,  plate  current  and  telephone  current  when  the  grid  was 


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FIG.  70. — Analysis  of  the  action  of  the  three-electrode  tube  as  detector  of  damped  wave 
signals;  assuming  a  certain  variation  in  grid  potential  the  resulting  fluctuation  in 
plate  current  can  be  plotted  from  the  plate  current,  grid  potential  curve  of  the  tube. 

made  normally  2.5  volts  negative  with  respect  to  the  filament.  A  large 
capacity  condenser  was  shunted  around  the  coil  representing  the  tele- 
phone of  an  ordinary  receiving  set  so  that  the  "  high-frequency  "  current 
was  not  forced  to  flow  through  this  coil.  This  condenser  charged  up 
during  the  first  part  of  the  wave  train  more  rapidly  than  it  discharged 
through  the  coil,  so  that  its  charge  increased.  Then  as  the  wave  train 


THREE-ELECTRODE   TUBE  AS  DETECTOR 


445 


446 


VACUUM   TUBES  AND   THEIR  OPERATION 


[ClIAP.    VI 


was  reduced  to  zero  by  damping,  the  fluctuations  in  plate  current  ceased 
and  the  condenser  continued  to  discharge  through  the  coil;  this  action 
caused  the  current  through  the  coil  to  lag  somewhat  behind  the  wave 
train  impressed  on  the  grid,  as  is  evident  from  the  film. 

The  signal  used  in  getting  this  film,  as  well  as  those  to  follow,  was  much 
stronger  than  an  actual  radio  signal;  the  change  in  "  telephone  "  current 
in  Fig.  71  is  about  5  milliamperes,  whereas  actually  a  fairly  strong  radio 
signal  does  not  produce  a  change  in  the  telephone  current  of  more  than 
a  few  microamperes.  Figs.  70  and  71  show  the  rectifying  action  of  a  tube 

brought  about  by  the 
increase  in  plate  cur- 
rent being  greater  than 
the  decrease;  the  grid 
was  put  as  such  a 
negative  potential  that 
the  tube  was  operating 
well  down  on  its  char- 
acteristic about  as  in- 
dicated at  A,  Fig.  72. 

The  grid  potential 
was  then  made  positive 
sufficiently  to  rectify 
by  giving  a  greater  de- 
crease then  increase  in 

Grid      o    potential  Plate  current;  Figs.  73, 

FIG.  72.— Form  of  the  plate  current,  grid  potential  curve  74,  an<i  75  show  the 
of  the  tube  used  in  getting  the  films  of  Figs.  71,  73,  74,  75.  forms  of  potentials  and 

currents  when  putting 

sufficient  positives  potentials  on  the  grid  to  bring  it  to  points  B,  C  and  D 
(Fig.  72)  respectively.  It  is  to  be  noted  in  the  film  shown  in  Fig.  75 
that  at  the  highest  positive  grid  potentials  the  plate  current  had  actually 
decreased;  the  amount  of  current  taken  by  the  grid  was  sufficient  to 
bring  about  a  decrease  in  plate  current.  In  each  film  the  zero  lines  of 
potential  and  currents  are  shown. 

An  elementary  analysis  shows  the  efficiency  of  a  tube  for  the  purpose 
of  detector,  (i.e.,  its  rectifying  power)  depends  largely  upon  the  radius 
of  curvature  of  the  plate-current  grid-potential  characteristic.  We  put 

IP=f(E6) 

With  no  signal  IOP  =f(E00)  and  when  the  signal  voltage  AEa  is  impressed 
on  the  grid 


THREE-ELECTRODE   TUBE  AS   DETECTOR 


447 


448 


VACUUM  TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


I 
¥ 


THREE-ELECTRODE  TUBE  AS  DETECTOR 


449 


450  VACUUM  TUBES  AND  THEIR  OPERATION  [CHAP.  VI 


Then  we  have  as  an  approximation 

dl 


If  AEg  is  periodic  the  average  value  of  the  first  term  &E0  -~-  is  zero, 


so  that  the  average  value  of  A7P  becomes  equal  to  the  average  value  of 
Now,  if  kE0  is  a  sine  function  of  time  of  the  form,  E  sin  pt, 


—  -        ™  • 

we  have  for  the  average  value  of  the  change  in  plate  current 


****«#>- 


T?2  fJ2  T 


•  •  • 

T  to  be  taken  as  an  even  number  of  cycles. 

The  increment  in  plate  current  therefore  varies  with  the  square  of  the 
signal  strength,  a  defect  practically  all  rectifying  devices  have.  At  a 

d2! 
point  of  inflection  of  the  Ip—Eg  curve,  j^rf  =0  and  the  rectifying  power 

is  lost.     The  increment  in  plate  current  will  be  negative  or  positive  accord- 

dl  2 
ing  to  the  sign  of  j-pr*,  as  illustrated  in  the  foregoing  films. 

OiEjg 

It  might  seem  that  the  best  point  to  operate  on  the  plate  current 
curve  is  where  the  radius  of  curvature  is  greatest,  but  this  is  not  quite  so. 
If  z  =  radius  of  curvature, 


d2Ip 

dEg2 
so  that 


dE 


It  is  evident  that  if  the  radius  of  curvature  is  not  changing  rapidly  the 
value  of  -JET  has  importance  in  determining  the  rectifying    power,  the 

dUlg 

greater  the  slope  the  greater  is  the  rectifying  action. 

As  shown  in  Figs.  71  and  74  there  are  two  points  where  the  detecting 
power  is  about  the  same,  one  with  negative  grid  and  one  with  positive 
grid  (A  and  C  of  Fig.  72).  The  negative  grid  is  to  be  preferred  to  the 
positive,  because  of  the  high  conductance  of  the  input  circuit  with  a  posi- 
tive grid,  and  consequent  excessive  damping  of  the  receiving  circuit  as 
explained  on  p.  443. 

The  curve  of  Fig.  70  is  obtained  by  maintaining  plate  voltage  constant  ; 
if  there  is  a  high  resistance  or  reactance  in  series  with  the  B  battery,  the 


ACTION  OF  GRID   CONDENSER  451 

effect  is  to  straighten  out  the  characteristic  curve,  and  so  decrease  the 

dl  2 
value  of  -7—5  throughout  the  whole  extent  of  the  curve  as  shown  by  the 

(l£jg 

dotted  line  curve  in  Fig.  72.  The  reactance  of  a  pair  of  phones,  for  radio 
frequency  current  may  be  very  high,  hence  the  effect  just  mentioned 
might  exist;  to  eliminate  it  a  condenser  should  be  used  in  shunt  with  the 
phones,  thus  furnishing  a  low  impedance  path  for  the  high-frequency 
current  and  so  maintaining  the  plate  voltage  essentially  constant  as  the 
grid  potential  fluctuates.  In  Figs.  71,  73,  74,  and  75,  a  condenser  "  by-pass  " 
around  the  phones  was  used,  its  impedance  for  the  frequency  used  was 
very  much  lower  than  that  of  the  phones,  so  that  practically  all  of  the 
high-frequency  pulsations  took  place  through  the  condenser,  the  telephone 
current  changing  only  as  the  average  value  of  the  plate  current  decreased. 

Effect  of  Grid  Condenser. — The  average  three-electrode  tube  will 
give  better  rectifying  action  if  the  curva- 
ture of  the  Iff— Eg  curve  is  used  instead  of 
that  of  the  IP—E0  curve.  The  use  of  a 
suitable  condenser  in  series  with  the  grid 
enables  us  to  utilize  the  curvature  of  the 
grid  current  curve;  the  ordinary  connec- 
tion is  shown  in  Fig.  76,  the  resistance  R 
being  about  one  megohm  for  the  average 
tube.  It  is  called  the  "  leak  "  resistance  FlG<  76.— Arrangement  of  three- 

,  ..      -         ..  .„    ,  ,    .       ,      ,       ,,  electrode  tube  for  detection  by 

and  its  function  will  be  explained  shortly.      use  of  a  condenser  in  series  with 

The  potential  of  the  grid  (when  no  signal      the  grid. 

is  coming  in)    depends  upon  the  value  of 

the  leak  resistance,  the  form  of  the  Ig—Eg  curve,  and  upon  the  potential 

of  the  point  to  which  the  ground  end  of  R  is  connected. 

The  form  of  the  Ig—Eg  curve  for  two  typical  detecting  tubes  is  shown 
in  Figs.  77  and  78 ;  the  curves  are  shown  for  comparatively  large  change 
in  the  grid  potential,  much  larger  than  ever  occurs  when  the  tube  is  being 
used.  Such  tubes  as  those  used  in  getting  the  curves  of  Figs.  77  and  78 
would  give  a  readable  signal  in  the  telephones  with  a  change  of  grid  poten- 
tial of  perhaps  0.03  volt.  As  would  naturally  be  supposed,  the  free  grid 
potential  is  that  for  which  the  grid  current  becomes  zero  in  the  graphs; 
when  free  the  grid  potential  will  decrease  to  such  a  potential  that  no  more 
electrons  tend  fco  accumulate  on  it. 

When  using  such  tubes  in  the  connection  scheme  shown  in  Fig.  76  the 
first  point  to  be  examined  is  the  potential  at  which  the  grid  will  set  itself 
when  no  signal  is  being  impressed  on  the  grid.  It  is  common  practice  to 
connect  the  end  of  resistance  R  to  the  positive  end  of  the  filament,  and 
we  will  so  assume  it  in  finding  the  normal  grid  potential.  In  Fig.  79  is 
shown  the  grid  current  (with  enlarged  scale  for  /?);  it  is  supposed  that 


452 


VACUUM   TUBES  AND   THEIR  OPERATION 


[CHAP.  VI 


the  IR  drop  in  the  filament  is  2  volts.  The  straight  line  A  B  is  drawn 
through  the  point  Eg  =  +2  and  at  an  angle  such  that  cot  0  =  #.  The 
point  C,  where  this  line  intersects  the  Ig—Eg  curve,  fixes  the  normal 
grid  potential  Eog.  This  follows  from  the  fact  that  whatever  current 
flows  to  the  grid  must  return  to  the  filament  (positive  end)  through  the 
resistance  R  and  so  cause  in  this  a  drop  of  IgR;  furthermore  this  drop, 
added  to  the  normal  grid  potential  Eoe,  must  give  a  voltage  equal  to 
+2  volts,  the  potential  of  the  positive  end  of  the  filament. 


x 

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1 

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-.6 


+.4 


+.8        +1.0       +1.2        +1.4     -f-1.6 


-4         —.2  0          +.2 

Grid  potential 
FIG.  77. — Plate  current  and  grid  current  curves  for  a  VTl  detector  tube. 


If  the  leak  resistance  is  106  ohms  cot  0  must  be  106  when  the  scales 
of  potentials  and  currents  are  in  corresponding  units  as,  e.g.,  volts  and 
amperes.  As  the  scale  of  current  in  Fig.  79  is  105  smaller  than  that  of 
potential,  the  angle  4>  in  this  diagram  is  so  drawn  that  cot  0  =  10.  If 
a  leak  resistance  of  only  5  X 105  ohms  were  used,  the  normal  value  of  grid 
potential  E00  would  be  as  shown  at  C',  obtained  by  making  cot  0=5. 

When  an  alternating  e.m.f.  is  now  impressed  on  this  input  circuit, 
the  grid  will  start  to  fluctuate  about  its  normal  value  of  potential,  Eog] 


ACTION  OF  GRID  CONDENSER 


453 


its  potential  will  be  increased  and  decreased  from  the  value  Eog  equally 
for  the  first  cycle.  Due  to  the  form  of  the  Ig—Eg  curve,  however,  the 
increase  in  current,  when  the  impressed  e.m.f .  is  positive,  is  greater  than 
the  decrease  in  current  when  the  impressed  e.m.f.  goes  negative,  and  this 
rectifying  action  tends  to  increase  the  number  of  electrons  accumulated 
on  that  side  to  the  condenser  C  (Fig.  76),  which  is  connected  to  the  grid. 
But  this  accumulation  of  electrons  must  depress  the  potential  of  the  grid 


10 


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VT 


23 


10 


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-.8 


-.6 


+.4         -K6          +.8       -fl.O        +1.2       4-1.4      41.6 


-A          ".2  0          +.2 

Grid  potential 

FIG.  78.  —  Curves  similar  to  those  of  Fig.  77  for  a  supposedly  identical  tube. 


below  its  normal  value,  and  so  cause  a  decrease  in  the  plate  current.  The 
amount  of  this  decrease  in  plate  current  for  a  given  alternating  e.m.f. 
impressed  on  the  input  circuit,  is  a  measure  of  the  efficiency  of  the  tube 
as  a  detector,  so  we  shall  investigate  this  point  more  fully. 

Before  starting  this  analysis  it  is  well  to  point  out  that  whereas  a  tube 
may  detect  by  either  an  increase  or  decrease  in  plate  current  when  no 
grid  condenser  is  used,  with  the  grid  condenser  a  signal  always  produces 
a  decrease  in  plate  current,  never  an  increase. 

At  the  end  of  the  wave  train  the  grid  condenser  C  (Fig.  76)  will  be 


454 


VACUUM  TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


charged  (negatively  on  the  side  connected  to  the  grid)  and  this  charge 
must  leak  off  before  the  next  wave  train  arrives,  otherwise  the  tube  will 
not  respond  to  a  signal  as  well  as  it  should.  The  time  taken  for  the 


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FIG.  79. — A  diagram  for  determining  the  normal  grid  potential  of  a  tube  connected  as  in 
Fig.  76;  the  leak  resistance  is  supposed  connected  to  the  positive  end  of  the  filament 
and  the  IR  drop  in  the  filament  is  assumed  as  2  volts. 

charge  to  leak   off  from  C  depends    upon    the    magnitude    of    C    and 
the    leak    resistance    R,    in    fact,    can     be     calculated     directly    from 
these  two  quantities.       In  a  time  equal   to    RC,    63   per   cent   of   the 
1 1  charge  will   have   leaked   off; 

Ao  1 1 1 1 1        if  the  tube  is  to  operate  effi- 

ciently as  a  detector  therefore 
the  product  RC  must  be  small 
compared  to  the  time  between 
the  successive  wave  trains  of 
the  signal. 

On  the  other  hand,  C  must 
Bo— 1 ' •        be   as  large   as   feasible   and 


FIG.  80. — A  circuit  equivalent  to  the  input  circuit  R  also  must  be  large,  other- 
of  a  detector  tube;  C'  represents  the  effective  wise  a  large  fraction  of  the 
capacity  of  the  input  circuit  and) /r  represents  gi  }  voltage  will  be  used  up 
the  conductance  of  the  input  circuit.  These  . 

quantities  for   different  tubes  were  shown  in   m  C,  and  thus  be  of  no  service 
Figs.  59-66.  in    producing   sound    in    the 

telephones.  The  input  cir- 
cuit of  Fig.  76  may  be  represented  as  in  Fig.  80;  C  is  the  external  con- 
denser used  in  series  with  the  grid,  C'  is  the  capacity  of  grid-to-ground 
inside  the  tube  and  r  is  the  leakage  inside  the  tube  itself.  The  values 


ANALYSIS  OF  ACTION  OF  CONDENSER  455 

of  C"  and  1/r  (tube  conductance)  for  various  tubes  were  given  in  Figs.  59- 
66;  the  impedance  between  D  and  B,  Fig.  80,  is  therefore  calculable 
when  R  is  given.  Designating  this  impedance  by  Zt,  we  then  find  that 
the  voltage  impressed  on  the  grid  of  the  tube  is  equal  to  the  input  voltage 

(across  points  A-B,  Fig.  80)  multiplied  by  the  fraction  —. —  — — ,  the  addi- 
tion and  division  being  carried  out  vectorially.  I Zt-\ — r^J 

In  addition  to  the  features  just  analyzed  we  must  remember  that  the 
impedance  between  points  A-B  is  to  be  kept  high  as  this  input  circuit 
is  connected  directly  across  the  tuning  condenser  of  the  receiving  set. 
With  the  detecting  tubes  commonly  used  (characteristics  about  like  tube 
No.  1,  page  432)  it  seems  that  C  =  5  X  H)-10  and  R  =  106  give  the  best  results. 
For  tubes  having  smaller  internal  capacity  lower  values  of  C  and  higher 
values  of  R  are  better  suited;  thus  the  detecting  tube  shown  at  J,  Fig. 
21,  is  generally  used  with  C  =4X10~10  and  R  =4X106. 

Analysis  of  Detector  Action  with  Grid  Condenser. — Let  the  voltage 
between  the  grid  and  the  negative  end  of  the  filament  (which  we  call 
zero  potential)  be  a,  then 

I00R+Eog  =  a (14) 

where  Ioa  and  Eog  are  the  normal  values  of  grid  current  and  potential 
respectively,  when  no  signal  is  being  impressed. 

When  a  signal  is  impressed  on  the  input  circuit,  the  grid  is  acted  upon 
by  a  voltage  E  sin  pt;  the  grid  current  will  pulsate  in  value  about  its 
normal  value,  but  owing  to  the  form  of  the  Ig—Eg  curve  the  increase  in 
grid  current  is  greater  than  the  decrease,  so  that  there  is  an  average  increase 

E2  d2! 

in  the  grid  current  which  is  equal  to  -  -  -yrrf  as  was  previously  proved  for 

4   atig 

the  plate  current — see  Eq.  (12).  This  increase  in  grid  current  must  pass 
through  the  resistance  R,  so  that  the  equation  for  grid  potential  when 
the  signal  is  being  impressed  is, 

7?2    (12  T 

J-J  \A/       J.   Q       f^       ,          -f~f/  /^     ^  * 

=  a (15) 


Also  we  have  at  E'g,  (being  the  new  average  value  of  grid  potential  when 
signal  is  being  impressed  on  the  grid)  I'g  corresponding  to  E'g  (see  Fig.  81),  l 

T,  T  A    £7      dig 

Ig-Io,-M,^, 

so  that  from  Eqs.  (14)  and  (15),  we  may  get  the  relation, 


1  It  is  to  be  noted  that  when  a  signal  is  coming  in  the  average  grid  potential  is 
decreased  (from  Eg  to  E'0)  although  the  average  grid  current,  flowing  through  the  leak 
resistance,  has  increased.  This  is  due  to  the  curvature  of  the  grid  current  curve,  which 
permits  a  greater  average  grid  current  at  a  lower  average  potential. 


2  d2I 


456  VACUUM  TUBES  AND  THEIR  OPERATION  [CHAP.  VI 

By  combining  terms,  we  get 
I00R-^E0-d 

or  AJ 

So  that 


d2!6 

E2     dE2 


(16) 


_4.^±£ 
R^dE, 


Grid  potential 

FIG.  81. — Change  in  grid  potential  due  to  the  increased  drop  in  the  leak  resistance  when 
a  signal  is  impressed  on  the  tube. 

TTjl 

If  R  is  small  compared  to  -r/,  this  simplifies  to 


E^  dEg2 

T        dig 

dE~g 


(17) 


The  decrease  in  plate  current  caused  by  this  drop  in  grid  potential 
depends  upon  the  shape  of  the  /„—  E0  curve,  or  -j=£     The  real  measure  of 

CiJli  g 

the  detecting  efficiency  of  a  tube  is  therefore, 


dL 


d2Ig 

E2  dE2  dlp 
4     dlff  dEg' 

dEg 


(18) 


ANALYSIS   OF  ACTION   OF  CONDENSER 


457 


It  must  be  remembered  that  E  is  not  the  voltage  impressed  upon  the 
input  circuit  (i.e.,  the  signal  voltage)  but  something  less  due  to  the  drop 


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Grid  Potential 


+.8       +.9     4 1.0 


FIG.  82. — Characteristic  curves  of  two  detector  tubes.  Using  Eq.  (18)  it  is  found  that  to 
change  the  average  plate  current  by  one  microampere  requires  a  signal  voltage  of 
.059  volt  for  tube  A  and  .052  volt  for  tube  B.  Without  grid  condensers  the  tubes 
require  about  three  times  as  much  grid  voltage  for  the  same  change  in  plate  current. 

in  the  grid  condenser.     The  solution  in  Eq.  (18)  supposes  the  signal  has 
persisted  long  enough  for  the  steady  state  to  be  reached ;   if  a  damped  sine 


458 


VACUUM   TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


wave  is  impressed,  the  detection  efficiency  will  depend  upon  the  decre- 
ment, size  of  grid  condenser,  etc.,  as  analyzed  on  p.  461.     The  solution 

d2! 
obtained  in  (18)  also  neglects  the  difference  in  value  of  -rg-|   at   the   two 

grid  voltages  E00  and  E'g. 


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Orid  potential 

FIG.  83. — Even  with  very  low  plate  voltage  and  filament  current  some  tubes  detect 
very  well;  with  half  normal  filament  current  and  a  plate  potential  of  only  1  or 
2  volts  this  oxide  coated  tube  requires  only  about  .3  volt  signal  to  give  one  micro- 
ampere change  in  plate  current. 

In  Fig.  82  are  shown  the  grid  and  pflate  currents  of  two  detecting  tubes 
such  as  were  used  by  the  Signal  Corps.  If  no  grid  condenser  were  used 
with  these  tubes  we  find  (using  Eq.  (12))  that  to  produce  an  increase 


ANALYSIS  OF  ACTION  OF  CONDENSER 


459 


of  1  microampere  in  the  average  value  of  the  plate  current  requires  an 
alternating  voltage  of  0.15  volt  on  the  grid  for  tube  A  and  0.19  volt  for 
tube  B.  These  values  were  calculated  on  the  assumption  that  the  nor- 
mal grid  potential  is  zero,  which  means  that  the  input  circuit  is  connected 
to  the  negative  end  of  the  filament. 

If  the  grid  condenser  were  used  with  these  tubes,  having  leak  resist- 
ances of  1  megohm,  these  leaks  being  connected  to  the  positive  end  of 
the  filaments,  the  normal  grid  potentials  would  be  as  indicated  by  the 
large  circles  on  the  Ig—  Eg  curves  of  Fig.  82.  Using  Eq.  (18)  we  find  that, 


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Grid  potential 


FIG.  84. — With  low  plate  voltages  it  makes  a  great  deal  of  difference  whether  the  grid 
is  connected  to  the  positive  or  negative  end  of  the  filament ;  plate  current  indicated 
by  circles  and  grid  current  by  crosses. 


to  produce  a  decrease  in  the  plate  current  of  1  microampere  for  tube 
A  requires  an  alternating  voltage  on  the  grid  of  0.059  volt  and  for 
tube  B  it  requires  0.052  volt.  Both  of  these  tubes  would  therefore  be 
much  better  detectors  with  grid  condensers  than  without  them,  and  such 
was  found  true  experimentally. 

An  oxide-coated  filament  tube  designed  for  1.1  ampere  in  the  filament 
and  20  volts  on  the  plate  served  quite  well  as  a  detector  with  only  0.6 
ampere  filament  current  and  1  to  3  volts  on  the  plate.  With  the  posi- 
tive end  of  the  filament  forming  the  common  connection  (instead  of  nega- 


460 


VACUUM   TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


tive  end)  curves  of  Ig  and  Ip  were  obtained  as  in  Fig.  83.  With  no  grid 
condenser  and  E  =  2.6  volts,  the  detecting  action  was  much  better  than 
might  be  expected  with  filament  current  and  plate  voltage  so  far  away 
from  their  rated  values.  By  Eq.  (12)  for  curves  A  an  input  voltage  of 
0.28  is  required  to  give  a  charge  of  1  microampere  in  the  average  value 
of  the  plate  current  and  for  curves  B  a  voltage  of  0.34  was  required. 

In  Fig.  84  is  shown  the  great  difference  in  the  form  and  magnitude 
of  Ig  and  Ip  when  the  junction  of  grid-filament  circuit  is  changed  from  the 


10 


-14    -12     -10     -8     -6     -4      -2        0       +  2      +4      +6      48      +10     -1-13     +U 

Grid  potential 

FIG.  85.— Peculiar  characteristics  of  an  old  Deforest  audion  detector;  such  a  tube 
detects  in  very  erratic  fashion,  probably  due  to  the  considerable  amount  of  gas  left 
in  the  tube. 

negative  end  of  the  filament  to  the  positive  end;  the  difference  is  very 
much  exaggerated  here  because  of  the  low  value  of  the  voltage  of  the 
battery  in  the  plate  circuit. 

In  Fig.  85  are  shown  the  characteristics  of  an  old  Deforest  detecting 
bulb,  the  filament  being  at  the  rated  value  for  this  type  of  bulb.  It  will 
be  readily  appreciated  that  such  a  tube  would  act  peculiarly  as  different 
adjustments  were  made.  Thus  with  a  plate  voltage  between  30  and 
50  the  tube  would  not  detect,  with  or  without  grid  conden^r  With 


EFFECT  OF  DECREMENT  ON  DETECTOR  ACTION 


461 


20  volts  in  the  plate  the  tube  gave  very  good  detection  with  or  without 
grid  condenser;  with  ten  volts  on  the  plate  the  tube  gave  fair  detection 
with  grid  condenser  and  none  at  all  without  grid  condenser. 

Effect  of  Frequency  and  Decrement  of  Signal. — The  previous  analyses 
have  not  taken  into  account  the  amount  of  electricity  available  for  charg- 
ing condenser  C;  only  relative  reactances,  etc.,  have  been  considered. 
But  it  is  evident  that  if  the  condenser  is  to  be  charged  the  grid  current 
must  supply  the  electrons  required,  and  it  maybe  that  the  current  is  not 
sufficiently  large  to  do  this,  in  the  short  time  the  signal  is  impressed. 

Suppose  the  signal  voltage  has  the  form  shown  in  Fig.  86;  it  reaches 
its  maximum  in  three  cy- 
cles and  then  rapidly  de- 
creases. If  possible  the 
grid  condenser  C  should  be 
charged  up  to  a  potential 
fixed  by  the  maximum 
value  of  this  signal.  To 
make  the  problem  simple 
we  will  suppose  the  ampli- 


FIG.  86. — In  analyzing  the  effect  of  the  decrement  of 
the  signal  on  the  detecting  action  we  assume  the 
first  three  cycles  of  a  wave-train  have  the  same 
amplitude,  the  maximum  value  of  the  signal  voltage. 


tude  of  the  voltage  to  have 

its  maximum  value  during 

the  first  three  cycles  and  examine  the  possibility  of  the  condenser  C 

having  reached  the  value  of  potential  fixed  by  Eq.  (16). 

If  the  condenser  is  to  have  its  potential  changed  b.y  AEg  the  required 
quantity  of  electricity  is  (A^XC).     The  current  available  for  charging 

E2  d2I0 


the  condenser  is  (very  nearly)  - 

4    ctiv, 

available  a  quantity  of  electricity  q  = 
compared  to  -T^r  we  get  from  Eq.  (16) 


and  for  three  cycles  this  makes 


3TE2  d2Ig 
4     dEa2' 


Now  if  -^  is  negligible 


So,  as  q  = 


we  may  put 


E2  d2I0dEg 
0 ~  4   dE2  dig' 

IffdEff^TE2  d2Ig 
I2  dlg        4     dE2' 


from  which  we  conclude  that  the  largest  condenser  which  can  be  used,  and 
still  be  fully  charged,  is  fixed  by  the  relation  C  =  3  T 


dl. 


dE' 


If  T^  = 

Oililg 


(which  is  about  the  value  obtained  from  Fig.  78,  when 
E0ffis  -0.6  volt)  and  77is2X10-6  (which  is  the  period  of  a  600-meter  wave), 


462 


VACUUM  TUBES  AND  THEIR  OPERATION  [CHAP.  VI 


EFFECT  OF  DECREMENT  ON  DETECTOR  ACTION      463 

the  maximum  value  of  capacity  should  be  10  X10~12  farads.  But  such  a 
low  value  for  C  would  result  in  a  very  small  fraction  of  the  signal  voltage 
being  impressed  on  the  grid,  so  that  a  much  larger  condenser  must  be  used 

and  the  value  of  -77^  must  be  made  larger. 
dH/ff 

By  using  a  lower  value  for  the  leak  resistance,  R,  the  normal  grid 
potential  Eog  may  be  made  higher,  which  will  result  in  a  higher  value  of 

4^ ;  in  Fig.  78  when  Eog  =  0,  ^  =  15  X  10~6.  If  the  decrement  of  the  sig- 
dbjg  dii/ff 

nal  is  low,  we-  may  allow  more  than  three  cycles  for  the  condenser  to  charge 
without  greatly  decreasing  AEg,  because  the  amplitude  of  signal  voltage 
will  still  be  nearly  its  maximum  value. 


FIG.  88. — By  increasing  the  value  of  the  grid  leak  the  form  of  the  plate  current  curve 
may  be  changed;  in  this  film  all  conditions  were  the  same  as  those  of  Fig.  87  except 
the  value  of  the  grid  leak  resistance  had  been  approximately  trebled. 

From  the  foregoing  discussion  it  is  evident  that  the  predetermination 
of  the  best  value  for  C  is  somewhat  involved;  moreover  it  will  be  found 
experimentally  that  C  may  be  varied  over  a  wide  range  without  appreci- 
ably changing  the  efficiency  of  the  tube  as  a  detector,  probably  due  to 
compensation  among  the  different  effects  just  mentioned.  A  large  C 
will  not  charge  completely,  e.g.,  but  it  will  permit  a  greater  fraction  of 
the  input  voltage  to  act  on  the  grid  than  would  a  smaller  one  which  would 
charge  more  completely.1 

The  action  of  the  tube  as  detector  with  grid  condenser  is  well  shown 
in  Fig.  87,  a  film  taken  by  the  author  in  1914.  In  the  upper  part  of  the 
figure  is  shown  the  input  voltage;  the  second  curve  shows  the  plate  cur- 

1  Analysis  also  shows  that  as  the  decrement  of  the  signal  increases  the  most  suit- 
able value  of  grid  condenser  capacity  decreases. 


464 


VACUUM  TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


rent,  having  pulsations  of  the  same  frequency  as  the  signal  voltage,  but 
having  also  a  large  average  decrease  due  to  the  grid  condenser  becoming 
charged;  the  "  telephones  "  (in  this  case  a  coil  of  high  inductance)  were 

shunted     by    a 
large  capacity  so 
that  the  "  high- 
frequency"  fluc- 
tuations in  plate 
current  did  not 
through 
but     the 


Voltage  impressed  on  grid 


Zero 


pass 
them, 


Zero 


Free  grid  potential 


_Free_gjrid_  potential, _  _( &)      1 0  W  -  frequency 

change  in  plate 
current  did  pass 
through  them, 
giving  a  current 
of  the  form 
(c)  shown. 

By  increasing 
the  value  of  the 
leak  resistance 
about  three 
times  the  time 
required  for  the 
grid  condenser- 
to  discharge  was 
increased  and  so 
the  plate  cur- 
rent was  held 
at  its  lowered 
value  for  a 
forms  shown  in 


FIG.  80. — This  diagram  shows  in  (b]  a  correct  representation  of 
the  grid  potential  when  signal  (a)  is  impressed  and  in  (c)  an 
incorrect  representation.  The  average  potential  of  the  grid 
will  not  be  further  depressed  unless  during  the  previous  cycle 
the  grid  is  forced  to  a  potential  higher  than  its  "  free  "  poten- 
tial. In  case  the  grid  leak  is  connected  to  the  positive  end  of 
the  filament  the  potential  of  the  grid  with  no  signal  coming  in 
is  higher  than  the  free  grid  potential  so  that  curve  (6)  might 
possibly  start  from  a  positive  value,  instead  of  the  negative 
value  as  shown. 


longer  interval   of   time;  the   currents   then   had   the 
Fig.  88. 

It  is  to  be  noted  that  the  mean  potential  of  the  grid  can  be  no  longer 
depressed  when  the  fluctuations  in  grid  potential  due  to  the  signal  do 
not  carry  it  to  a  potential  more  positive  than  its  free  potential.  Unless 
its  potential  exceeds  the  free  potential  it  will  not  attract  any  excess  elec- 
trons (i.e.,  more  than  it  attracts  when  no  signal  is  coming  in)  and  hence 
cannot  depress  the  average  potential  of  the  grid.  In  this  respect  many 
writers  have  shown  the  action  of  the  three-electrode  tube  incorrectly; 
in  Fig.  89  curve  (a)  shows  the  voltage  impressed  on  the  grid  due  to  the 
signal  and  in  (6)  is  shown  correctly  the  resulting  grid  potential,  the  aver- 
age potential  being  shown  by  the  dotted  line.  After  the  third  cycle  the 


REQUIREMENTS  FOR  A  GOOD  DETECTING  TUBE  465 

signal  voltage  is  not  of  sufficient  magnitude  to  carry  the  grid  potential 
higher  than  its  free  value;  after  this  time,  therefore,  the  average  grid 
potential  must  rise  due  to  the  accumulated  charge  escaping  through  the 
leak  resistance. 

In  curve  (c)  is  shown  the  grid  potential  as  frequently  given  in  texts; 
the  average  potential  is  shown  as  decreasing  further  even  when,  during 
the  previous  cycle,  the  grid  potential  did  not  rise  as  high  as  its  "  free  " 
value;  this  illustration  is  incorrect. 

The  term  "  accumulative  amplification  "  has  been  used  in  describing 
the  action  of  a  tube  with  grid  condenser,  but  it  is  to  be  noticed  that  there 
is  no  true  amplification;  the  grid  potential  is  in  no  case  depressed  by 
an  amount  in  excess  of  the  amplitude  of  the  signal  e.m.f.,  as  it  is  when  real 
amplification  is  used. 

Measurement  of  Detecting  Efficiency  of  a  Three-electrode  Tube. — 
It  is  possible  to  experimentally  determine  the  detection  coefficient  of  a 
tube  by  such  a  scheme  as  that  originated  by  Van  der  Bijl;1  in  his  treat- 
ment it  is  shown  that  the  strength  of  signal  given  by  the  telephone  varies 
as  the  fourth  power  of  the  voltage  impressed  on  the  grid.  This  follows 
at  once  also  from  Eq.  (12),  page  450,  in  which  it  is  shown  that  the  incre- 
ment of  plate  current  varies  with  the  square  of  the  voltage  impressed 
on  the  grid;  as  the  amount  of  noise  given  off  from  the  telephone  varies 
with  the  square  of  the  current  through  it,  it  is  evident  that  the  noise 
varies  with  the  fourth  power  of  the  grid  voltage. 

Using  a  receiver  which  required  3X10~12  watts  input  to  produce  the 
"  least  audible  signal "  Van  der  Bijl  found  that  the  ordinary  detector 
tube  (without  a  condenser  in  series  with  the  grid,  depending  only  on 
shape  of  plate  current  curve  for  rectification)  required  a  signal  voltage 
of  0.025.  Unless  some  very  radical  change  is  made  in  either  telephone 
receiver  or  detecting  tube,  it  may  be  assumed  that,  for  a  readable  signal, 
it  is  necessary  to  impress  on  the  grid  of  a  detector  a  voltage  (high  frequency) 
of  between  .01  volt  and  .05  volt. 

Requirements  for  a  Good  Detecting  Tube.— Besides  the  necessary 
mechanical  features  of  ruggedness,  ease  of  duplication,  long  life,  etc., 
there  are  certain  electrical  features  which  should  be  embodied  in  a  good 
detecting  tube.  The  present  forms  of  detecting  tubes  use  altogether 
too  much  power  in  heating  the  filament,  and  more  voltage  in  the  plate 
than  should  be  required.  The  excessive  power  used  in  the  filament  has 
two  disadvantages;  the  filament  battery  required  is  much  larger  than 
necessary  and  there  is  altogether  too  much  emission  from  the  filament. 
A  power  consumption  in  the  filament  of  less  than  one  watt  is  feasible, 
and  the  emission  should  not  be  more  than  about  100  microamperes,  the 

1  H.  J.  Van  der  Bijl,  "  On  the  Detecting  Efficiency  of  the  Thermionic  Detector," 
Proc.  I.R.E.,  Dec.,  1919. 


466 


VACUUM   TUBES  AND   THEIR  OPERATION  [CHAP.  VI 


plate  voltage  being  ten  or  less.  Such  a  tube  would  probably  have  an 
alternating-current  resistance  in  the  plate  circuit  of  perhaps  105  ohms,  so 
the  telephones  could  not  be  efficiently  introduced  directly  in  the  plate 
circuit;  a  step-down  transformer  or  another  low  impedance  tube  would 
be  required  to  supply  the  telephones. 

The  advantages  of  using  a  tube  with  comparatively  low  emission  from 
the  filament  come  from  its  limitation  on  the  strength  of  disturbances 
which  may  occur.  Atmospheric  disturbances  constitute  the  present  limit- 
ing condition  of  radio;  irregular  cracks  and  hisses  are  produced  in  the 
phones,  perhaps  hundreds  of  times  louder  than  the  signal  and  so  make 
the  signal  unreadable.  If  these  disturbances  can  be  limited  in  strength, 


(6) 


Grid  potential  Grid  potential 

FIG.  90. — A  detector  tube  having  the  characteristic  shown  in  (6)  is  preferable  to  the  one 
shown  in  (a)  because  of  the  lesser  effect  of  static  interference  in  one  than  in  the 
other. 

so  that  they  are  not  more  than  five  or  ten  times  the  signal  strength,  a 
good  operator  will  read  right  through  them;  with  the  present  tubes  these 
disturbances  may  be  thousands  of  times  as  strong  as  the  signal.  Graph 
(a)  of  Fig.  90  illustrates  the  present  detector  tube;  normal  plate  current 
may  be  500-1000  microamperes  and  the  total  emission  may  be  5000 
microamperes.  A  strong  signal  (such  as  an  atmospheric  pulse)  may 
decrease  the  plate  current  to  zero  or  increase  it  to  5000  microamperes, 
whereas  the  signal  is  probably  not  changing  it  by  more  than  one  or  two 
microamperes.  The  effect  of  strong  disturbing  noises  such  as  static  is 
to  deafen  the  operator's  ear  for  the  weaker  signal. 

If  the  tube  used  for  detector  has  the  characteristic  shown  in  graph 
b  of  Fig.  90,  the  effect  of  stronger  pulses  of  e.m.f.  impressed  on  the  grid 
is  much  less;  the  saturation  current  of  the  tube  does  not  permit  a  large 
increase  of  plate  current,  no  matter  how  high  a  positive  potential  may 


THREE-ELECTRODE   TUBE  AS  OSCILLATOR 


467 


be  impressed  on  the  grid  and  the  reduction  of  the  plate  current  to  zero 
by  a  negative  potential  in  the  grid  cannot  produce  as  great  a  disturbing 
noise  as  for  the  other  tube,  because  the  normal  plate  current  for  tube 
(b)  is  only  1  /20  as  much  as  it  is  for  tube  (a) . 

A  tube  having  the  characteristic  shown  in  (b)  would  probably  not 
be  as  efficient  a  detector  as  tube  (a),  but  this  defect  would  be  remedied 
by  a  suitable  amplification.  Another  advantage  of  tube  (b)  would  be 
its  comparatively  small  internal  capacity,  because  its  parts  could  be  much 
smaller  than  the  present  detecting  tube;  this  feature  alone  would  make 
the  smaller  tube  preferable,  because  the  capacity  of  the  input  circuit  of 
a  tube  is  a  serious  factor  in  the  design  of  amplifiers,  especially  those  used 
for  amplifying  high-frequency  currents. 

The  Three-electrode  Tube  as  a  Source  of  Alternating  Current.  Gen- 
eral Field  of  Application. — A  three-electrode  tube,  if  connected  to  a  cir- 
cuit having  a  natural  period  of  oscillation,  will,  if  certain  conditions  are 
satisfied,  generate  alternating-current 
power  of  the  frequency  fixed  by  the  L 
and  C  of  the  circuit  to  which  it  is  con- 
nected. The  action  is  nearly  analogous 
to  that  of  a  violin  bow;  although  the 
force  and  velocity  of  the  bow  are  essen- 
tially constant  the  peculiar  friction 
between  the  bow  and  string  enables 
the  string  to  absorb  more  power  from 
the  bow  when  string  and  bow  are  mov- 
ing in  the  same  direction  than  is  given 
back  to  the  bow  by  the  string  when  the 
motions  of  bow  and  string  are  in  oppo- 
direction. 


site 


If  the    frictional    force 


Velocity 


violin  string  and  bow,  as  a  function 
of  their  relative  velocities,  the  great- 
er the  difference  in  their  velocities 
the  less  is  the  frictional  force  be- 
tween them.  Putting  resin  on  the 
bow  changes  curve  a  to  curve  b. 


between  string    and  bow  is  plotted  as   FlG-   91.— Frictional  force  between  a 

•      !•  .   A       '11  F  i  • 

a  function  of  the  relative  velocity  of 
the  two,  the  graph  will  have  the  form 
given  in  Fig.  91;  curve  (a)  is  for  the 
bow  without  resin  and  curve  (b)  shows 
the  change  in  this  friction  after  resin 
has  been  put  on  the  bow. 

The  muscles  of  the  arm  actuating  the  bow  constitute  a  source  of  con- 
tinuous power;  it  is  obviously  impossible  for  an  arm  muscle  to  supply 
(directly)  power  to  a  string  vibrating  1000  times  a  second.  The  arm 
supplies  energy  to  the  bow  at  an  essentially  constant  rate,  the  reactions 
between  the  bow  and  string  serve  to  utilize  this  power  to  maintain  the 
string  in  a  state  of  rapid  vibration. 

The  system  which  drives  the  balance  wheel  of  a  watch  is  also  some- 


468  VACUUM   TUBES  AND  THEIR  OPERATION  [CHAP.  VI 

what  analogous;  the  mainspring  furnishes  power  by  a  continuous  force, 
but  the  escapement  system  serves  to  feed  energy  into  the  moving  balance 
wheel  in  such  a  way  as  to  maintain  it  in  a  state  of  oscillation,  the  period 
being  fixed  by  the  mass  of  the  wheel  and  stiffness  of  the  hairspring. 

It  is  to  be  noted  that  neither  the  balance  wheel  nor  violin  string  will 
vibrate  if  the  damping  of  the  oscillating  member  is  too  high;  if  too  much 
friction  occurs  in  the  bearings  of  the  balance  wheel  the  watch  will  stop. 
The  same  effect  exists  in  the  oscillating  tube  circuits  to  be  described  later. 

The  efficiency  of  the  three-electrode  tube  as  a  generator  of  alternating 
current  power  is  normally  rather  low;  in  small  tubes  such  as  used  for  aero- 
plane telephony  the  circuits  are  generally  arranged  to  give  an  efficiency  1 
of  about  25  per  cent,  and  in  the  larger  tubes  to  get  an  output  of  150  watts 
requires  an  input  of  about  300  watts.  In  a  later  section  of  this  Chapter 
the  efficiency  of  a  tube  is  discussed  and  analyzed  in  detail.  In  spite  of 
its  rather  low  efficiency  'it  will  probably  be  always  used  when  a  small 
amount  of  power  is  desired  at  a  frequency  of  100  kilocycles  or  more, 
because  there  is  no  other  simple  method  of  generating  power  at  these 
frequencies.  The  Poulsen  arc  is  at  present  a  better  method  2  of  generating 
high-frequency  power  when  many  kilowatts  of  power  are  required  and  the 
frequency  is  not  too  high,  say  not  over  400  kilocycles.  For  frequencies 
greater  than  this  the  vacuum  tube  has  no  competitor  as  a  generator,  and 
for  small  amounts  of  power  the  frequency  of  which  is  preferably  variable, 
the  vacuum  tube  is  probably  better  than  any  other  device,  no  matter 
what  this  frequency  may  be. 

There  are  two  general  fields  in  which  the  oscillating  vacuum  tube 
is  used  in  radio,  as  a  source  of  high-frequency  power  for  a  continuous- 
wave  transmitting  station,  and  as  a  necessary  part  of  any  station  receiving 
continuous-wave  signals,  by  means  of  the  heterodyne  or  "  beat  "  method. 

It  has  been  used  as  a  source  of  power  for  transmitting  up  to  several 
kilowatts  of  high-frequency  output,  but  its  application  in  such  instal- 
lations at  present  is  of  doubtful  utility;  unless  the  frequency  desired  is 
above  the  possible  limits  of  a  high-frequency  alternator,  it  seems  that 
a  machine  is  preferable  because  of  the  high  expenses  for  tubes  and  their 
short  life  compared  to  that  of  a  machine.  It  seems  quite  likely,  however, 
that  new  developments  in  high-power  vacuum  tubes  will  soon  make 
them  superior  to  any  other  type  of  high-frequency  apparatus. 

When  used  as  part  of  a  continuous-wave  receiving  set  the  oscillating 
tube  is  required  to  generate  but  a  very  small  fraction  of  a  watt  and  the 
smallest  type  of  detecting  tube  will  suffice. 

1  In  speaking  of  the  efficiency  of  an  electron  tube  the  "  input  "  does  not  ordinarily 
include  the  power  necessary  for  heating  the  filament;    it  is  the  power  supplied  in  the 
plate  circuit  only. 

2  Not  because  of  greater  efficiency  or  ease  and  reliability  of  operation  but  because 
of  lesser  cost  of  maintenance. 


ACTION  OF  TUBE  AS  OSCILLATOR 


469 


For  general  laboratory  use  the  small  oscillating  vacuum  tube  should 
prove  of  great  service,  as. a  source  of  a  few  watts  of  alternating-current 
power  for  bridge  measurements  of  frequency  adjustable  to  any  degree 
desired;  as  a  source  of  complex  alternating-current  forms,  from  which 
exact  octaves  are  obtainable;  in  combination  with  a  suitable  sound 
generator,  such  as  piezo  electric  crystal  or  untuned  telephone  receiver, 
it  is  invaluable  in  a  laboratory  for  measurements  on  sound. 

Elementary  Analysis  of  the  Operation  of  a  Three-electrode  Tube 
or  Generator  of  Alternating-current  Power. — The  three-electrode  tube 
may  be  used  as  a  self-exciting  device  or  the  power  required  to  excite  its 
grid  circuit  may  come  from  some  other  source.  This  scheme  is  often 
used  when  it  is  desired  to  get  maximum  possible  power  from  several 
tubes,  operating  in  parallel.  Their  input  circuits  (grid-filament)  are  all 
connected  in  parallel  and  excited  from  some  other,  self-exciting,  vacuum- 
tube  circuit,  the  power  capacity  of  which  may  be  small  compared  to  that 
of  the  tubes  excited. 

The  operation  of  the  separately  excited  tube  is  extremely  simple;  if 
an  alternating  voltage  is  applied  on  the  input  circuit,  the  plate  current, 
which  is  fixed  by  Eq.  (5), 
must  rise  and  fall  as  this  grid 
potential  alternately  increas- 
es and  decreases.  The  sim- 
plest circuit  to  be  considered 
for  using  the  alternating- 
current  power  generated  in 
the  plate  circuit  is  that 
shown  in  Fig.  92;  a  choke 
coil  L  is  put  in  series  with 
the  machine  Af,  furnishing 
the  plate  circuit  voltage,  the 
value  of  L  being  large  enough 
so  that  its  reactance  is  large  FIG  92>_Circuit  diagram  of  a  tube  to  be  ^  for 
compared  to  the  alternating  generating  alternating-current  power;  the  output 
current  resistance  Rp  of  the  circuit  indicated  in  dotted  lines  is  shunted  around 
plate-filament  circuit.  Shunt-  the  choke  coil  L. 
ing  this  choke  coil  is  the  out- 
put circuit  or  load  circuit  of  the  tube;  it  consists  of  a  condenser  C,  having 
a  reactance,  the  magnitude  of  which  is  small  compared  to  RP,  in  series 
with  a  resistance  R  of  about  the  same  value  as  Rp.  A  condenser  Cj 
shunts  the  machine  M  to  make  the  reactance  of  this  part  of  the  circuit, 
negligible  compared  to  R. 

With  the  conditions  named  (large  L,  C,  and  Ci),  the  external  impe- 
dance of  the  plate  circuit  will  consist  of  R  only.  As  the  voltage  of  the  grid 
goes  alternately  positive  and  negative  the  plate  current  will  fluctuate 


470 


VACUUM   TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


about  its  normal  value,  IOP,  and  the  plate  voltage  will  also  fluctuate 
about  its  normal  value,  Eop.  The  actual  plate  current  may  be  considered 
as  made  up  of  the  constant  value  IOP  which  flows  through  L,  and  does 
not  appreciably  vary  as  Ec  is  varied,  and  an  alternating  component  Ip, 
which  flows  in  the  plate  circuit  by  the  path  C,  R,  Ci.  The  plate  voltage 
similarly  will  be  considered  as  made  up  of  a  constant  term  EOP  on  which 
is  superimposed  the  alternating  voltage  Ep\  at  any  instant  the  actual 
plate  voltage  will  be  equal  to  Eb  —  iPR,  where  ip  is  the  instantaneous 


\ 


FIG.  93.—  Theoretical  curves  of  voltages  and  currents  in  a  tube;    actually  the  plate 
voltage  does  not  go  through  such  wide  variations. 


value  of  Ip.  As  the  magnitude  of  Eg  is  increased  the  maximum  value 
of  Ip  increases  until  it  is  practically  equal  to  Iop.  Under  this  condition, 
the  actual  current  through  the  plate  will  fluctuate  between  2  Iop  and  zero 
and  the  value  of  plate  voltage  will  fluctuate  between  2Eb  and  zero  if 
R  is  chosen  of  proper  value.  (Actually  this  amount  of  current  and  volt- 
age fluctuation  is  not  reached;  the  values  named  are  limiting  values.) 
The  characteristic  curves  are  shown  in  Fig.  93. 

If  the  excitation  is  still  further  increased  and  the  circuit  L,  C,  R,  is 
properly  adjusted,  the  forms  of  Ep  and  Ip  may  be  made  to  differ  very 


OUTPUT  AND  EFFICIENCY  OF  AN  OSCILLATOR"  471 

materially  from  the.  sinusoidal  forms  here  shown.  It  is,  however,  dif- 
ficult to  write  the  theory  of  the  various  circuits  for  any  but  sinusoidal 
functions,  and  we  shall  assume  that  IP  and  Ep  are  such,  unless  specific 
mention  is  made  to  the  contrary.  We  shall  call  the  oscillations  normal 
when  Ip  is  sinusoidal  or  approximately  so,  that  is  for  (/P)max  =  or</op. 

Output,  Efficiency  and  Internal  Losses,  for  Normal  Oscillation. — 
The  effect  of  the  load  resistance  R  on  the  output  of  a  tube  could  be  pre- 
dicted by  noticing  that  the  alternating  current  Ip  really  flows  through 
R  and  the  tube  resistance,  Rp,  in  series;  as  R  is  decreased  IP  increases, 
just  as  the  load  current  from  any  alternator  increases  when  the  resistance 
of  its  load  circuit  is  decreased.  The  voltage  Eg  impressed  on  the  grid 
circuit  generates  in  the  plate  circuit  an  alternating  current  through  Rp 
and  R  in  series. 

If  sufficient  excitation  is  supplied  to  the  grid  circuit  to  force  the  actual 
plate  current  to  vary  between  zero  and  21  op,  the  maximum  value  of  the 
alternating  current,  Im,  though  R  and  Rp  (in  series)  is  Iop.  The  alternating 
current  power  delivered  to  the  external  circuit  is 


Emg  being  the  maximum  value  of  the  voltage  impressed  on  the  grid. 
If  now  R  —  Rp,  we  have, 


8R 


(20) 


The  generated  voltage,  t*oE0,  is  used  up  in  overcoming  the  two  drops 
IPRP  and  IPR,  so  we  have, 


and  if  Rp  =  R, 


But  the  maximum  possible  value  of  the  drop  across  R  ,is  Eop',  we  there- 
fore have  fjLoEmo=2E0p.  Hence  from  Eq.  (20),  we  get, 

p     _4fW  __  ho?    _&oV(-r       T>\_Eovj      7?       EOPIOP  ,Q    , 

^m~  8R    ~~2~R  -2R(lmpK)-2Rlo*K-  ~2~'     '     '     (2l) 

But  the  input  to  the  plate  circuit  is  EOPIOP,  the  value  of  which  we  assume, 
is  independent  of  the  magnitude  of  the  external  resistance  R.  It  there- 
fore follows  that  a  separately  excited  tube  having  sinusoidal  variations  in 
the  plate  current  has  a  maximum  efficiency  of  50  per  cent,  and  that  this  occurs 
for  the  same  condition  as  gives  maximum  output,  i.e.,  R  =  RP. 

This  theoretical  limit  of  efficiency  is  never  reached,  because  the  plate 
current  cannot  be  made  to  execute  harmonic  changes  and  still  be  forced 


472  VACUUM   TUBES  AND  THEIR  OPERATION  [CHAP.  VI 

to  zero  value.  The  reason  for  this  is  the  variation  in  ^o  when  the  plate 
voltage  becomes  very  small  and  the  grid  voltage  large  (in  positive  value) ; 
neither  does  JUQ  hold  constant  when  the  plate  voltage  is  very  high  and  with 
a  high  negative  potential  on  the  grid. 

Of  course  the  efficiency  factor  of  50  per  cent  neglects  the  losses  in  the 
grid,  or  exciting  circuit,  which  really  should  be  charged  up  to  the  tube, 
and  also  the  power  required  to  heat  the  filament.  These  two  factors 
very  materially  reduce  the  possible  efficiency  of  the  tube  as  a  generator. 

As  mentioned  above,  this  limiting  figure  of  50  per  cent  for  efficiency 
holds  only  for  sinusoidal  plate  current;  it  is  possible  to  so  operate  the  tube 
that  the  plate  current  is  much  distorted  and  at  the  same  time  the  effi- 
ciency is  increased  to  perhaps  85  per  cent  or  more.  This  case  will  be  taken 
up  later  in  this  chapter. 

A  large  power  tube  was  connected  as  indicated  in  Fig.  92  and  the 
effect  of  variation  in  R  was  noted.  The  grid  excitation  Eg  was  kept 
sufficiently  low  so  that  the  tube  was  not  being  worked  near  its  limiting 
output  for  any  value  of  R  used. 

The  results  are  given  in  Fig.  94,  and  serve  well  to  show  how  the  power 
output  varies  with  the  resistance  of  the  load  circuit;  the  magnitude  of 
the  alternating  current  generated  by  the  tube  is  also  shown  on  the 
curve  sheet.  It  is  apparent  that  this  tube  should  be  used  with 
a  load  circuit  resistance  close  to  1000  ohms  if  maximum  power  is  to  be 
obtained. 

The  effect  of  continued  operation  on  the  characteristics  of  the  tube 
is  shown  by  the  dotted  curve;  it  shows  the  output  (for  exactly  the  same 
conditions  as  were  used  for  the  solid  curve)  after  the  tube  had  been  oper- 
ating for  twenty  minutes.  The  temperature  of  the  filament  depends  not 
only  on  the  filament  current,  but  also  on  the  temperature  of  the  plates; 
the  hotter  the  plates  the  higher  will  be  the  filament  temperature  for  a 
given  filament  current,  and  of  course  the  more  will  be  the  emission  of 
electrons. 

For  the  lower  values  of  R  (less  than  500  ohms)  it  will  be  noticed  that 
the  alternating  current  exceeds  0.707  of  the  current  supplied  by  the  machine 
in  the  plate  circuit;  with  sinusoidal  current  in  the  load  circuit  this  con- 
dition could  not  occur;  it  must  therefore  be  that  the  current  in  the  load 
circuit  was  distorted  in  form  when  the  lower  values  of  load  circuit  resist- 
ance were  used. 

The  curves  do  not  show  faithfully  the  characteristics  of  the  tube  as 
a  generator  for  the  higher  values  of  the  load  circuit  resistance  because 
the  choke  coil  used  in  the  plate  current  circuit  had  an  impedance  of  only 
8000  ohms,  so  that  the  supply  current  was  far  from  constant  for  the  higher 
values  of  R.  This  supply  circuit  acted  as  a  partial  short  circuit  for  the 
load  circuit,  more  so  as  R  increased  in  value. 


POWER  LOST  ON  PLATES 


473 


Heating  of  the  Plates  of  a  Tube. — The  safe  limit  of  operation  of  a 
power  tube  is  fixed  by  the  allowable  heating  of  the  plates;  with  no  oscil- 
lations taking  place  (no  excitation  of  input  circuit)  the  total  power  delivered 
by  the  plate  circuit  battery  or  generator  must  be  used  in  heating  the 
plate,  the  resistance  of  the  choke  coil  L  (Fig.  92)  being  negligible.  When 
the  tube  is  oscillating  to  the  extent  indicated  by  the  curves  of  Fig.  93, 
one-half  the  input  EbI0p  is  delivered  to  the  output  circuit  R,  hence  only 
one-half  of  EbI0p  is  used  in  heating  the  plates,  whereas  if  the  excitation  is 
removed  the  heating  of  the  plates  is  given  by  EbI0p.  If,  therefore,  a  tube  is 


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Resistance  of  load  circuit 
FIG.  94. — Variation  in  output  of  a  power  tube  as  the  resistance  in  the  load  circuit  is 
varied  grid  excitation  remaining  constant;   circuit  connected  as  shown  in  Fig.  92, 
with  600  volts  used  in  the  plate  circuit. 

rated  as  250  watts  on  the  plate,  the  product  EbI0p  must  not  exceed  250 
when  the  tube  is  not  oscillating,  but  if  the  tube  is  generating  alternating- 
current  power,  and  conditions  are  adjusted  for  maximum  output  (sinu- 
soidal variations  of  Ip  assumed)  the  input,  EbI0p,  may  be  safely  increased 
to  practically  double  the  rating,  or  500  watts. 

Another  way  of  obtaining  the  amount  of  power  used  on  the  plate  is 
to  write  the  expression  for  E'pl'p  from  Fig.  92  (where  E'p  and  I'P  are 
the  voltage  between  plate  and  filament,  and  current  through  tube,  respect- 
ively) and  find  its  average  value.  It  is 

1    CT 
Power  expended  on  olates=^  I    E'prpdt.     Now  as  Ep  and  Ip  are  180° 

1Jo 
out  of  phase  (high-plate  voltage  occurring  at  the  same  instant  as  low-plate 


474  VACUUM  TUBES  AND  THEIR  OPERATION  [CHAP.  VI 

current  occurs  for  resistive  load),  we  have  for  the  power  used  on  the  plates 
(where  E'p  and  I'v  are  fluctuating  as  much  as  shown  in  Fig.  93), 

Power      =i  CT(Eb+Eb  sin  pt)(Iop+Iop  sin  (pt+ir))dt 


-j,  C 


T(EJOP  sin2  pf)dt 


Eblo»  C 
]p-  I 


(21) 


If  the  circuit  is  not  adjusted  to  give  maximum  output  the  proportion  of 
the  input  power  which  is  used  in  heating  the  plates  is  increased,  so  the 
input  power  must  be  reduced  if  safe  rating  of  the  plates  is  not  to  be 
exceeded.  The  input  can  in  general  be  cut  down  by  decreasing  either 
the  filament  current  or  plate  voltage,  or  by  introducing  a  suitable  battery 
or  other  device  into  the  grid  circuit  so  as  to  lower  its  normal  potential. 

Phase  Relations  of  Voltages  and  Current  in  a  Vacuum-tube  Gener- 
ator. —  We  have  previously  mentioned  the  fact  that  there  is  no  appreci- 
able lag  or  lead  of  the  electron  current  in  a  vacuum  tube  with  regard 
to  the  electric  field  causing  the  current  to  flow  ;  this  is  true  for  the  highest 
frequencies  ever  generated  by  vacuum-tube  circuits.  As  the  electric  field 
is  produced  by  both  the  plate  and  grid  acting  together  we  have  the  funda- 
mental fact  expressed  by  Eq.  (5),  which  holds  for  the  instantaneous 
value  of  the  current  as  well  as  for  the  steady  state.  If  then  ep  designates 
the  instantaneous  value  of  the  alternating  component  of  the  plate  voltage, 
ea,  the  same  for  the  grid  voltage  and  iv  is  the  instantaneous  value  of  the 
alternating  component  of  the  plate  current  (grid  current  to  be  neglected 
in  this  discussion)  we  have, 

(22) 


This  equation  holds  true  only  if  the  value  of  (ep+  MO^)  is  sufficiently 
low  to  produce  sinusoidal  values  of  ip]  under  this  condition  it  is  evident 
that  the  constant,  A,  is  the  reciprocal  of  the  alternating-current  plate 
circuit  resistance,  which  we  have  previously  called  Rp.  The  value  of  this 
Rp  will  depend  upon  the  constant  values  of  plate  and  grid  potentials, 
Eop  and  Eog,  increasing  with  a  decrease  of  either  of  them. 

If  the  external  impedance  in  the  plate  circuit  is  R,  as  in  Fig.  92, 
ep=—  ipR,  the  minus  sign  arising  from  the  condition  that  plate  current 
greater  than  normal  (7'P>/op,  or  ip  positive)  causes  a  plate  voltage  less 
than  normal  (E'p<Eop  or  ep  negative).  Using  this  relation  in  Eq.  22  and 

substituting  -^-  for  A,  we  get, 
HP 

.......    ,     (23) 


PHASE   RELATIONS   IN  AN  OSCILLATING   TUBE 


475 


from  which  we  get, 


or  in  effective  values 


.  RP+R 


MO 


RP+R 

MO 


(24) 


In  this  case  the  grid  voltage  and  plate  current  are  exactly  in  phase 
with  one  another  and  the  required  value  of  grid  excitation,  for  a  certain 
magnitude  of  Ip,  is  at  once  calculable  from  Eq.  (24).  The  plate  voltage 
eP  is  equal  to  —  ipR  and  so  is  exactly  180°  out  of  phase  with  the  grid,  or 
exciting  voltage.  The  vector  diagram  is  shown  in  Fig.  95;  it  will  be 
noticed  that  noEg  must  be  greater  than  Ev  by  an  amount  equal  to  IPRP. 


1PRP 


tan.0  = 


R+Rp 


FIG.  95. 


FIG.  96. 


FIG.  95. — Phase  relations  of  voltages  in  the  tube  circuit  of  Fig.  92,  the  load  circuit 

being  resistive  only. 

FIG.  96. — Phase  relations  of  voltages  in  the  tube  circuit  of  Fig.  92,  the  load  circuit 
having  resistance  and  inductive  reactance. 

In  case  an  inductive  reactance  is  used  in  the  plate  circuit,  we  have 
the  relation  ep=  —ip(R -\-jpL)  and  this  relation  used  in  Eq.  (22)  gives 

,  (Rp+R)+jPL 


or  in  effective  values 


MO 


(25) 


The  vector  construction  for  this  case  is  shown  in  Fig.  96;  the  various 
phase  relations  will  evidently  depend  upon  the  ratio  *=-  and  upon  the  rela- 

JK 

tion  between  Rp  and  R.  In  case  the  reactance-resistance  ratio  of  the 
coil  used  in  the  plate  circuit  is  high  (an  efficient  coil)  the  voltage  Ep  will 
lag  behind  the  plate  current  Ip  by  practically  90°,  but  the  grid  voltage 
nannot  lead  the  plate  current  by  such  a  large  angle;  even  if  the  resistance 


476 


VACUUM  TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


of  the  coil  in  the  plate  circuit  is  negligible  the  angle  of  lead  of  Eg  with 


respect  to  Ip  is  fixed  by  the  angle  whose  tangent  is 


pL 
R' 


In    case   the   reactance   in  the    plate  circuit  is  large   and   negative 

(which  would  be  the  case  in 
Fig.  92  if  C  is  decreased  so  that 
its  reactance  is  appreciable)  the 
phase  relations  are  as  shown  in 
Fig.  97;  the  plate  current  now 
leads  the  exciting  voltage  Eg 
and  lags  behind  the  plate  volt- 
age EPj  by  some  angle  between 
90°  and  180°. 

The   grid  voltage   required 
to  produce   a   certain  current, 
FIG.  97.— Phase   relations   of  voltages   in   the   Ip,  through    the    condenser   C, 
tube  circuit  of  Fig.  92,  the  load  circuit  hav-  shunting  the  choke  coil   in  the 
ing  resistance  and  capacitive  reactance.  pkte  circuit>    ig    given  by  the 

equation, 


?.-/, 


(26) 


If  there  is  power  used  in  the  circuit  through  which  IP  flows,  it  must 
be  taken  care  of  by  a  suitable  resistance  in  series  with  C;  Eq.  (26)  must 
then  have  its  resistance  term  increased  by  the  value  of  the  equivalent 
series  resistance. 

In  Figs.  98,  99,  and  100  are  shown  oscillographic  proofs  of  the  fore- 
going statements;  the  voltages  and  currents  are  not  pure  sine  waves 
and  so  do  not  obey  exactly  the  relations  just  obtained  on  the  assumption 
that  all  currents  and  voltages  were  sine  waves.  The  distortion  in  Ip  is 
explained  by  the  fact  that  Rp  varies  through  the  cycle;  its  average  value 
for  the  conditions  existing  when  the  films  of  Figs.  98,  99,  and  100  were 
obtained  was  about  2500  ohms. 

Effect  of  Phase  Relations  on  the  Possible  Power  Output  of  a  Tube 
Generator. — From  the  foregoing  analysis  it  is  evident  that  a  tube  gener- 
ator can  act  on  its  output  circuit  with  a  voltage  Ep,  the  maximum  value 
of  which  is  somewhat  less  than  the  normal  plate  voltage  1  Eop-,  also  that  it 
can  supply  to  the  output  circuit  an  alternating  current  IP,  the  maximum 
value  of  which  is  somewhat  less  than  the  normal  plate  current  Iop.  If 
I  and  E  represent  the  effective  values  of  voltage  and  current  which  the 
tube  furnishes  to  its  output  circuit,  it  is  evident  that  the  maximum  power 

1  For  resistive  load  this  normal  plate  voltage  is  approximately  one-half  the  voltage 
of  the  machine  used  in  the  plate  circuit 


PHASE  RELATIONS  IN  OSCILLATING  TUBES 


477 


output  will  occur  when  the  load  circuit  is  such  as  to  bring  /  and  E  in  phase 
case  of  maximum  output)  to  \EQV1QV. 

Now  if  the  load  circuit  is  such  that  E  and  7  are  in  phase,  it  is  evident 
that  its  impedance  must  be  resistance  only,  furthermore  the  value  of  this 
resistance  must  be  equal  to  E/I,  which  is  also  the  alternating-current 
resistance  of  the  plate  circuit  of  the  tube.  The  truth  of  this  statement 
was  shown  in  Fig.  94. 

For  such  a  circuit  as  that  given  in  Fig.  92,  the  magnitude  of  current 
IP  must  be  directly  proportional  to  Eg,  as  indicated  by  Eq.  (25).  Due 


FIG.  98. — Oscillogram  of  grid  voltage,  plate  voltage,  and  plate  current,  corresponding 

to  conditions  of  Fig.  95. 

to  the  non-sinusoidal  currents  and  voltages,  however,  this  relation  does 
not  hold  good,  except  for  low  values  of  grid  excitation;  the  alternating 
current  does  not  change  as  rapidly  as  indicated  by  Eq.  (25).  In  Fig. 
101  are  shown  curves  of  load  circuit  power  and  current  as  functions  of 
Eg,  the  resistance  of  the  load  circuit  having  been  adjusted  equal  to  the 
tube  resistance  at  low  excitation.  The  output  increases  with  the  square 
of  the  grid  voltage  for  very  low  grid  voltages  only  and  for  the  higher  values 
of  excitation  the  output  is  increasing  at  a  rate  lower  even  than  the  first 
power  of  the  grid  voltage. 


478 


VACUUM  TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


There  is  shown  also  in  Fig.  101  the  value  of  the  current  taken  by  the 
grid;  as  long  as  the  grid  was  not  forced  positive  with  respect  to  the  filament 
the  reading  of  the  continuous  current  ammeter  in  the  grid  circuit  was  zero, 
but  when  the  value  of  alternating  voltage  impressed  on  the  gird  exceeded 

—7=  of  the  normal  negative  grid  potential,  E^  the  grid  was  positive  for  a 

small  portion  of  the  cycle  and  so  took  current.     The  variation  of  the  reading 
of  the  grid  ammeter  is  shown  by  the  curve  marked  Ig;  it  was  zero  until 


FIG.  99. — Oscillogram  of  plate  voltage,  grid  voltage,  and  plate  current,  corresponding 

to  conditions  of  Fig.  96. 


Eg  reached  a  value  of  80  volts  (effective)  which  is  approximately  equal 
to  70  per  cent  of  the  voltage,  Eog,  and  for  higher  voltages  rose  to  a  value 
of  several  milliamperes.  This  is  the  average  value  of  the  grid  current, 
because  a  continuous  current  ammeter  reads  average  values;  the  grid 
current  flows  for. only  a  small  fraction  of  the  cycle,  so  that  the  actual 
maximum  value  of  Ig  is  probably  ten  times  as  large  as  the  value  given 
on  the  curve  sheet.  An  accurate  analysis  of  these  voltages  and  currents 
will  be  given  in  a  later  section  of  this  chapter. 

General  Analysis  of  the  Conditions  Necessary  for  Self-excitation. — 
From  the  analysis  given  so  far  it  is  evident  that  if  a  vacuum  tube  is  going 


POSSIBILITY  OF  SELF-EXCITATION 


479 


to  operate  efficiently  as  a  generator  of  alternating  current  power,  it  is 
necessary  to  have  in  the  plate  circuit  a  load  having  a  resistance  equal  to 
that  of  the  tube;  it  is  also  necessary  to  have  such  reactions  occurring 
in  the  circuit  to  which  the  tube  is  connected  that  when  the  plate^  current 
undergoes  sinusoidal  variations  the  plate  potential  and  grid  potential 
both  undergo  sinusoidal  variations  of  potential  in  opposite  phases,  and 
that  the  relative  magnitudes  of  these  two  potential  variations  be  properly 
adjusted  for  the  tube  being  used.  The  fundamental  requirements  of  the 


FIG.  100.— Oscillogram  of  plate  voltage,  grid  voltage,  and  plate  current  corresponding 

to  conditions  of  Fig.  97. 

problem  can  be  readily  specified.  In  Fig.  102  are  shown  the  filament, 
plate,  and  grid  terminals  1,  2,  and  3;  the  filament  battery  and  plate  cir- 
cuit battery  (or  machine)  are  omitted,  as  they  do  not  enter  directly  into 
the  determination  of  the  conditions  for  self-excitation  of  the  tube. 

If  the  normal  plate  voltage  and  plate  current  are  E-op  and  Iov  respect- 
ively, we  know  that  the  tube  can,  when  operating  properly,  generate  an 
amount  of  power  somewhat  less  than  \EOVIOV;  let  us  call  this  available  power 
P.  If  this  power  is  supplied  to  a  circuit  of  L,  C  and  R,  in  series,  it  will 
produce  a  current  fixed  in  magnitude  by  the  relation  P  =  I2R.  This 
current,  7,  will  produce  an  alternating  voltage  between  the  terminals  of 


480  VACUUM   TUBES  AND   THEIR  OPERATION  [CHAP.  VI 

L,  the  effective  value  of  which  is  equal  to  7coL,  where  w  is  nearly  equal 


VLC 

When  generating  the  amount  of  power  P  the  potential  of  point  2  must 
be  fluctuating  in  voltage  (with  respect  to  the  filament)  by  an  amount 
approximately  equal  to  Eop.  The  potential  of  point  3  must  be  fluctuating, 
with  respect  to  the  filament,  by  an  amount  Emg,  such  that  noEmg  is  about 
equal  to  2EOP,  as  shown  in  Fig.  95. 


100         2          4          6          8        200         2          4          6          8        300 
Value  of  E  g  (effective") 

FIG.  101.— Variation  of  output  current  and  power  as  the  exciting  voltage  on  the  grid  is 
increased;  the  circuit  was  arranged  as  shown  in  Fig.  92.  Variations  of  /&  and  the 
average  grid  current  are  also  shown. 

It  is  then  evident  (referring  to  Fig.  102),  that  if  we  connect  the  filament 
to  point  4  of  the  coil,  we  must  connect  points  2  and  3  to  points  in  the  .coil, 
(on  opposite  sides  of  point  4,  such  as  5  and  6)  such  that  the  maximum  value 
of  voltage  between  4-5  is  equal  to  Eop  and  the  maximum  voltage  between 

2 
points  4-6  is  equal  to  —  EOP. 

MO 

Tf  the  resistance  drop  in  the  coil  is  negligible  compared  to  the  react- 
ance drop,  we  must  have  (neglecting  the  effect  of  mutual  induction  between 
Z/4-5  and  L-i-e), 


J2 

MO 


(27) 
(28) 


CONDITIONS  FOR  SELF-EXCITATION 


481 


The  current  flowing  through  the  coil  L 
between  points  4  and  5  is  really  the  com- 
bination of  the  actual  pulsating  plate 
current  and  the  current  /  which  is  flow- 
ing in  the  oscillatory  circuit.  If  I  is  large 
compared  to  the  alternating  component 
of  the  plate  current  IP,  the  error  made  in 
assuming  the  drop  between  points  4  and 
5  as  due  to  I  only  is  small.  In  a  typical 
radio  circuit  I  was  0.50  ampere  and  the 
effective  value  of  Ip  (alternating  com- 
ponent of  plate  current)  was  only  0.03 
ampere.  It  will  be  noticed,  however,  that 
if  the  resistance  of  the  oscillating  circuit  is 
large  /  decreases  in  value  so  that  the 
assumption  is  no  longer  justified. 

If  we  now  use  the  approximate  relation, 


WWAM 


FIG.  102.— Diagram  to  show  the 
conditions  required  for  self  exci- 
tation; an  oscillatory  circuit,  of 
suitably  low  resistance,  must  be 
connected  to  plate,  filament,  and 
grid  about  as  indicated.  (Fila- 
ment and  plate  circuit  batteries 
not  shown.) 


we  get  from  (27) 


or 


CO  1/4-5  = 


on  the  assumption  that  Rop=2Rp.] 

If  we  now  make  the  assumption  that  co  = 


VLC 


(which  would  be  nearly 


true  if  the  input  and  output  circuits  of  the  tube  had  negligible  capacities) 
we  find, 

~£.  (29) 


And  for  the  proper  grid  excitation,  we  should  have, 

2_ 

MO 


(30) 


As  an  illustration  of  how  these  approximate  relations  are  applied  to 
an  actual  circuit,  we  suppose  a  set  designed  to  generate  a  frequency  of 

1  In  case  Rp  is  greater  than  specified  by  this  equation  L4_s  must  be  correspondingly 
increased;  thus  if  R#  =  Rop  then  we  must  have 


As  previously  mentioned  Rp  varies  with  the  amount  of  excitation  on  the  grid;   a 
curve  showing  the  variation  in  Rp  is  given  in  Fig.  115,  p.  499. 


482  VACUUM  TUBES  AND  THEIR   OPERATION  [CHAP.  VI 

600,000  cycles  per  second  (500-iineter  wave),  the  capacity  C  being  .0004 
rf.  The  total  resistance  of  the  oscillating  circuit  is  10  ohms,  the  /zo  of 
the  tube  to  be  used  is  4  and  Rp  is  3000  ohms.  Using  the  relation  X  =  1885 
Vie,  we  find 

LC  =  .0705, 

and  therefore  L  =  176/^. 

Then  we  find,  L4_5=65M  and  for  L4_6,  we  find  32/^/i.  If  the  tube  can 
supply  4  watts  of  power,  the  current  in  this  oscillating  circuit  would  be 

f^=  0.632  ampere. 
If  Rp  =3000,  we  have  ^  =6000,  and  also  we  have  Eoplop  -8.     From  these 

lop 

two  equations,  we  find  that  Eop  =  220  and  70i;  =  .037.  From  the  above 
values,  we  have 

coL4_57  =  (2x6  X 105)  X  (65  X  10~6)  X  .632  =  153, 

this  being  the  effective  value  of  the  voltage  impressed  on  the  plate.  But 
this  is  equal  to  Eop+^2,  as  we  have  already  assumed  necessary  for  gen- 

TTf        T 

Crating  a  power  equal  to     op  op. 

This  elementary  analysis  serves  for  an  approximate  solution  of  the 
circuit;  the  filament  would  be  connected  to  point  4,  somewhat  lower  than 
the  middle  of  the  coil  and  points  5  and  6  should  be  adjustable  by  multi- 
point switches.  Normally  there  should  be  65M  between  points  4  and  5 
for  the  plate  connection,  and  32  ^h  between  points  4  and  6  for  the  grid 
connection. 

The  foregoing  calculations  have  been  made  on  the  assumption  that 
the  alternating-current  output  of  the  tube  was  50  per  cent  of  the  input. 
Actually  on  a  small  tube  like  this  25  per  cent  efficiency  would  be  more 
likely  than  50  per  cent;  this  would  decrease  the  value  of  7  and  so  require 
an  increase  in  the  required  values  of  7/4-6  and  £4-5- 

As  the  alternating  component  of  the  plate  current  Ip  is  practically 
90°  out  of  phase  with  the  power  circuit  current  7,  the  required  phase  dif- 
ference of  180°  between  Ep  and  Eg  will  not  be  obtained  if  Ip  is  appreciable 

compared  to  7.     This  shift  in  phase  of  Ep  as  the  ratio  -j-  increases,  very 

materially  reduces  the  possible  output  of  the  tube. 

If  it  should  happen  that  R  and  Rp  are  so  high  that  the  7/4-s  required 
is  more  than  about  two-thirds  of  the  whole  coil  L,  the  conditions  required 
by  Eqs.  (27)  and  (28)  could  not  be  satisfied  by  this  circuit,  so  it  would  not 
oscillate. 


DETECTION   OF  CONTINUOUS  WAVE  SIGNALS  483 

The  case  has  many  features  in  common  with  a  shunt-wound 
self-excited  generator.  In  such  a  machine  maximum  output  is  reached 
when  the  external  resistance  is  equal  to  the  internal  resistance  of  the 
machine  (if  the  generated  e.m.f.  is  kept  constant);  also  if  there  is  too 
much  resistance  in  the  shunt  field  circuit  of  the  machine,  it  will  not  excite 
itself,  or  "  build  up,"  as  it  is  called.  This  corresponds  somewhat  to  a 
tube  circuit  having  too  high  a  resistance  in  the  oscillating  circuit. 

The  Oscillating  Tube  as  a  Detector  of  Undamped  Waves.  —  From 
the  explanation  of  the  action  of  the  three-electrode  tube  as  a  detector  of 
high-frequency  currents,  given  on  page  440  et  seq.,  it  is  evident  that  the 
amplitude  of  the  high-frequency  current  must  vary  with  audible  fre- 
quency if  an  audible  reponse  is  to  be  given  by  the  telephone.  In  contin- 
uous-wave telegraphy  the  signal  received  by  the  antenna  does  not  have 
variations  in  amplitude;  a  dot,  e.  g.,  might  consist  of  5000  cycles  of  a 
50,000-cycle  current,  the  amplitude  of  the  current  being  constant  for  the 
duration  of  the  5000  cycles. 

If  the  input  circuit  of  the  detecting  tube  is  continually  excited  by  a 
locally  generated  frequency  of  49,000  cycles,  when  the  signal  comes  in 
the  input  circuit  is  excited  by  both  49,000  cycles  and  50,000  cycles,  the 
result  being  a  high-frequency  excitation  the  amplitude  of  which  varies 
1000  times  a  second.  This  high-frequency,  variable  amplitude,  input 
voltage  will  give  a  1000-cycle  note  in  the  telephones,  connected  in  series 
with  the  plate  circuit  of  the  tube.  In  case  the  locally  generated,  high- 
frequency  current  is  produced  by  the  detecting  tube  itself,  it  is  called 
autodyne  reception,  in  case  some  device  other  than  the  detecting  tube  is 
used  for  impressing  the  local  high-frequency  current  on  the  grid  the  scheme 
is  called  heterodyne  reception. 

The  excitation  of  the  input  circuit  when  no  signal  is  arriving  is  due  to 
the  voltage  E'mg  sin  coZ,  and  when  the  signal,  Emg  sin  pt,  is  being  received 
the  actual  excitation  of  the  grid  circuit  is  (E'mg  sin  ut-\-Emg  sin  pt)  as 
indicated  in  Fig.  103. 

Detection  with  no  Grid  Condenser.  —  We  have  previously  shown  that 
if  the  grid  is  actuated  by  a  voltage  Efmg  sin  ut  and  if  the  plate  current 
varies  as  the  square  of  the  grid  potential,  the  increase  in  plate  current  is 

d2! 
given  by  J  (average  value  of  0«)2X-j~r5      Hence  when  the  excitation  is 

CLUjg 

such  as  given  by  curve  Fig.  103,  the  increase  in  plate  current  is, 


,  (E'mg  sin  wt+Ew  sin  pt}2  d2I 
Mp  =  average  value  of  -  ~-  -  - 


{F    2      V    2  1  /727" 

^  +-  7  +  average  value  of  E^E'm  sin  ut  sin  pt  \  |^f. 
44  j    U/H/g 


484  VACUUM  TUBES  AND  THEIR  OPERATION  [CHAP.  VI 

The  first  two  terms  give  the  increase  in  the  plate  current  which  is  con- 
stant, as  long  as  the  excitation  is  applied;  their  effect  would  produce  an 
increase  in  the  value  of  the  plate  current  as  read  by  a  continuous-current 
ammeter  in  the  plate  circuit,  but  they  would  not  produce  a  readable  sig- 
nal in  the  phones,  giving  only  a  slight  click  in  the  phones  when  the  excita- 
tion is  put  on  the  grid  and  another  when  it  is  taken  off. 

Whatever  audible  signal  is  obtained  must  come  from  the  third  term; 
this  may  be  written  in  the  expanded  form 

d2! 


The  average  value  of  both  these  cosine  terms  is  zero,  but  cos  (u—p)t 
may  fluctuate  so  slowly  as  to  produce  an  audible  signal  in  the  phones,  and 

'"VWVWWVW 

(t)A   A    A   A   A   A    AE7\  A 

v  v  v  V  V  V  V  V  v 


Actual  excitation  of  grid 

FIG.  103. — Conventional  diagram  of  a  continuous  wave  signal  voltage  Eg,  a  locally 
generated  voltage  of  slightly  different  frequency,  and  the  sum  of  the  two,  which  is 
the  voltage  acting  on  the  grid. 

it  is  this  term  which  is  useful  in  continuous-wave  detection.     The  strength 
of  signal  is  then  measured  by  this  term. 

Tjl         T?t  MT 

A/p(of  audible  frequency)  =— ^ — —  cos  (u  —  p)t-r^!   .     .  (31) 

Zl  &&Q 

The  frequency  of  this  fluctuation  in  the  plate  current,  which  is  the 
note  heard  in  the  phones,  is  adjustable  by  the  operator,  as  he  can  make 
the  value  of  o>  anything  he  may  desire.  The  ear  and  phone  are  both  most 
sensitive  at  a  frequency  of  about  800  cycles  per  second,  so  co  is  generally 

adjusted  to  give  ^o~^  =800,  or  *-= —  =800. 

It  is  to  be  noticed  that  whereas  the  response  of  the  tube  detector  is 
proportional  to  the  square  of  the  signal  strength  for  damped  wave  signals 
Eq.  (12),  it  is  proportional  to  the  first  power  of  this  signal  strength  when 
used  for  continuous-wave  receiver.  This  fact  makes  the  tube  a  better 


DETECTION  OF  CONTINUOUS  WAVE  SIGNALS 


485 


Crystal  detector 

actuated  by  single 

frequency 


detector  of  signals  for  undamped,  than  for  damped,  waves,  its  sensitive- 
ness not  decreasing  with  the  strength  of  signal  so  rapidly  for  one  as  it  does 
for  the  other.  Eq.  (31)  shows  also  that  the  response  to  a  given  signal 
varies  with  E'g,  the  amplitude  of  the  local  oscillations,  so  long  as  the  vari- 
ed2/ 
ation  of  E'a  does  not  change  the  value  of  TTT|. 

ClMlg 

This  increase  in  response  with  the  strength  of  the  local  oscillations 
is  similar  in  character  to  the  increase  in  response  of  a  telephone  receiver 
due  to  the  use  of  the  perma- 
nent magnet.      It  is    not    a 
characteristic    peculiar   to    a 
vacuum  tube,  but  holds  for 
any  detecting  device  in  which 
the  response  varies  with  square 
of  the  impressed  force  (when 
a    single    frequency    is    im- 
pressed).    A  crystal   rectifier 
has  a   nearly  parabolic   rela- 
tion    between     the     current  strength  of  signal 
through  it  and  the  impressed  FIG.  104.— Rectifying  action  of  a  crystal  actuated 
voltage  (see    Fig.  60,  p.  347)                        by  a  single  frequency, 
and  the  curve  of  response  as 

a  function  of  the  signal  strength  is  as  shown  in  Fig.  104,  when  it  is  used 
to  detect  spark  signals.  If,  however,  the  crystal  is  used  to  detect  con- 
tinuous-wave signals  by  use  of  an  auxiliary  source  of  continuous  wave 

excitation  (Fig.  105),  its  response 
follows  the  same  law  as  obtained 
for  the  vacuum-tube  receiver,  given 
in  Eq.  (31);  its  response  will  be 
proportional  to  the  first  power  of  the 
voltage  of  the  received  signal,  not  as 
the  square.  This  is  indicated  in 
Fig.  106. 

The  crystal  rectifier  will  also 
act  like  the  vacuum  tube  in  that 
the  response  of  the  rectifier,  for  a 
given  signal  strength,  will  vary  as 
the  first  power  of  the  locally  generat- 
ed e.m.f.  until  the  value  of  this  e.m.f. 

is  such  that  the  region  of  parabolic  rectification  is  exceeded.  The  re- 
ponse  of  the  crystal,  for  given  signal  voltage,  as  the  value  of  E'a  is  varied 
is  about  as  shown  in  Fig.  107;  the  response  is  proportional  to  E'g  for 
a  certain  range,  then  ceases  to  increase  with  E'f  and  if  E'g  is  still  further 


To  continuous 
wave  generator 


Crystal 


Telephone 


FIG.  105. — A  possible  scheme  for  hearing 
continuous-wave  signals  with  a  crystal 
detector. 


486 


VACUUM  TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


Response  of  crystal 

detector  used  for 

beat  reception 


increased  the  response  falls  and  may  reach  practically  zero  for  excessively 
large  values  of  E'ff. 

This  same  characteristic  holds  for  the  vacuum  tube  used  as  a  beat 

receiver,  the  static  charac- 
teristic of  a  tube  being  as 
indicated  in  Fig.  108;  if 
the  amplitude  of  the  lo- 
cally generated  e.m.f.  is 
OC,  the  response  (for  given 
signal  strength)  will  be 
about  twice  as  strong  as 
if  E'g  had  the  amplitude 
OB  only,  whereas  a  value 
of  E'g  equal  to  OD  would 
result  in  a  signal  perhaps 

less    than    for    E'g  =  OB. 

If  E'g  is  increased  to  the 

FIG.  106. — Rectifying  action  of  a  crystal  used  as  indi-  value  OE  the  response  to 
cated  in  Fig.  105.  the  signal  will  be  practi- 

cally zero. 

Detection  with  Grid  Condenser. — In  case  a  condenser  is  used  in  series 
with  the  grid  of  the  tube  being  used  as  a  beat  receiver  Eq.  (18)  must  be 
used  in  predicting  the 
detection  efficiency.  The 
question  is  somewhat 
more  involved  than  for 
the  tube  with  no  grid  con- 
denser, because  the  nor- 
mal grid  potential  (aver- 
age value  with  no  signal 
coming  in)  varies  with 
the  value  of  E'a,  the 
potential  decreasing  as 
E'g  is  increased  in  value. 
As  all  three  of  the  deriv- 


Vaiueof  E; 


FIG.  107. — Rectifying  action  of  a  crystal  detector  as  a 
function  of  the  amplitude  of  the  locally  impressed 
voltage,  the  signal  voltage  being  of  constant  am- 
plitude. 


atives  used  in  Eq.  (18) 
vary  as  the  normal  grid 
potential  is  varied  an 
exact  expression  for  the 
detection  factor  must  be 

rather  complex.  As  the  tube  is  used  in  practice  the  most  sensitive  con- 
dition is  easily  found  as  will  be  described  in  a  succeeding  paragraph,  deal- 
ing with  the  self-excited,  oscillating  tube  as  detector. 


CIRCUITS   USED   FOR  SELF-EXCITATION 


487 


Analysis  of  Some  of  the  More  Commonly  Employed  Circuits  for  the 
Self-excited  Vacuum-tube  Oscillator. — The  first  circuit  to  be  analyzed 
is  one  having  a  tuned  plate  circuit,  the  grid  being  excited  by  magnetic 
coupling  with  this  tuned  circuit;  the  connections  are  as  indicated  in 
Fig.  109.  The  actual  plate  current  is  IOP+iP,  actual  plate  voltage  Eop+ePl 
and  actual  grid  voltage  Eog-\-eg.  We  suppose  that  (Eop-}-fjiQEoo)  is  of  such 
a  value  that  IOP  is  about  one-half  of  the  saturation  current  of  the  tube 

as  shown  in  Fig.  110; 
when  the  tube  is  in  the 
oscillating  state  the  value 
of  (Ep+wEg)  fluctuates 
between  OF  and  OE,  and 
the  plate  current  fluc- 
tuates between  the  values 
CF  and  DE.  Through 
this  range  of  fluctuation 
in  the  plate  current,  the 
relation  between  Ip  and 
(Ep+iJLoEg)  is  nearly 
linear  so  that 

A  being  a  constant. 
This  relation  is  not  true 

of  course  for  the  extreme 

B  Grid  potent  vames  of  z'P,  the  propor- 

FIG.  108.— The  response  of  a  tube  used  for  receiving  con-  tionality  factor  decreas- 
tinuous-wave  signals  will  vary  with  the  strength  of  the  ing    as  the    value    of     ip 
local  oscillations,  the  same  as  the  crystal;  a  local  oscil-  approaches     the     values 
lation  of  amplitude  OC  would  give  (for  a  fixed  incoming    rip  an(j  n  fl 
signal)  response  about  twice  as  great  as  if  the  ampli-          ,_,,.         .  '    .    .,, 
tude  were  OB,   but  an  amplitude  OE  would  give  but  ThlS  POlnt  1S  lllustrat- 

very  little  response.  ed  in  Fig.  Ill,  in  which 

a  sine  wave  of  (eP-\- MO^) 

is  shown  and  below  it  in  full  line  the  alternating  plate  current  ip\  the 
dotted  additions  to  this  curve  serve  to  show  how  ip  differs  from  a  sine 
wave.  The  curve  ip  shown  in  Fig.  Ill  is  symmetrical  about  the  zero 
axis,  a  condition  rarely  obtained  in  an  actual  tube  circuit.  It  occurs  only 
if  the  plate-current  curve  shown  in  Fig.  110  is  symmetrical  about  the 
point  A.  This  supposes  that  the  upper  part  of  the  curve  (caused  by 
saturation)  is  of  the  same  form  as  the  lower  part  of  the  curve  (caused  by 
effect  of  space  charge)  and  also  that  (Eop+iJioEog)  has  been  properly  adjusted 
to  bring  point  A  to  the  middle  part  of  the  curve. 

For  such  a  special  state  of  affairs  two  effects  exist  which  are  practi- 


488 


VACUUM   TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


cally  never  found  in  practice;  the  value  of  plate  current,  as  read  by 
a  continuous-current  ammeter,  does  not  change  when  oscillations  begin 
and  the  alternating  component  of  the  plate  current  contains  no  even 
harmonics.  Generally  the  plate  current  does  change  when  oscillations 
are  started  and  the  plate  current  has  very  pronounced  even  harmonies. 
On  the  basis  of  Eq.  (32),  we  can  write  at  once, 


From  the  notation  given  in  Fig.  109 


ii  being  the  alternating  component  of  current  through  L\. 
Also 


and 


di\ 


(33) 
(34) 

(35) 
(36) 


To  make  Eq.  (36)  true  the  grid  circuit  must  be  so  adjusted  that  no 
current  flows  in  it  as  the  voltage,  eg,  goes  through  its  cycle  of  values; 

this  requires  that  at  no  time  throughout  the 
cycle  must  the  grid  be  positive  with  respect 
to  the  filament,  and  that  the  capacity  of 
the  grid-filament  circuit  is  negligible.  The 
first  condition  can  be  brought  about  by 
using  a  proper  value  of  Ec  (Fig.  109),  but 
the  second  condition  cannot  be  brought 
about  by  any  adjustment  of  the  tube  cir- 
cuit. In  some  cases  this  capacity  is  of  ex- 
treme importance;  for  very  high-frequency 
circuits  it  may  be  one  of  the  limiting  fac- 
tors of  operation.  It  must  be  borne  in 
'RfJ  7,  B  mind  that  the  capacity  to  be  considered  is 

FIG.  109.— A  commonly  employed  not  tne  geometrical  capacity  of  the  tube, 
circuit  for  producing  oscilla-  but  the  effective  capacity  as  explained  on 
tions;  the  frequency  is  fixed  by  page  432  et  seq.  (An  oscillating  tube 
the  constants  of  the  plate  circuit  furnishes  maximum  power  when  the  ex- 
and  the  value  of  M  is  the  critical  ,  ,  .  .  , ,  .  ... 

factor  for  production  or  non-  ternal  resistance  in  the  plate  circuit  is  equal 
production  of  oscillations.  "to  RP,  so  in  calculating  the  probable  effect 

of  the   grid-filament    capacity  of  an  oscil- 
lating circuit  the  proper  value  of  /*  to  use  in  Eq.  (10),  p.  434,  is  /zo/2.) 
We  have  also 

n  dep 


CIRCUITS  USED  FOR  SELF-EXCITATION 


489 


FIG.  110. — A  sinusoidal  variation  in  grid  potential  will  produce  a  sinusoidal  variation 
in  plate  current  only  if  the  fluctuation  in  plate  current  occurs  over  a  limited  range. 


490  VACUUM   TUBES  AND  THEIR  OPERATION  [CHAP.  VI 

which  by  using  (35)  becomes 


By  combining  the  foregoing  equations  'to  eliminate  ep,  eg,  ip,  and  i->,  we  get, 


Such  a  differential  equation  is  satisfied  by  writing  i\  as  an  exponential 
function,  the  form  of  the  function  (trigonometric,  hyperbolic,  etc.), 
depending  upon  the  relative  values  of  the  various  constants  in  Eq.  (38). 


*»•»•/*  ,,«0 


FIG.  111.  —  Due  to  the  upper  and  lower  curves  of  the  plate  current  curve  of  Fig.  110 
the  actual  alternating  component  of  the  plate  current  is  flat  topped  (sine-wave 
shape  shown  by  dotted  lines). 


The  roots  of  Eq.  (38)  are  real  if  we  have,1 


(39) 


For  this  condition,  the  current  i\  must  be  non-oscillatory,  the  circuit  i 
aperiodic.     If 


TD~   (Z/iH-MoAf)>0,    the   exponential    function    is    a 


decreasing  one  and  in  case  some  disturbance  occurs  in  the  circuit  the  dis- 
turbance soon  disappears  and  the  circuit  resumes  its  normal  condition. 
This  can  evidently  occur  if  M  is  positive  and  also  if  M  is  negative  provided 

its  value  is  less  than  —  (Li  +  CRLRp). 

MO 


If 


^T  »    (la  +MoAf  )  <  0,  any  disturbance  set  up  in  the  system  tends 


1  For  an  analysis  of  an  equation  of  this  kind  see  the  first  few  pages  of  Chapter  IV. 


CIRCUITS   USED   FOR  SELF-EXCITATION  491 

to  increase  itself;    this  occurs  if  M  is  negative  and  its  value  such  that 
M  >  —  (Li+CRLRp) .     The  plate  current  then  tends  to  increase  or  decrease 

MO 

(according  to  the  sense  of  this  disturbance)  and  does  so  as  long  as  the 
characteristic  curve  (Fig.  110)  is  straight. 

In  the  case  the  constants  of  Eq.  (38)  are  such  as  to  make  its  roots 
imaginary,  we  have, 

The  current  i\  must  then  be  of  the  form, 

?i=Aea'sin  (ut+6), (41) 

in  which,  we  must  have 

1    r  1  T 

(42) 


and 

1       IAT  ~/       p  \      T~          i  12 

.     .     (43) 


The  exponential  in   Eq.    (41)   is   decreasing  if 

p 

which  is  true  for  all  positive  values  of  M,  or  if  M  is  negative,  but  its  value 

is  such  that  M<~(Li+CRLRp). 

MO 

For  such  conditions  any  shock  on  the  circuit  will  produce  oscillations, 
of  frequency  as  determined  from  Eq.  (43),  but  the  oscillations  will  die 
away  because  of  the  negative  value  of  a. 

The  last,  and  most  important,  case  to  consider  is  given  by 


that  is,  when  M  is  negative  and  its  absolute  value  is  such  that, 


P)  ........     (44) 

MO 

For  this  condition  any  disturbance  to  the  circuit  will  start  oscilla- 
tions, and  these  oscillations  will  increase  in  magnitude  until  the  straight 
part  of  the  curve  in  Fig.  110  is  exceeded. 

The  effect  of  making  the  plate  current  fluctuate  through  such  large 
values  is  to  make  Rp  variable  throughout  the  cycle,  resulting  also  in  an 
increase  in  the  average  value  of  Rp\  the  oscillations  will  therefore  increase 
in  amplitude,  after  once  being  started,  until  the  value  of  Rv  is  increased 
to  such  an  extent  that  the  inequality  given,  in  Eq.  (44)  is  changed  to  an 


492  VACUUM   TUBES  AND  THEIR  OPERATION  [CHAP.  VI 

equality.  When  this  condition  is  brought  about  the  value  of  a  becomes 
zero,  and  the  exponential  in  Eq.  (41)  reduces  to  unity,  giving  neither 
increase  or  decrease  in  the  amplitude  of  the  current. 

From  the  foregoing  it  is  evident  that  if  the  circuit  of  Fig.  109  is  to 
produce  oscillations,  M  must  be  somewhat  greater  than  its  critical  value 
given  by  the  relation 


(45) 


If  M  exceeds  (in  absolute  value)  this  value  oscillation  will  start;  if 
oscillations  are  already  present  and  M  is  made  slightly  less  than  this  value 
(in  absolute  magnitude),  the  oscillations  will  stop,  hence  the  use  of  the 
term  critical  value. 

The  frequency  of  the  oscillations  is  obtained  from  Eq.  (43)  and  is, 


, '  •  •  (46) 

and  if  M  is  adjusted  to  its  critical  value, 

~RL 

R 

.     •     (47) 


27r\    LiC  ' 
which  in  the  average  radio  circuit  is  practically  the  same  as, 


(48) 


If  the  coupling  between  the  grid  and  plate  circuits  is  made  tighter  than 
required  for  the  limiting  value,  the  frequency  is  somewhat  decreased. 

If  we  suppose  Eq.  (48)  to  give  the  frequency  the  critical  value  of  M 
may  be  written  in  the  form, 

•      •     •      (49) 


MLi/  -.  ,   RLRP\     C  (     1 
=  —  I  1  +  /    r  \2  )  =  —  I  (   r 
jio\      («Li)V     Mo\(cot 


From  this  relation  it  is  evident  that  if  a  circuit  is  oscillating  with  a  value 
of  M  equal  to  the  critical  value  any  decrease  in  the  frequency,  accomplished 
by  varying  either  L\  or  C,  must  be  accompanied  by  an  increase  in  the 
coupling,  otherwise  the  oscillations  will  cease. 

Prediction  of  Oscillatory  Condition  by  Putting  Total  Resistance 
Equal  to  Zero.  —  The  condition  for  oscillations  in  any  circuit  can  be 
expressed  by  putting  the  total  resistance  of  the  circuit  equal  to  zero.  In 
Fig.  109  the  external  plate  circuit  has  a  resistance  RA-B  and  this  is  in  series 
with  the  effective  tube  resistance  R'p.  This  R'p  is  the  relation  between 
ep  and  ip,  when  the  values  of  ip  are  determined  not  only  by  ep  but  by  the  simul- 
taneously acting  eg]  as  eg  may  be  180°  out  of  phase  with  ep  and  of  such  value 


CIRCUITS   USED   FOR  SELF-EXCITATION  493 

that  juo60>ep,  it  is  possible  to  have  ip  180°  out  of  phase  with  ePl  so  that  R'p 
may  be  negative,  whereas  Rp  is  always  positive.1  We  have  then  as  the 
condition,  for  self-sustained  oscillations 


=0  .......      ___  (50) 

From  Eq.  (50),  Chapter  I,  we  find  that  at  resonance, 


Now  eff  =  <i)Mii,  ep  is  nearly  equal  to  coLin,  and  iP=-^-(ep-\-fjL0eg). 


RpLi 


—    i 

I       1 


Hence  using  Eq.  (50),  the  critical  value  of  M  may  be  obtained  from  the 
relation, 

RpLi        LI    1      „  (  _ 

-  =  °  ........ 


If  we  use  the  approximate  relation  C  =—^r~,  Eq.  (53)  yields  the  solution, 

co  L/i 


which  is  the  same  as  obtained  in  Eq.  (49). 

Phases  of  Voltages  and  Currents  in  the  Steady  State.  —  When  the 
value  of  M,  being  increased  from  zero,  slightly  exceeds  the  critical  value 
as  determined  by  Eq.  (45),  oscillations  start  and  build  up  to  a  certain 
steady  value;  how  quickly  they  reach  the  steady  state  depends  upon  how 
much  M  exceeds  its  critical  value,  when  the  oscillations  start  and  on  the 
value  of  RL.  The  steady  state  is  reached  when  Rp  has  sufficiently  increased 
(in  average  value)  to  reduce  (45)  to  an  equality. 


When  ^+-(Li+MoM)  =0, 


This  difference  between  RP  and  R'P  may  be  indicated  by  writing  —  =  —-  and 


-  =  -  ;  for  the  latter  case  it  must  be  remembered  that  as  ep  changes  eg  undergoes 
R'P     dep 

dip 

simultaneous  changes  which  may  result  in   the  total  derivative  —  -    being   negative 

aip 

8e 
whereas  the  partial  derivative  —  -  is  always  positive. 


494  VACUUM   TUBES  AND  THEIR  OPERATION  [CHAP.  VI 

Eq.  (38)  reduces  to  the  form, 

RL\ 

(55) 


The  solution  of  this  is  ii  =  /i  sin  at,  in  which 


The  grid  voltage  eg  =  —M~  =  —  coM/i  cos  ut. 
But  as  M  is  negative,  this  may  be  written, 

......    (56) 


which  makes  the  grid  voltage  lead  the  current  /i  by  90°. 
The  plate  voltage 

ep  =  —  RLii  —  Li~  =  —  RL!I  sin  u>t—  coLi/i  cos  cot 


sn 


in  which  tan     =  ~ 


R 


In  practically  all  radio  coils  p—  is  so  large  that  0  may  be  put  equal  to 

KL 
90°  without  much  error,  so  that, 


€p  =  -  /ij?+(coLi)2  sin  (wj+,r/2)  .....     (57) 

From  (56)  and  (57)  it  is  evident  that  ep  and  eff  are  practically  180° 
out  of  phase,  a  condition  we  have  previously  shown  necessary  for  oscillation. 
The  plate  current  is  fixed  by  the  condition, 


di\ 
~dt* 

As  ep  —  Rpip,  we  have, 


Cp  =  —  fiill  — 


RL. 

-5-^1  ---  5  —      ~JT  =  —  W  ^  sm  ^  ---  ^  --  w*l  cos 
HP  £ip        at          lip  tip 


sn 
p 

in  which 

tan  ^  =  "( 

llL 


CIRCUITS  USED   FOR  SELF-EXCITATION  495 

As  M  is  negative  and  MoM  is  greater  in  absolute  value  than  LI,  the  angle 
$  is  nearly  —  ~- 
Then 


sn 


.      .     (58) 


It  is  therefore  evident  that  the  plate  current  leads  the  current  in  LI 
by  practically  90°. 

Amplitude  of  Oscillation  in  the  Steady  State. — The  greatest  current 
is  generally  obtained  in  a  low  resistance  oscillating  circuit  with  the  least 
coupling  that  can  be  used  to  maintain 
oscillations.  The  lower  the  value  of 
M  the  greater  must  I\  be  to  maintain 
the  required  grid  excitation  and  I\  will 
vary  with  M  about  as  shown  by  the  full 
line  curve  in  Fig.  112;  if  the  value  of 
M  is  decreased  beyond  the  critical  value 
oscillations  will  generally  cease  entirely. 
In  certain  tubes  it  is  possible,  how- 
ever, to  get  maximum  current  with 
somewhat  greater  coupling  than  that 
at  which  oscillations  start;  in  that 
case  the  curve  between  M  and  I\ 
has  the  form  indicated  by  the  dotted 
line.  The  form  depends  upon  the 
static  characteristic;  in  Fig.  113  are 
shown  two  possible  curves.  The  full- 
line  curve  corresponds  with  the  full- 


Value  of  M 

FIG.  112. — Showing  possible  relations 
between  amplitude  of  oscillatory  cur- 
rent and  value  of  M  in  Fig.  109;  the 
dotted  line  curve  shows  the  ordinary 
condition.  (See  Figs.  178  and  179 


of  this  chapter.) 

line  curve  of  Fig.  112,  and  the  dotted  curve  of  113  corresponds  to  the  dotted 
curve  in  Fig.  112. 

If  the  value  Iop  (no  oscillations)  is  so  adjusted  that  it  is  equal  to  one- 
half  the  saturation  current,  then  the  maximum  possible  value  of  ip  is  Iop. 
But  from  Eq.  (58)  we  have  the  maximum  value  of  ip  given  by  the  relation 


Imp  and  Im\  being  the  maximum  possible  values  of  the  effective  values  of 
ip  and  ii,  and  this  value  of  Imp  must  be  equal  to  Iop.     So  we  put, 


Io  = 


496 


VACUUM   TUBES  AND  THEIR  OPERATION  [CHAP.  VI 


or 


and  by  substituting  the  condition 


and  assuming 


which  for  the  average  tube  is  practically  the  same  as, 

r  lov     lL[ 

/ml=£-\/-£.          .       •       • 


(59) 


For  this  condition  we 
conclude  that  increasing  C 
must  result  in  a  decrease 
in  /i,  but  in  trying  out  this 
relation  experimentally  we 
often  find  that  /i  may  be 
increased  by  increasing  C. 
There  must  be  in  the  circuit 
some  other  limitation  which 
must  also  be  considered  in 
using  [the  relation  of  Eq. 
(59).  Indeed  this  is  at  once 
evident,  because  Eq.  (59) 
would  lead  to  a  value  of  /i, 

approaching  infinity  as  C  is 
FIG   113.-A  tube  having  a  plate  current  curve  as  made  to  approach  zero< 
shown  by  the  full  line  will   behave   as  indicated  .    . 

for  the  full  line  of  Fig.  112;  similarly  for  the          B^  examining  the  pOSSl- 
dotted  lines.  ble  values  of  ep  we  find  the 

other    limiting    factor;  it  is 

evident  that  the  maximum  value  of  ep  is  Eop,  so  that  we  have  as  another 
limiting  condition  on  the  amplitude  of  the  oscillating  current, 


This  follows  from  Eq.  (57),  putting  the  maximum  value  of  ep  equal  to 
Ecp.    We  then  have, 

T       = 

ml 


CIRCUITS   USED   FOR  SELF-EXCITATION  497 

which  for  critical  value  of  M  and  assuming 


\Zo 


iC 
gives,  I  mi  = 


and  as  the  value  of  Hi?  is  ordinarily  small  compared  to  -^,  we  have  as 

o 

another  limitation  on  the  value  of  the  oscillating  current, 

(60) 

Eqs.  (59)  and  (60)  then  constitute  two  limits  on  the  possible  amplitude 
of  /i ;  whichever  gives  the  lower  value  will  determine  the  maximum  value 
of  /i.  The  best  condition  makes  the  two  limits  the  same  which  occurs 
when 

lop      RL   C 

The  symbols  Iop  and  Eop  have  been  used  to  indicate  the  limiting  values 
of  ip  and  ep,  so  that  Eq.  (61)  is  properly  written,  using  effective  values  of 
voltage  and  current. 

maximum  value  Ep  _  J_  LI  f 

maximum  value  Ip    RL  C' 

But  from  Eq.  (50),  Chapter  /, 

1    Li 
RL  C  =  *A-B' 

the  external  resistance  of  the  plate  circuit,  and 

maximum  value  of  Ep 
maximum  value  of  Ip 

is  really  Rp,  the  internal  resistance  of  the  tube. 

The  foregoing  analysis  therefore  yields  the  same  result  as  obtained  on 
page  471,  namely,  for  maximum  output  the  external  resistance  of  the  tube 
circuit  should  be  equal  to  the  tube  resistance  itself. 

By  comparing  Eqs.  (62)  and  (61),  it  is  seen  that  the  resistance  of  the 

TjJ 

tube  for  maximum  output  is  equal  to  -y^,  which  we  previously  called  ROP, 

J-op 

the  continuous-current  resistance  of  the  tube.  We  also  showed  that  Rp, 
the  alternating-current  resistance,  was  generally  about  one-half  the  con- 
tinuous-current resistance  Rop  (Eq.  (7)  and  Fig.  48).  This  apparent  dis- 
crepancy arises  from  the  fact  that  Rv  is  really  a  variable  quantity,  depend- 


498 


VACUUM   TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


ing  for  its  value  upon  the  amount  of  change  in  the  plate  current.  The 
discussion  of  Rp  on  page  471  et  seq.  and  the  measurements  recorded  in 
Fig.  94  had  to  do  with  Rp  for  very  small  variations  in  plate  current,  and 

in  such  a  case  Rop  is  about  twice  as 
great  as  RP. 

For  the  conditions  obtaining  when 
Eqs.  (61)  and  (62)  are  applicable, 
the  plate  current  is  supposed  to  vary 
from  zero  to  2  7op,  and  furthermore 
the  relation  between  Ip  and  (Ep+noEo) 
is  supposed  to  be  linear;  for  such 

conditions  Rn  =  Rll1}  =  ~^.     The  differ- 


ence  in  Rp  with  weak  excitation  and 
strong  excitation  is   indicated  in  Fig. 

114;     the    full-line    curve    represents 

0  E«p  the  actual  relation  between  IP  and  Ep, 

FIG.  114.— If  the  Rp  of  a  tube  is  to  be  when  there  is  no  resistance  in  series 
constant  the  relation  between  Ip  and  with  the  plate  circuit  and  the  dotted 
must  be  a  straight  line  as  curve  shows  the  assumed  relation  on 

the  basis  °f  Eq.  (33)-    The  dotted 

[at  point  -A) 


the   solid   line  curve  gives  the  plate   ,.  -       „ 

current,  hence  it  is  evident  that  Rp  lme  CUrve  S1VeS  f°r  R 


must  vary  with  the  magnitude  of  fluc- 
tuation Of 


A/ 


A  T? 


whereas  the  full  line  curve  gives  for  Rp  at  the  point  A  a  value  of 

P 

W 

about  half  as  great  as  -j*. 

J-op 

Of  course,  it  is  not  possible  to  excite  a  tube  to  the  limits  set  by  Eqs. 
(59)  and  (61),  so  Rp  actually  never  increases  to  the  value 


as  the  intensity  of  the  oscillations  varies;  the  value  of  Rp  for  the  ordinary 
tube  will  undergo  changes  about  as  shown  in  Fig.  115. 

Stability  of  Oscillations.  —  In  the  average  circuit  the  value  of  the 
oscillating  current  is  greatest  when  the  coupling  is  as  weak  as  can  be 
permitted  and  still  maintain  oscillations.  For  this  condition,  however, 
the  stability  of  the  circuit  is  very  poor;  the  slightest  decrease  in  either 
//  or  Eb  is  likely  to  stop  the  oscillations.  Also  for  this  condition  it  is 
necessary  to  readjust  the  coupling  for  every  change  in  the  oscillating 
circuit;  if  either  RL,  Z/i,  or  C  is  increased  the  oscillation  will  cease.  To 


VARIATION   OF  PLATE  CIRCUIT  RESISTANCE 


499^ 


make  this  circuit  stable  it  is  necessary  to  have  the  coupling  at  a  setting 
considerably  in  excess  of  its  critical  value,  perhaps  twice  as  much.  This 
of  course  will  diminish  some- 
what the  magnitude  of  the 
oscillating  current,  but  the 
increased  reliability  of  the 
generating  action  of  the  tube 
generally  compensates  for  this. 
It  many  times  happens 
that  the  critical  value  of 
coupling  for  starting  oscilla- 
tions is  greatly  different  from 
the  critical  value  to  stop  oscil- 
lations; in  a  Certain  circuit  Intensity  of  oscillations 
this  critical  value  of  coupling  FlG<  n5._The  resistance  of  the  plate  circuit  of 
for  starting  the  oscillations  a  tube  varies  with  the  fluctuation  of  (Ep+pvEg) 
was  17  per  cent,  whereas  it  about  as  shown  here;  intense  oscillations  require 
could  then  be  decreased  to  12  Iar8e  fluctuations  in  (E9+i*Eg). 
per  cent  before  the  oscillations 

ceased.  This  is  due  to  the  variable  value  of  Rp,  as  brought  out  in  a  pre- 
vious paragraph;  when  the  oscillations  start  their  amplitude  is  neces- 
sarily small  and  Rp  is  determined 
by  the  slope  at  the  value  of  /•„,  as 
shown  in  Fig.  116  at  A.  After  the 
oscillations  are  started,  the  plate 
current  fluctuates  between  0  and  BC, 
and  the  average  resistance  between 
these  limits  is  less  than  the  value  of 
Rp  at  A .  The  plate  current  for  such 
oscillations  would  be  very  complex 
and  so  the  behavior  of  the  circuit 
could  not  be  predicted  from  the 
analyses  previously  given,  which 
have  assumed  sine  waves  of  current. 
Starting  and  Stopping  Oscilla- 

its  resistance  is  fixed  by  "the  slope"of  t">ns.— It  is  sometimes  necessary  to 
the.lp-Ev  curve,  and  this  resistance  give  a  circuit  some  sort  of  a  shock  to 
may   be  very  different  from  the  value  start  oscillations;  if  normal  filament 
when  intense  oscillations  are  occurring,   current   and   plate   voltage    are   im- 
pressed and  then  the  coupling  gradu- 
ally increased,  it  will  be  found  that  M  may  greatly  exceed  its  critical  value 
without  causing  the  tube  to  oscillate.   If,  however,  the  plate  circuit  is  opened 
and  then  closed,  thus  giving  a  pulse  to  the  circuit,  oscillations  will  start. 


0  Plate  voltage 

FIG.  116. — When  a  tube  starts  to  oscillate 


500 


VACUUM   TUBES  AND   THEIR  OPERATION 


[CHAP.  VI 


In  case  a  tube  is  used  for  generating  power  in  a  transmitting  station, 
the  oscillation's  must  be  continually  started  and  stopped,  as  the  signals 
are  sent  out  by  the  key.  The  vacuum-tube  generator  permits  this  oper- 
ation to  be  carried  out  readily;  a  small  hand  key  properly  introduced 

in  the  grid  circuit  may  control  kilowatts 
of  power  with  imperceptible  sparking. 
Probably  the  most  convenient  scheme 
for  "  keying  "  a  tube  generator  is  that 
shown  in  Fig.  117;  with  the  key  open 
the  grid  is  forced  to  such  a  negative  po- 
tential by  the  battery  Ec  (which  can  be 
small  dry  cells)  that  the  circuit  stops 
oscillating  and  when  the  key  is  closed 
the  coil  Z>2  is  connected  to  ground  which 
is  its  normal  connection  for  oscillation. 
Of  course  when  the  key  is  closed,  the 
battery  Ec  is  short-circuited  through  the 
resistance  R,  but  this  will  do  them  no 
harm  if  R  is  chosen  sufficiently  high. 

With  a  battery  Ec  of  200  volts  a  resistance 
FIG.  117.-This   diagram  shows  a  R   of  2Q  Q()()  ohmg  wiu  be  guitable    for  a 
convenient  method  of    keying    a  »****»'•••.          i       -        n 

tube  circuit;  if  the  proper  values  type  P-20  pliotron  having  ^  =  1000  volts, 
of  R  and  Ec  are  chosen  a  small  Condenser  Cg  shunts  the  contact  points 
hand  key  may  control  kilowatts  of  the  key;  this  condenser  must  be  of 
of  power  with  imperceptible  sufficiently  small  capacity,  otherwise  the 
sparking.  set  will  continue  to  oscillate  for  an  appre- 

ciable time  after  the  key  is  opened,  and 

the  starting  of  the  oscillations  will  not  occur  as  soon  as  the  key  is  depressed; 
about  0.1  microfarad  seems  satisfactory  when  R  is  20,000  ohms. 

Effect  of  Oscillation  on  the  Grid  and  Plate  Currents. — In  such  a 
circuit  as  that  shown  in  Fig.  109,  the  grid  current  is  very  nearly  zero 
until  oscillations  start;  when  the  tube  is  oscillating  the  grid  becomes 
positive  during  part  of  the  cycle  and  so  takes  current.  The  value  of  the 
grid  current  is  larger  than  would  be  at  first  supposed,  because,  although 
the  grid  potential  does  not  reach  high  positive  values,  the  plate  potential 
is  low  at  the  time  the  grid  is  positive. 

In  a  small  power  tube  designed  for  #6  =  300  and  Eop=.04:  ampere  the 
average  value  of  Ig  when  the  tube  is  adjusted  for  maximum  value  of 
power  output  is  about  .003  ampere.  The  maximum  value  of  the  grid 
current,  when  its  average  value  is  .003,  is  probably  from  .02  to  .05  ampere. 
In  a  large  power  tube,  excited  for  maximum  power  output,  I0  may  be 
considerably  greater  than  the  values  given  above. 

If  the  plate  current  Iop  has  been  adjusted  equal  to  half  the  saturation 
current,  for  the  values  of  //  and  EOP  used,  a  continuous-current  ammeter 


MAXIMUM  OUTPUT  WITH  SELF-EXCITATION 


501 


will  indicate  no  change  in  the  value  of  the  plate  current  when  oscillations 
start.  In  general,  however,  there  will  be  a  change;  when  oscillations 
start  the  average  plate  current  will  generally  increase  if  the  circuit  is 
such  that  no  condenser  is  used  in  series  with  the  grid  and  will  decrease 
if  such  a  condenser  is  used.  Conditions  may  occur  in  which  this  general 
statement  is  not  true. 

Adjustments  to  Give  Maximum  Output  of  Tube. — With  a  circuit 
arranged  as  in  Fig.  109,  there  are  two  adjustments  to  carry  out  before 
the  tube  will  give  its  maximum  out- 
put; the  grid  must  have  the  proper 
excitation  and  the  plate  circuit  resist- 
ance must  equal  the  tube  resistance. 
The  circuit  of  Fig.  109  is  reproduced, 
with  slight  modification,  in  Fig.  118. 
The  oscillating  circuit  LI,  RL,  C,  is 
many  times  an  antenna,  with  loading 
coil,  so  it  is  evident  that  RL  itself 
is  not  adjustable,  yet  the  resistance 
between  points  A  and  0  must  be  made 
equal  to  the  tube  resistance.1 

The  plate  circuit  inductance  is 
made  with  taps  as  indicated  in  Fig. 
118;  point  B  is  adjusted  to  give  the 
right  frequency  to  the  oscillating  cir- 
cuit, and  then  point  A  is  adjusted 
to  give  the  plate  circuit  the  right  re- 
sistance. Neglecting  the  effect  of  the 
plate  current  compared  to  the  oscillat- 
ing current  (an  ordinary  radio  set  makes 
we  have, 


FIG.  118. — To  make  the  circuit  shown 
in  Fig.  109  useful,  the  inductance  in 
the  oscillatory  circuit  must  be  fitted 
with  two  sets  of  taps  as  indicated 
here;  the  mutual  induction  between 
the  two  coils  L2  and  Lp  must  also  be 
adjustable.  For  short  waves  (say 
150  meters)  maximum  current  will 
probably  be  obtained  with  no  mutaal 
induction  at  all. 


equal  to  about  1/20  of  7), 


If  RO-A  is  to  be  equal  to 
we  so  adjust  tap  A  that 


E 

,  =  Y~^  (f°r  conditions  of  maximum  power) 

lop 

L* 


or 


(63) 


This  required  value  of  Ly  may  be  either  greater  or  less  than  LI. 

1  In  this  circuit  it  sometimes  happens  that  the  frequency  of  oscillations  is  determined 
mostly  by  the  capacity  between  grid  and  ground;  to  make  the  adjustment  of  C  effective 
in  changing  wave-length  the  inductance  of  L2  must  be  kept  as  small  as  feasible. 


502  VACUUM   TUBES  AND  THEIR  OPERATION  [CHAP.  VI 


In  a  certain  radio  circuit  RL  =3  ohms,  C  =4X  10  ~10  farads,  LI  = 
Eop  =  3QQ  volts,  /op  =  .03  ampere.  Using  Eq.  (63),  the  required  value  of 
Lp  proves  to  be  42ju/i.  The  tap  A  would  therefore  be  made  between  0 
and  tap  B. 

The  current  in  the  oscillating  circuit  can  be  calculated  from  the  relation 
I  =  uCE,  where  E  is  the  effective  voltage  across  OB,  which  is    equal   to 

pi          r  I    : 

——Xj^.1    Using  these  relations  and  also  remembering  that  u=\j—.  ^, 
V2     Lip  \LiC 

we  get, 

E0pI0 


(64) 

Substituting  the  values  above  gives  a  value  for  7  of  1.23  amperes. 
Actually  1.05  amperes  was  the  maximum  obtainable  from  the  circuit. 

The  resistance  RL  was  then  increased  to  50  ohms,  and  it  was  found 
experimentally  that  tap  A  was  outside  of  tap  B  for  maximum  output. 
By  calculation,  Eq.  (63),  we  find  the  proper  value  for  Lp  =  171  /Ji.  The 
oscillatory  current,  from  Eq.  (64),  should  be  0.31  ampere,  whereas  only 
0.26  was  actually  obtained. 

After  the  right  position  for  tap  A  has  been  found  the  coupling  between 
L2  and  LI,  is  reduced  until  the  critical  value  of  M  is  nearly  reached,  and 
then  a  slight  readjustment  of  tap  A  may  be  necessary.  It  will  be  found 
that  varying  M  and  the  position  of  tap  A  will  have  only  minor  effects 
on  the  frequency  being  generated  by  the  tube. 

The  value  of  L^  should  be  kept  as  low  as  possible;  if  it  should  happen 
that  the  natural  period  of  L<2,  combined  with  the  capacity  of  the  input 
circuit  of  the  tube  is  about  the  same  as  the  period  of  the  L\C  circuit, 
trouble  may  be  experienced  in  making  the  tube  oscillate  because  of  the 
unexpected  phase  of  the  voltage  impressed  on  the  grid ;  the  voltage  changes 
its  phase  nearly  180°  as  the  natural  frequency  of  the  L\C  circuit  is  made 
to  pass  through  the  natural  frequency  of  the  grid  circuit. 

Oscillations  at  Other  than  the  Desired  Frequency. — It  may  happen 
that  if  the  grid  circuit  has  its  natural  frequency  in  the  neighborhood 
of  the  frequency  of  the  L\C  circuit  the  tube  will  generate  power  of  the 
frequency  of  the  grid  circuit,  instead  of  that  of  the  L\C  circuit. 

1  This  relation  is  approximate  only,  because  of  the  mutual  induction  between  the 
inductance  between  points  O-A  (Fig.  118)  and  that  between  points  A-B.  If  the  coil 
is  short,  so  that  the  turns  are  all  close  together,  the  effect  of  this  mutual  induction  will 

be  considerable  and  the  relation  given  above  is  more  accurately  written  ~~/~X— —  where 

V  2    A' 2 

Ni  =  number  of  turns  between  points  0-B 
and 

Ar2  =  number  of  turns  between  points  O-A . 


HIGH  RESISTANCE  IN  OSCILLATORY  CIRCUIT 


503 


To  remedy  this  trouble  the  grid  circuit  is  sometimes  tuned  to  nearly 
the  same  frequency  as  the  L\C  circuit.  Another  method  of  ensuring  the 
desired  frequency  of  oscillations  is  to  couple  the  grid,  not  to  the  plate 
coil,  but  to  a  coil  in  the  L\C  circuit,  which  is  so  placed  that  no  current 
flows  in  it  unless  the  main  circuit  is  oscillating.  This  idea  is  depicted 
in  Fig.  119.  Coil  L\  will  carry  no  current  unless  the  main  circuit, 
including  L\  and  C,  is  oscillating. 

The  difficulty  occurs  principally  when  the  resistance  of  the  main 
oscillating  circuit  is  high  so  that  the  current  7  is  relatively  small ;  to  suf- 
ficiently excite  the  grid  in  this  case  requires  a 
comparatively  large  value  of  Z/2,  which  of  course 
lowers  the  natural  period  of  the  grid  circuit. 

Oscillating  Current  Comparable  in  Value  with 
Plate  Current. — When  the  resistance  of  the 
oscillating  circuit  gets  very  high  the  oscillating 
current  I  may  decrease  to  such  an  extent  that 
it  is  of  about  the  same  value  as  lv  or  even  less. 
In  this  case  it  is  not  easy  to  produce  oscillations, 
because  the  e.m.f.  for  the  excitation  on  the  grid 
tends  to  get  the  wrong  phase.  The  scheme  of 
Fig.  119  may  not  work  because  Li,  which  must 
be  small  compared  to  Lp  (because  of  the  high 
value  of  RL),  may  not  induce  a  sufficient  voltage 
in  Z/2,  so  resort  must  be  had  to  coupling  LI  with 
Lp.  Now  the  oscillatory  current  in  Lp  is  ordi- 
narily 90°  out  of  phase  (nearly)  with  Ip,  and 
such  condition  results  in  a  correct  phase  for  the 
voltage  Eg.  But  if  now  IP  is  comparable  with  /, 
the  actual  current  in  Lp  (which  produces  the 

magnetic  field  affecting  Lo)  tends  to  come  into  phase  with  Ip,  that  is, 
shift  its  phase  90°  from  its, normal  value.  But  such  a  shift  in  phase 
will  result  in  such  a  phase  for  Ett  that  oscillations  cannot  be  main- 
tained; in  fact  a  comparatively  small  shift  will  materially  cut  down  this 
possible  power  output  of  the  tube. 

For  a  condition  of  this  sort  it  is  better  ^o  use  separate  excitation  for 
the  tube,  instead  of  trying  to  make  it  self-exciting.  Another  tube  cir- 
cuit, having  a  low  resistance,  is  self-excited  at  the  desired  frequency,  and 
from  this  circuit  a  suitable  voltage  may  be  obtained  (either  directly  or 
magnetically)  for  excitation  of  the  tube  furnishing  power  to  the  high 
resistance  circuit. 

Coupling  between  Grid  and  Plate  Circuit  by  Capacity. — In  the  fore- 
going discussions  of  a  self-excited  tube  the  voltage  for  excitation  of  the 
grid  has  been  obtained  by  a  magnetic  coupling  with  the  oscillating  circuit, 


M 


FIG.  119. — To  prevent  spu- 
rious oscillations  it  is  ad- 
visable to  couple  the  grid 
circuit  to  some  part  of 
the  main  oscillatory  cir- 
cuit through  which  the 
plate  current  does  not 
flow;  the  grid  is  then  not 
excited  unless  the  main 
circuit  is  oscillating, 


504 


VACUUM   TUBES   AND   THEIR  OPERATION 


[CHAP.  VI 


but  it  is  of  course  possible  to  use  electrostatic  coupling,  or  even  a  com- 
bination of  both.  Such  a  circuit  is  shown  in  Fig.  120;  in  order  to  make 
the  discussion  more  general  only  a  part  of  the  inductance  in  the  oscillating 
circuit  is  included  in  the  plate  circuit.  The  extra  inductance  L2,  in  com- 
bination with  €2  and  R,  represents  an  antenna,  thus  making  the  circuit 


//////// 


FIG.  120. 


FIG.  121. 


FIG.  120.  —  Another  oscillatory  circuit  in  which  the  grid  is  excited  by  inductive  coupling 

between  LI  and  L3  as  well  as  by  the  capacitive  coupling  produced  by  Ci. 
FIG.  121.  —  Showing  how  the  circuit  of  Fig.  120  is  applied  to  an  actual  radid  circuit. 

the  direct  equivalent  of  the  actual  circuit  shown  in  Fig.   121.     From 
Fig.  120  using  directions  of  current  shown  in  the  diagram,  we  have, 


dll 

dt 


dt 


dt 


dt 


dt 


(65) 
(66) 


Also  we  know  that  eCl  and  ec*  are  fixed  by  the  relation  —  €2  -~r^=i2,  and 


de( 


By  the  use  of  these  relations,  and  deriving  Eq.  (65),  we  get 


the  equations, 


12 


(67) 


We  can  write 


dt2 


'    p  dt  dt '     ° 


di\ 


— 


Using  these  conditions,  and  Eq.  (65),  we  get, 


=0.     .     .     (69) 


CIRCUITS  USED  FOR  SELF-EXCITATION  505 

Eqs.  (67),  (68)  and  (69)  permit  the  precise  determination  of  u,  12,  and 
is,  but  it  is  evident  that  the  solution  would  be  tedious  and  the  solution 
can  be  easily  guessed.  If  oscillations  occur  at  all  they  will  be  sinusoidal 
and  as  they  are  all  supplied  with  power  from  the  same  source  (the  plate 
circuit)  we  can  write, 

=/i  sin  co£,  i2  =  /2  sin  (co£+02),  13  =  h  sin 


By  deriving  these  expressions  and  substituting  in  Eqs.  (67),  (68)  and  (69), 
and  for  each  equation  thus  obtained,  equating  the  coefficents  of  cos  ut  and 
sin  cot,  we  find 

RP(Ii  +  l2  cos  02+/3  cos  03)  —  co(Mo^/3+^)/3  sin  03  =0.  .     .     (70) 
Rp(l2  sin  02+^3  sin  03)-f-aj(Zyi-f-juo-M^)/i-hco(^QjL3-hAf)73  cos  03=0.      (71) 

CoL/i  +  CoM/3  COS  03  =  (  CoL2 77-  )/2  COS  02  +  /2#  SU1  02.     .       (72) 

\  COC2/ 

coM/3  sin  02  =  (coL2 ^r)  /2  sin  fo  —  IzR  cos  02.  .     .     .     (73) 

$  cos  03.     ...     (74) 


1    } 
(Ls  —  M) -^  y /s  sin  03  =  0 (75) 

Eq.  (75)  shows  that  unless  co(L3— M) 77- =  0,  sin  03  must  be  equal 

to  zero,  which  means  that  €3  and  13  are  either  in  phase  or  180°  out  of  phase. 

In  case  00(1/3— M) TT  =0>  we  have  resonance  in  the  L^  —  Ci  circuit. 

coCi 

Using  Eqs.  (74)  and  (75)  to  get  values  of  sin  03  and  cos  03,  then  using 
Eqs.  (70)  and  (71)  to  get  values  of  sin  02  and  cos  02  and  putting  these 
values  in  Eqs.  (72)  and  (73),  we  get  the  two  equations 


-0>     .     (76) 

1  ^-^) 

and 


1+- 


506  VACUUM   TUBES   AND   THEIR  OPERATION  [CHAP.  VI 

The  frequency  might  be  calculated  from  Eq.  (76),  and  this  frequency 
carried  into  Eq.  (77)  would  permit  the  calculation  of  the  critical  coupling 
for  oscillations.  From  inspection  of  Fig.  Ill  it  is  evident  there  will  be 
two  possible  frequencies  and  of  course  each  of  these  must  be  used  in 
solving  Eq.  (77).  This  general  solution  is  lengthy,  so  we  will  investi- 
gate only  two  of  the  more  important  cases. 

In  case  C\  —  0  and  Z/2  =  0,  the  circuit  degenerates  into  that  of  Fig. 
109  and  so  our  general  Eqs.  (76)  and  (77)  should  reduce  to  the  simpler 
forms  obtained  for  this  case.  Eq.  (76),  becomes  (if  we  put  Ci  =  L2  =0) 

=0, 


which  we  previously  obtained,  and  if  -p-  is  small  enough  to  be  negligible, 

f*i 

T 


LiC2' 

and  if  thfe  value  of  co  is  substituted  in  Eq.  (77),  in  addition  to  the  condition 
that  Ci=L/2=  0,  we  find  as  the  condition  for  oscillation, 


which  we  have  already  obtained  from  the  circuit  of  Fig.  109. 
In  case  M  =0  and  Z/2  =0,  Eq.  (76)  becomes, 


1  \     Li  _  1_      ,  R  I 

--  7r)-7r-          —  j  —  h^-/ 

coC2/      62      j          1        rtjA 

coL3  --  77-          \ 

coCi  \ 


r> 

and  if  again  -^-  is  negligibly  small,  we  find, 
tip 


(78) 


This  is  evidently  the  condition  for  zero  reactive  current  in  the  three- 
branched  plate  circuit,  one  branch  having  LI,  another  having  C2,  and  the 
third  having  L3  and  Ci  in  series.  Eq.  (78)  may  be  put  into  the  form 

^-[LiC2+(L3+Li)Ci]^+L1C2L3Cyi=0.      .     .     .     (79) 

If  we  put  [LiC2+(L3+Li)Ci]  =a,  and  L^L^Ci  =b  we  can  write  the  two 
positive  roots  of  this  equation, 


CIRCUITS   USED   FOR  SELF-EXCITATION  507 

Of  these  two  roots  for  co  one  is  greater  than  \/  y"7>  and  the  other  is  less 

than  A  /  T          We  shall  show  that  the  only  possible  oscillation  is  the  lower 
\L3Gi 

one  of  the  two. 

If  we  substitute  M=0  and  L2  =0  in  Eq.  (77),  we  find  that  the  critical 
conditions  for  maintaining  oscillations  as  given  by, 


.0|   ...    (80) 


the  condition  for  oscillation  making  the  left-hand  member  less  than  zero. 
The  condition  for  oscillations  is  then  determined  by  the  inequality 


>.     .    .    .    (81) 

coCi 
This  can  evidently  be  satisfied  only  by  having 

coL3 ir<0,          (82) 


which  shows  that  the  circuit  cannot  sustain  oscillations  at  a  frequency 

which  makes  ooL3  greater  than  —7T.    This  bears  out  the  prediction  made 

coCi 

above  that  of  the  two  roots  of  Eq.  (79),  only  that  one  having  a  value  less 

than  \-r~rr  is  a  possible  frequency  for 
\  L>zL  i 

rlitional  inequality  (82)  may  be  written, 


than  \-r~rr  is  a  possible  frequency  for  the  oscillations  because  the  con- 


(83) 


Eq.  (81)  also  serves  to  further  limit  Ci,  because  from  it  we  get  the 
relation, 


So  we  have  C\  fixed  by  the  double  condition, 

1  1  Li+RpRC2 


w  being  fixed  as  the  smaller  of  the  roots  of  the  equation  on  bottom  of 
p.  500.     The  relation  given  in  (84)  shows  that  if  fjL0L^>Li  (which  will 


508 


VACUUM  TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


generally  be  the  case),  --JT  is  positive,  so  that  as  the  resistance  of  the 

oscillating  circuit  is  increased,  the  value  of  Ci  must  also  be  increased  to 
maintain  the  oscillations.  By  similar  reasoning,  we  see  that  Ci  must 
be  increased  as  the  frequency  of  the  oscillations  is  diminished. 

If  we  consider  both  magnetic  and  static  coupling  as  given  in  Fig.  120, 
we  can  much  simplify  the  general  equations  obtained — (76)  and  (77) — by 

r> 

supposing  Z/2  absent  and  -=  -  negligibly  small.     Eq.  (76)  then  becomes, 


«c2  r    "ft/^i'ji) L 


.    .    .     (85) 


and  Eq.  (77)  becomes, 


R+' 


=  0.       ...     (86) 


The  capacity  coupling  serves  to  increase  the  magnetic  coupling  if  M 

is  negative  and  if  ^(L^—M) rr<0.     Even  if  M  is  positive  the  con- 

coui 

.  dition  for  oscillations  may  be  still  maintained  by 

A      ^  using  sufficient  capacity  coupling. 

/   \     <  ip  It  is  to  be  noted  that  even  if  no  actual  con- 

*     '     denser  C\  is  used  in  the  circuit,  there   is  always 
such  a  capacity  present  in  the  tube  itself,  due  to 
capacity  between  the  actual  grid  and  plate,  as  well 
as  that  of  the  lead-in  wires  connecting  to  them. 
At  very  high  frequencies  this  internal  tube  capacity 
may  very  seriously  affect  the  behavior  of  the  tube; 
in  certain  tubes  of  foreign  manufacture  the  lead-in 
wires  of  the  plate   and   grid  are  kept  as  far  from 
FIG.  122. — This  circuit  is  each  other  as  the  structure  of  the  tube  permits 
similar  to  that  of  Fig.  with  the  idea  of  minimizing  this  internal  capacity. 
120,  but  simplified  by  (See  tube  (0)  of  Fig.  21,  page  389.) 
eliminating  the  dummy          Another  circuit  which    may  be  used  ig  ghown 

antenna  circuit.  -TV      -,nn      -^      ^i  • 

in  Fig.  122.     For  this  case,  we  have, 

T  dii 


and  as 


CIRCUITS   USED  FOR  SELF-EXCITATION  509 

we  have  the  relation 

=0.       .     .     (87) 


When  the  reactance  across  the  machine  or  battery  furnishing  the  plate 
voltage  is  negligible  (it  should  always  be  made  so  by  shunting  with  a  large 
capacity,  if  necessary),  we  have 


ndec 
and  as  Z2  =  —  C  -3—  , 

we  can  write  (88)  in  the  form, 


+    .....     (89) 


From  this  i\  might  be  eliminated  and  so  enable  a  solution  of  12  to  be 
obtained.     Instead  of  this  formal  procedure,  we  guess  at  the  solution  and 

put, 

i\  =/i  sin  cot  and  ^'2  =  /2  sin 


Using  these  two  values  and  substituting  in  Eq.  (89),  we  get, 


/  f  4/">    I  \          / 

and 


_Af)__=o.     .     (91) 

r> 

If  in  (90)  we  neglect  the  terms  —  and  R2,  we  get  for  the  natural  period 

KP 

of  the  circuit, 

(92) 


And  using  this  value  of  co  in  Eq.  (91),  which  determines  the  critical  con- 
dition for  oscillation, 

M}2.     (93) 


This  conditional  inequality  requires, 

JU0^2  >  Li  +  (HQ  —  1)  M  . 


510 


VACUUM   TUBES   AND   THEIR   OPERATION 


[CHAP.  VI 


If  we  suppose  there  is  no  magnetic  coupling  M=0  and  the  frequency 
of  oscillation  becomes, 

•     •     (94) 


and  the  condition  for  oscillation 


(95) 


FIG.  123.— This  is  the 
circuit  generally  used 
when  an  oscillating 
tube  is  used  to  re- 
ceive a  continuous- 
wave  signal;  the  os- 
cillatory circuit  is 
here  associated  with 
the  grid. 

and 

Also 


or 


Now 


Oscillating  Circuit  in  the  Grid  Circuit. — When  a 
three-electrode  tube  is  used  as  detector  for  con- 
tinuous waves,  it  is  necessary  to  have  an  addi- 
tional tube  for  producing  the  local  oscillations  or 
else  to  use  the  detecting  tube  itself  to  generate  the 
local  oscillations.  While  any  arrangement  which 
makes  the  tube  oscillate  will  serve  for  the  purpose, 
the  one  which  is  probably  used  more  frequently 
than  any  other  is  shown  in  Fig.  123;  the  tuned 
circuit  is  now  associated  with  the  grid,  being 
coupled  to  the  plate  circuit  by  a  coil  in  the  plate 
circuit,  LI.  This  coil  is  generally  called  the  "  tick- 
ler "  coil. 

If  we  make  the  same  assumption  as  has  been 
made  for  all  the  other  circuits  so  far  considered 
namely,  the  grid  takes  no  current,  then  12=1  and 
the  equations  of  the  circuits  arc, 

di'2     j   div 
€p=~M~dt~Ll~dt> 


dt 


dip 
dt 


*-°- 


(96) 


By  deriving  above  equation  and  substituting  value  of  i,  then  eliminating 
ip  between  the  resulting  equation  and  Eq.  (96)  we  get  (substituting  the 
symbol  i  for  both  i  and  12,  which  are  the  same) 


i      7>, 

++  --+=0- (97) 


CIRCUITS   USED   FOR  SELF-EXCITATION  511 

Guessing  the  solution  to  be  i  =  I  sin  «£  substituting  the  proper  derivatives 
in  Eq.  (97),  we  get  for  the  period  of  oscillation, 

1  (98) 


which  is  practically  the  same  as  — •/==- 

V  CZ/2 

For  the  limiting  condition  of  oscillations,  we  find, 

^S_JgW  (99) 


Eq.  (99)  can  be  written  in  the  form, 

=0, 


from  which,  using  (98)  and  neglecting  terms  involving  -=5-,  we  get, 

tip 


tip 

and  this  can  be  satisfied  only  if  M  is  negative  and  its  absolute  value  is 
greater  than  Mo-^2-  The  condition  imposed  by  (100)  will  be  satisfied  if 
M  is  negative  and  its  absolute  value  lies  between  the  two  roots  of  Eq. 
(100).  So  the  absolute  value  of  M  is  limited  by  the  relation, 


The  condition  is  evidently  different  from  that  existing  when  the  oscillating 
circuit  was  in  series  with  the  plate.  In  that  case  if  M  exceeded  its  critical 
value  the  value  of  the  oscillating  current  was  reduced,  but  there  was  no 
upper  limit  for  the  permissible  value  of  M.  With  the  oscillating  circuit 
in  series  with  the  grid,  however,  the  oscillations  will  cease  if  the  absolute 
value  of  M  exceeds  a  certain  critical  value. 

Circuits  of  Very  High  Frequency.1 — Vacuum-tube  circuits  will  gener- 
ate any  frequency  between  one  per  second  or  less  to  many  millions  per 
second;  the  low  frequencies  require  very  high  values  of  L  and  C,  but 

1  Many  other  circuits  than  the  few  here  analyzed  have  been  designed  and  used.  The 
reader  is  referred  to  an  article  by  L.  A.  Hazeltine  in  Proc.  I.R.E.,  April,  1918,  one  by 
W.  C.  White  in  G.  E.  Review  for  September,  1916,  and  one  by  G.  C.  Southworth  in  the 
Radio  Review  for  September,  1920.  Southworth  has  been  able  to  obtain  frequencies 
as  high  as  3  X 108  cycles  per  second. 


512 


VACUUM  TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


are  comparatively  easy  to  produce.  To  get  the  very  high  frequencies, 
it  is  necessary  to  consider  carefully  all  the  capacity 
in  the  circuit,  especially  that  in  the  tube. 

The  circuit  shown  in  Fig.  124  will  generate 
perhaps  as  high  as  108  cycles  per  second,  if  the 
internal  capacity  of  the  tube  is  low.  The  oscil- 
lating  circuit  is  indicated  by  the  arrow,  and  must 
be  made  with  very  short  leads;  the  condensers  Ci 
and  €2  should  each  be  several  milli-microfarads, 
and  the  values  of  LI  and  L  have  to  be  properly 

1  selected  for  maximum  oscillating  current, 
for  generating  very  high  . 

frequency;   the  oscilla-          rhese  veiT  high-frequency  currents  often  occur 

tory  circuit  is  indicated  when  neither  expected  nor  wanted.     Thus  in  the 

by  the  arrow.  connection  scheme  shown   in  Fig.  125,  the  circuit 

in  which  oscillations  are  desired  is  made  up  of  Lg, 

LP,  R,  and  C,  the  current  being  indicated  by  ammeter  A\.     If  either  R  or 

C  is  too  large,  the  conditions  for  oscillations  in  the  main  oscillatory  circuit 

may  not  be  satisfied,  but  the  adjustment  may  serve 

to  maintain  oscillations  in  the  circuit  indicated  by 

the  arrow.     That  the  tube  is  oscillating  is  known  by 

indication  of  the  continuous-current  ammeter  in  the 

plate  circuit,   but  ammeter  A\  shows  nothing.     If, 

however,    a    hot-wire    meter    of    low  resistance  be 

inserted  in  the  grid  lead,  as  shown  at  A^  it  will  be 

found  that  a  comparatively   large  current  is  being 

generated  in  the  local  path. 

A  similar  condition  may  occur  in  the   circuit  of 

Fig.  126;  the  main  oscillating  circuit  L-C  may  show  FlG-  125-~ In  a  circuit 

no  current  at  all,  but  oscillations  of  very  high  fre- 
quency may  be  flowing  through  Lg  and  Lp  as  indicated 

by  the  arrow,  the  dotted  condenser  really  being  the 

internal  capacity  of  the  tube.1 

Elimination  of    Undesired    Frequencies. — These 

undesired    high-frequency    currents    are    sometimes 

troublesome,   but    may,   in    general,   be    eliminated 

by  suitable  precautions.      Thus  in   a    circuit  used 

with  a  Type   P  pliotron    the    arrangement    of   ap- 
paratus    was    nearly    as    shown    in    Fig.    122;    in 

series  with  R  and  (7   was  another  inductance,  the 


such  as  this  the  os- 
cillatory circuit  is 
made  up  of  R,  Lg,Lp, 
and  C  in  series;  the 
circuit  is  very  likely, 
however,  to  set  up 
spurious  high-fre- 
quency oscillations  in 
the  circuit  including 
grid,  plate,  and  C  as 
indicated  by  the  ar- 
row. 


1  The  circuit  shown  in  Fig.  126,  without  the  main  oscillating  circuit,  (L-C-A)  is 
frequently  used  to  produce  oscillations  of  high  frequency  in  a  receiving  set.  The  values 
of  Lg  and  Lp  must  be  adjustable  for  different  frequencies.  A  very  complete  discussion 
of  this  circuit  is  given  by  A.  S.  Blatterman  in  Vol.  1,  No.  13,  of  the  Radio  Review. 


GENERATION  OF  UNDESIRED   FREQUENCIES 


513 


actual  connection  being  as  shown  on  the  curve  sheet  given  in  Fig.  178, 
p.  (570). 

With  Lp,  of  this  figure,  below  a  critical  value,  the  main  circuit,  Lg-Lp- 
C-L-R,  will  not  oscillate;  it  is  quite  likely,  however,  that  when  the  main 
circuit  is  not  oscillating,  high-frequency  currents  will  be  generated  in  the 
circuit  made  up  of  Lg  and  Lp  in  series  with  the  internal  capacity  of  the 
tube.  Thus,  with  Lg=2QQ  ph,  Lp=400  /z/i,  L  =  8000  >/*,  C  =  .002  /*/,  the 
ammeter  I  (Fig.  178)  gave  no  indication,  but  the  meter  Ip  showed  that 
the  tube  was  oscillating  violently.  Test  with  wave-meter  showed  the 
circuit,  L0-Lp-tube-capacity,  to  be  generating  a 
complex  current  of  fundamental  wave-length  equal 
to  800  meters;  this  is  about  the  natural  frequency 
of  the  circuit. 

The  desired  wave-length,  of  about  6000  meters, 
was  not  started  until  Lp  was  adjusted  in  excess  of 
1200  ,u/i;  the  frequency  changed  suddenly  from  one 
value  to  the  other,  as  Lp  was  varied  through  its 
critical  value.1  There  is  a  tendency  in  such  a  cir- 
cuit, however,  to  maintain  the  existing  oscillation; 
thus  if  Lp  was  increased,  the  high-frequency  oscil- 
lation persisted  until  Lp  exceeded  1200  ph.  As  Lp  , 

,  ,    ,  , ,       ,  .  ,    ,.  .,     r  IG.  126. — In  a  circuit  of 

decreased,  however,  the  high-frequency  oscil-      thig  kind  (often  called 

Meissner 


a  Meissner  circuit) 
spurious  oscillations 
may  be  set  up  in  the 
circuit  indicated  by 
the  arrow,  the  main 
oscillatory  circuit  re- 
maining unexcited. 


lation  did  not  start  until  Lp  was  made  less  than 
1000  ph,  so  that  with  Lp  =  1100  ph,  either  900  meter 
or  6000  meter  oscillations  might  exist,  depending 
upon  whether  Lp  had  been  decreased  from  a  high 
value  to  1100  ph,  or  had  been  brought  up  to  the 
value  from  something  lower. 

An  interesting  condition  was  found  in  this  test : 
if  the  condenser  across  machine  Eb  was  taken  out  the  high-frequency 
oscillation  was  very  persistent,  whereas  the  6000-meter  oscillation  would 
not  start,  no  matter  what  value  Lp  might  have.  Evidently  for  the  lower 
frequency  the  machine  offered  a  high  inductive  reactance  and  resistance, 
whereas  for  the  high-frequency  current  it  acted  like  a  condenser  of  low 
impedance. 

The  undesired  high-frequency  current  for  the  circuit  above  described 
was  completely  eliminated  by  introducing  a  suitable  resistance  directly 
in  series  with  the  grid,  as  indicated  at  A  in  Fig.  178;  100  ohms  sufficed 
to  diminish  their  amplitude  considerably  and  2000  ohms  at  this  point 
resulted  in  such  high  losses  for  the  800-meter  wave  that  it  could  not 
sustain  itself.  This  high  resistance  had  a  negligible  effect  on  the  6000- 

JSee  also  article  by  Moller,  Jahrbuch  der  Drahtlosen  Telegraphic,  December, 
1920. 


514 


VACUUM  TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


meter  oscillation,  because  of  the  comparatively  small  charging    current 
flowing  to  the  grid  at  this  frequency. 

Constancy  of  Frequency  of  an  Oscillating  Tube. — The  foregoing 
formulae  for  frequency  of  oscillation  of  a  tube  circuit  have  all  been  derived 
on  the  assumption  that  the  grid  current  was  zero,  and  do  not  involve 
any  characteristics  of  the  tube,  except  no  and  Rp.  It  is  a  fact,  however, 
that  there  is  an  appreciable  capacity  between  the  grid  and  filament  of 
a  tube,  and  that  the  value  of  this  capacity  varies  with  any  factor  which 
affects  the  /*  (not  MO)  1  of  the  tube  and  circuit,  as  shown  on  page  432  et 
seq.  This  grid-filament  capacity  is  always  shunted  across  a  part  of  the 
oscillating  circuit  and  so  must  have  an  effect  on  the  frequency  of  oscil- 
lation of  the  circuit. 

It  is  therefore  evident  that  any  factor  which  influences  either  tube 
resistance  or  grid-filament  capacity  must  also  effect,  to  some  extent,  the 
frequency  of  oscillation,  and  such  is  found  to  be  the  case.  A  change  in 
either  of  the  filament  current  or  plate  voltage  will  produce  variations  in 
frequency  the  variation,  some- 
times amounting  to  1  per  cent 
or  2  per  cent,  without  excessive 
change  in  either  //  or  Eb.2 

The  Oscillating  Tube  as  De- 
tector of  Continuous  Waves — 
Autodyne. — The  circuit  given  in 
Fig.  123  is  generally  used  for 
exciting  a  tube  used  as  autodyne 
receiver;  with  no  grid  condenser,  FIG.  127.— This  is  the  arrangement  generally 


used  when  an  oscillating  tube  is  to  act  as 
detector  for  continuous-wave  signals.  The 
frequency  of  the  local  oscillations  is  fixed 
by  the  values  of  L2  and  C,  the  tickler  coil,  L, 
serving  to  make  the  tube  oscillate. 


as  shown  in  Fig.  127,  the  detect- 
ing efficiency  of  the  tube  is  in- 
dicated by  Eq.  (31).  The  an- 
tenna circuit  LzCa  is  tuned  to 
incoming  signals  and  the  circuit 

L2C  is  tuned  to  a  frequency  differing  from  this  signal  frequency  by 
about  800  cycles  per  second,  so  as  to  give  a  beat  note  for  which  both  the 
ear  and  ordinary  telephone  receiver  are  sensitive. 

From  Eq.  (31)  it  seems  that  the  more  violently  the  tube  is  oscillating, 
thereby  making  E'Q  as  large  as  possible,  the  more  sensitive  will  the  tube 

,  act  as  detector,  and  so  it  does  as  long  as  -r-f  remains  constant.     This 

1  Changing  the  plate-circuit  impedance  changes  the  effective  value  of  the  tube  capacity 
(and  hence  its  effect  on  the  frequency  of  oscillation),  because  the  n  of  the  tube  and 
circuit  has  been  changed;  the  /u0  of  the  tube,  however,  has  not  been  altered  by  changing 
the  plate-circuit  impedance. 

2  Transmitter  tubes  should  never  have  their  frequency  fixed  by  the  capacity  of  the 
antenna,  which  varies  as  it  swings  in  the  wind;  a  small  master  oscillator,  working  into 
a  closed  oscillating  circuit  should  be  used  for  setting  the  frequency  of  the  big  tubes. 


OSCILLATING  TUBE  AS  DETECTOR  515 

term  j- 1  is  really  a  measure  of  the  assy  me  try  of  the  change  in  plate  cur- 
aeg 

rent  when  Eg  is  positive  and  when  it  is  negative,  in  other  words,  it  measures 
the  excess  of  the  increase  of  plate  current  for  positive  Eg  over  the  decrease 
for  negative  Eg.  So  long  as  the  relation  between  Ip  and  Eg  is  parabolic 

di2 
the  value  of  -  |  is  constant,  but  for  this  condition  the  tube  resistance  Rp 

de/ 


is  also  constant.  We  have  previously  shown,  however,  that  to  make  a  tube 
oscillate,  the  coupling  (of  whatever  kind  is  used)  must  be  increased  beyond 
a  certain  critical  value,  and  that  after  this  value  is  past  the  oscillations 
start  and  automatically  increase  in  amplitude,  until  the  plate  resistance  Rp 
is  sufficiently  increased  to  restore  a  certain  balance  which  was  destroyed 
by  increasing  M.  This  change  of  resistance  was  analyzed  in  discussing 
Fig.  114.  The  plate  current  in  an  autodyne  receiver  will  fluctuate  over 
the  straight  part  of  the  full-line  curve  of  this  figure  if  the  value  of  M 
(between  L\  and  Lz  of  Fig.  127)  is  kept  sufficiently  low:  if  it  is  increased 
much  beyond  its  critical  value  the  fluctuation  in  plate  current  will  extend 
over  the  upper  and  lower  bends  of  the  curves. 

The  tube  will  act  best  as  a  detector  of  continuous-wave  signals  for  that 
coupling  of  LI  and  LI  (Fig.  127)  which  results  in  the  greatest  product 

of  E'0-7— f.     This  product  will  generally  be  a  maximum  for  the  weakest 

Ci(/g 

coupling  which  will  maintain  the  tube  in  the  oscillating  state;  such  is 
nearly  always  found  to  be  the  case  in  practice.  If  the  coupling  between 
Z/2  and  LS  is  held  constant  and  the  coupling  between  Z/2  and  LI  is  dimin- 
ished, the  signal  strength  will  be  a  maximum  for  the  weakest  possible 
coupling.  In  carrying  out  this  test  it  is  necessary  continually  to  change 
C  to  keep  the  beat  note  of  constant  pitch,  because  of  the  effect  of  LI  on 
the  value  of  the  effective  self-induction  of  L^ 

Three  possible  conditions  of  the  adjustment  of  a  beat  receiver  are  shown 
in  Fig.  128.  In  (a)  the  coupling  is  so  adjusted  (tight)  that  the  grid  poten- 
tial, with  no  incoming  signal,  fluctuates  between  A  and  E\  the  plate  cur- 
rent fluctuates  with  a  frequency  nearly  the  same  as  that  of  the  signal, 
between  the  values  AG  and  BH,  its  average  value  being  01.  This  cur- 
rent 01  flows  through  the  phones  and  the  high-frequency  alternating 
component  of  the  plate  current  is  carried  by  the  condenser  shunting  the 
phones.  In  case  no  actual  condenser  is  used  to  shunt  the  phones  this 
current  will  utilize  the  capacity  of  the  phone  cords  or  the  distributed 
capacity  of  the  windings  to  by-pass  the  high  inductance  circuit  of  the  wind- 
ings themselves. 

When  the  signal  voltage  Eg  is  superimposed  on  the  grid  it  alternately 
increases  and  decreases  the  amplitude  of  the  grid  fluctuations  of  poten- 
tial; the  value  of  grid  potential  now  fluctuates  with  variable  amplitude, 
the  amplitude  being  fixed  by  the  limiting  values  EF  and  DC,  the  fre- 


516 


VACUUM  TUBES  AND  THEIR  OPERATION  [CHAP.  VI 


quency  of  these  cycles  of  variation  of  amplitude  being  equal  to  the  dif- 
ference in  frequency  of  Eff  and  E'g. 


FIG.  128. — This  diagram  shows  the  effect  of  the  strength  of  the  local  oscillations  on  the 
signal  strength;  the  audio  frequency  current  through  the  phones,  which  gives  the 
audible  signal,  is  indicated  by  the  wavy  dashed  line  in  each  diagram.  In  (a)  the 
local  oscillations  are  too  violent  to  give  a  good  signal,  in  (6)  the  signal  is  somewhat 
improved  and  in  (c)  it  is  best.  It  is  doubtful  if  the  local  oscillation  could  be  cut 
down  as  much  as  indicated  in  (c)  without  stopping  the  oscillations  altogether. 
For  all  three  diagrams  the  amplitude  of  the  high-frequency  signal  voltage  is  the 
same. 


OSCILLATING  TUBE  AS  DETECTOR 


517 


The  plate  current  will  now  be  of  the  form  shown  in  the  right-hand 
part  of  the  diagram,  and  the  average  value  of  this  high-frequency  plate 
current  will  be  as  shown  by  the  dashed  line  shown  at  K,  L,  M,  etc.,  and 
it  is  this  pulsating  current  which,  flowing  through  the  telephone  receivers, 
gives  the  signal. 

In  diagram  (6)  of  Fig.  128  is  shown  the  effect  on  the  signal  strength 
of  reducing  somewhat  the  amplitude  of  the  locally  generated  oscillations 
E'ffj  which  occurs  as  a  result  of  decreasing  the  coupling  between  L\  and 
L2  in  Fig.  127  (dotted  line  of  Fig.  112).  Although  E'g  is  less  than  in 
diagram  (a),  the  value  of  the  signal  current  (shown  again  by  the 
dashed  line)  is  greater  for  (6)  than  it  is  for  (a). 

In  diagram  (c)  of  Fig.  128  is  shown  the  result  of  still  further  decreasing 
the  value  of  the  local  oscillation  E'g;  it  is  likely  that  M  could  not  be  suf- 


Tube  A 


TubeB 


FIG.  129. — In  order  to  control  easily  the  strength  of  the  local  oscillations  impressed  on 
the  detecting  tube  it  is  best  to  have  a  separate  oscillator  and  couple  this  properly 
to  the  detector,  Tube  A.  In  this  diagram  Tube  B  is  the  oscillator;  it  is  coupled 
to  the  detector  by  the  two  coils  L3  and  L.4 

ficiently  reduced  to  make  the  tube  oscillate  in  this  fashion  without  stopping 
the  oscillations  altogether.  The  signal  current  is,  however,  greater  for 
this  condition  than  for  either  of  the  two  other  values  of  E'g  shown  at 
(a)  and  (6). 

Use  of  a  Separate  Tube  for  Generating  the  Local  Oscillations. — In 
order  to  use  the  vacuum  tube  as  detector  most  efficiently  it  is  necessary 
to  have  the  amplitude  of  the  voltage  E'g  under  control,  and  this  can  best 
be  done  by  using  a  separate  tube  for  generating  the  voltage  E'g,  in  addition 
to  the  detecting  tube.  The  scheme  of  connection  is  then  as  shown  in 
Fig.  129.  The  local  oscillations  are  generated  in  tube  B,  their  frequency 
being  fixed  approximately  by  L±,  L*>,  and  Ci,  and  intensity  by  the  coupling 
between  Ls  and  LG.  This  coupling  should  be  considerably  greater  than 
the  critical  value,  so  that  as  conditions  in  the  circuit  are  changed  the 
oscillations  of  tube  B  are  not  stopped. 


518 


VACUUM   TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


The  value  of  E'g  impressed  on  the  grid  of  the  detecting  tube  A  can 
be  controlled  by  varying  the  mutual  inductance  between  Ls  and  L^ 
either  by  moving  the  coils  with  respect  to  one  another  or  by  changing 
the  value  of  either  of  them.  The  value  of  M  should  be  so  adjusted  that 
the  condition  obtained  is  that  shown  in  Fig.  128,  diagram  (c). 

The  antenna  circuit  and  LzCz  circuit  are  each  tuned  for  the  frequency 
of  the  incoming  signal,  and  the  coupling  between  L\  and  L%  is  adjusted 
as  near  the  critical  value  as  possible.  We  have  shown  that  the  effect 
of  the  coupling  between  LZ  and  L\  is  to  decrease  the  resistance  of  the 
Z/2C2  circuit,  and  this  resistance  may  be  made  to  approach  zero,  if  the 
coupling  is  suitably  adjusted.  Further,  the  LzCz  circuit  can  be  exactly 
tuned  for  the  incoming  signal,  so  that  the  reactance  is  zero  also,  hence 

the  impedance  of  the  L^Ci 
circuit  may  be  made  to 
approach  very  close  to  zero, 
so  that  the  current  caused 
to  flow  by  a  weak  signal 
may  be  perhaps  a  hundred 
or  more  times  greater  than 
it  would  be  if  the  coupling 
Li  —  L2  were  not  used.1 

The  impedance  of  the 
L2C2  circuit,  as  a  function 
of  the  impressed  frequen- 
cy, has  the  form  shown  in 

Fig.  130;  it  is  evident  from 
FIG.  130.— By  properly  adjusting  the  coupling  of  coils   tnig    curye    that  not  omy 
la  and  I,  of  Fig  129  (keeping  the  coupling  too  low    fe  ^       ^       f    ^ 
to  produce  oscillations  in  L2  — C2)  the  resistance  of  °. 

the  circuit  L2-C2may  be  made  to  approach  zero.  one  to  amplify  Signal 
This  curve  shows  how  the  impedance  of  the  L2-C2  strength,  but  also  that 
circuit  will  then  vary  with  frequency  of  impressed  this  amplification  is  very 
sisnal-  selective.  With  a  low 

resistance  coil  for  Li  and 

a    well-insulated    condenser,  and  the  grid    circuit  of  the  tube  adjusted 
to  absorb  but  little  power,  the  selectivity  is  extremely  sharp. 

Effect  of  Condenser  in  Series  with  the  Grid  on  the  Critical  Coupling.— 
In  the  foregoing  analyses  of  the  conditions  required  for  self-excitation 
of  tubes  no  mention  was  made  of  the  effect  of  a  condenser  in  series  with 
the  grid,  as  affecting  the  possibility  of  oscillation.  In  some  common 
oscillating  circuits  it  is  necessary  to  use  a  grid  condenser  to  insulate  the 
grid  from  a  high  positive  potential;  such  a  one  is  shown  in  Fig.  131. 

1  An  experimental  investigation  of  the  magnification  obtainable  in  such  circuits  was 
carried  out  by  E.  H.  Armstrong  and  reported  in  Proc.  I.R.E.,  Vol.  5,  No.  2,  April,  1917. 


.99  x  10" 


1x10° 
Frequency 


1.01  x  10 


5     \ 


OSCILLATING   TUBE   AS   DETECTOR 


519 


The  oscillating  circuit  is  made  up  of  L  with  Ci  and  C2  in  series,  and 
the  tube  is  connected  to  it  as  shown.  The  excitation  for  the  grid  is  sup- 
plied by  the  drop  of  potential  between  the  points  A-C  and  the  plate  volt- 
age is  fixed  by  the  drop  across  condenser  £2.  The  scheme  of  connection 
results  in  the  coil  L  being  at  plate  potential,  i.e.,  it  is  positive  witM  respect 
to  the  filament  by  an  amount  equal  to  £*&;  if  the  grid  were  connected 
directly  to  point  C,  the  tube  would  at 
once  burn  out,  due  to  excessive  plate 
and  grid  currents. 

The  grid  is  therefore  insulated  (in  so 
far  as  continuous  voltage  is  concerned) 
by  the  condenser  Cs;  a  suitable  leak 
resistance  R  serves  to  hold  the  grid  at  a 
proper  average  potential.  The  excitation 
impressed  on  the  grid  is  now  not  equal 
to  the  potential  drop  between  points 
A-C,  but  somewhat  less  than  this  due 
to  the  drop  across  the  condenser  Ca; 
moreover,  due  to  the  absence  of  the 
leak  path  across  Ca  and  the  presence  of 
such  a  leak  across  the  grid-filament  cir- 
cuit, the  phase  of  the  voltage  impressed 
on  the  grid  is  not  the  same  as  that  of  the 
voltage  across  condenser  C\. 

The  effect  of  the  drop  across  Ca  is  to  require  a  higher  drop  across 
A-C  than  would  otherwise  be  required;  if  it  should  happen  that  the 
capacity  of  Ca  is  equal  to  the  capacity  of  the  input  circuit  of  the  tube, 
then  Ci  must  be  made  only  one-half  as  large  as  it  would  otherwise  have 
to  be. 

Effect  of  Oscillations  on  the  Magnitude  of  the  Plate  Current. — If 
an  oscillatory  circuit  has  a  condenser  in  series  with  the  grid,  the  average 
value  of  the  plate  current  will  always  decrease  when  oscillations  begin; 
this  is  due  to  accumulation  of  electrons  on  the  grid  forcing  its  average 
potential  more  negative  when  oscillations  start,  causing  an  accompanying 
decrease  in  the  plate  current.  This  effect  is  shown  by  the  decrease  in 
the  reading  of  a  continuous-current  meter  in  series  with  the  plate. 

When  the  oscillating  circuit  is  such  that  no  grid  condenser  is  required, 
and  none  is  used,  the  reading  of  the  continuous  current  meter  in  the  plate 
circuit  will  generally  increase  when  oscillations  start,  the  increase  being 
more  the  greater  the  excitation  of  the  grid.  This  statement  is  not  univer- 
sally true ;  it  is  possible  to  so  adjust  the  conditions  that  when  oscillations 
start  the  average  value  of  the  plate  current  stays  the  same,  or  even 
decreases.  This  effect  can  be  noted  if,  with  all  other  conditions  constant, 


FIG.  131. — In  a  circuit  of  this  kind  it 
is  necessary  to  use  a  condenser  Cs 
to  insulate  the  grid  from  the  high 
continuous  voltage  impressed  on 
coil  L  by  machine  Eb. 


520  VACUUM  TUBES  AND  THEIR  OPERATION  [CHAP.  VI 

the  filament  current  is  varied  throughout  a  sufficient  range  of  values;  with 
high  filament  current,  the  plate  current  will  increase  when  oscillations 
start,  and  with  low  filament  current  it  will  decrease.  The  case  is  similar 
to  the  action  of  the  tube  as  a  detector,  without  grid  condenser  as  described 
in  p.  444;  it  is  there  shown  that  the  effect  of  an  incoming  signal  may  be 
to  either  increase  or  decrease  the  average  value  of  the  plate  current. 

Criterions  of  the  Oscillating  Condition  of  a  Detecting  Tube. — In  the 
case  of  a  power  tube  the  oscillatory  condition  is  indicated  by  the  meters 
used  either  in  the  grid  circuit,  plate  circuit,  or  oscillating  circuit.  In  the 
case  of  a  small  tube  used  for  the  detection  of  continuous-wave  signals 
there  are  generally  no  meters  in  the  circuit  to  indicate  oscillations;  it  is, 
however,  extremely  important  that  the  operator  should  know  at  all  times 
whether,  or  not  his  tube  circuit  is  oscillating,  because  if  it  is  not  oscillating 
he  cannot  possibly  hear  the  signal  for  which  he  is  listening.  The  only 
method  of  testing  for  oscillations  in  the  ordinary  continuous-wave  detecting 
set  is  to  properly  interpret  the  noises  in  the  telephone  receivers;  to  an 
experienced  operator  they  serve  as  well  as  do  the  meters  on  a  power  set. 

When  no  condenser  is  used  in  series  with  the  grid  it  is  very  easy  to 
tell  when  the  tube  is  oscillating  and  when  not;  when  grid  condenser  is 
used  the  determination  is  not  so  easy.  There  are  two  methods  of  testing 
for  oscillations;  first,  by  making  the  coupling  of  the  tickler  coil  (or  other 
type  of  coupling)  so  weak  that  the  circuit  is  not  generating  oscillations 
and  then  gradually  increasing  the  coupling  past  the  critical  value,  listen- 
ing for  the  characteristic  noise  which  occurs  when  the  critical  coupling 
is  exceeded  and,  second,  by  properly  interpreting  the  noises  heard  in  the 
receivers  when  the  grid  terminal  is  grounded  by  putting  the  thumb  or 
one  finger,  on  the  negative  end  of  the  filament  circuit  and  touching  the 
grid  terminal  with  another  finger.  These  two  schemes  may  be  called  the 
coupling  test  and  finger  test. 

As  has  been  noted  above  when  a  tube  circuit  starts  to  oscillate  the  plate 
current  practically  always  changes  its  average  value,  generally  increas- 
ing when  no  grid  condenser  is  used.  The  change  in  the  plate  current 
is  not  extremely  rapid  because,  with  the  critical  value  of  coupling,  ifc  takes 
many  cycles  before  the  steady  state  is  reached;  the  result  of  the  slow 
change  in  plate  current  is  to  produce  a  peculiarly  soft  quality  of  click 
in  the  receiver.1  This  noise  resembles,  perhaps  more  than  anything  else, 
the  "  plucking  "  of  a  loose  violin  string  and,  when  once  noted,  is  very 
easy  to  recognize. 

In  the  case  of  no  grid  condenser  this  coupling  test  is  very  reliable 
and  easy  to  make.  If  grid  condenser  is  used  the  distinctness  of  this  pluck- 
ing sound  is  by  no  means  as  pronounced  as  is  the  case  for  no  grid  con- 

1  When  listening  for  this  noise  the  coupling  must  not  be  increased  too  slowly;  with 
a  very  slow  increase  in  the  coupling  the  noise  is  so  soft  that  it  may  not  be  heard  at  all. 
When  first  listening  for  this  noise  the  tickler  coupling  should  be  changed  quite  rapidly. 


CRITERIONS  OF  OSCILLATIONS  IN  DETECTOR  TUBE  521 

denser;  for  some  values  of  capacity  and  leak  resistance  it  is  almost  impos- 
sible to  hear  it  at  all,  even  though  the  critical  coupling  is  known  and 
especial  care  is  used  in  listening.1 

In  the  case  of  no  grid  condenser  the  finger  test  gives  very  distinct 
indication  of  the  oscillating  condition;  with  the  moistened  thumtLplaced 
on  a  filament  connection  (binding  post)  a  finger  is  touched  to  the  grid 
connection  of  the  tube,  thus  grounding  the  grid  to  an  extent  sufficient 
to  stop  oscillations.2  The  cessation  of  oscillations  is  accompanied  by 
a  sharp  click  in  the  receivers  and  when  the  finger  is  removed  from  the  grid 
connection  the  starting  of  oscillations,  with  accompanying  change  in  plate 
current,  is  indicated  by  another  click,  generally  less  distinct  than  the  first. 
For  coupling  of  the  tickler  coil  considerably  in  excess  of  the  critical  value, 
the  two  clicks  (starting  and  stopping  oscillations)  are  of  about  the  same 
intensity. 

With  grid  condenser  and  leak  the  finger  test  does  not  give  reliable 
results,  except  to  the  experienced  operator;  even  with  no  oscillations 
two  clicks  are  heard  when  the  finger  is  touched  to  the  grid  connection  and 
when  it  is  removed  therefrom.  With  the  tube  not  oscillating  the  grid  is 
practically  always  positive,  with  respect  to  the  potential  of  the  negative  end 
of  the  filament;  when  the  grid  is  grounded  by  the  finger,  thus  suddenly 
bringing  it  to  the  same  potential  as  the  filament ,3a  sudden  change  occurs  in 
the  plate  current  with  resultant  click  in  the  receiver;  when  the  finger  is 
removed  the  grid  at  once  resumes  its  normal  positive  potential  and  so 
again  gives  a  change  in  plate  current  and  click  in  the  phones.  As  has 
been  previously  noted,  when  grid  condenser  is  used  the  grid  leak  resist- 
ance is  best  connected  by  the  positive  end  of  the  filament;  such  has 
been  assumed  in  statements  just  made. 

The  same  two  clicks  are  observed  if  the  tube  is  oscillating,  and  there  is 
not  much  difference  between  the  clicks  in  the  two  cases.  This  is  especially 
true  if  the  grid  condenser  is  small  and  electron  supply  in  the  vicinity  of 
the  grid  plentiful;  if,  for  example,  with  an  ordinary  detecting  tube  the 
grid  condenser  is  100  MM/  (a  commonly  used  value)  and  filament  temper- 
ature normal,  even  a  good  operator  may  not  distinguish  any  difference 
in  the  clicks  for  the  oscillatory  and  non-oscillatory  condition. 

If,  however,  the  grid  condenser  is  much  larger,  say  5000  MM/  or  larger, 

1  The  distinctness  of  the  noise  depends  upon  the  rapidity  of  change  in  plate  current; 
if  a  large  condenser  is  used  it  changes  slowly  and  hence  the  change  in  plate  current  is 
slow,  with  corresponding  indistinctness  in  the  sound  in  the  telephones. 

2  On  most  receiving  sets  it  will  be  found  that,  even  though  the  grid  connection 
directly  at  the  tube  is  not  accessible,  some  screw  or  binding  post  connected  to  the  grid, 
is  available. 

3  It  may  possibly  happen  that  when  the  tube  is  oscillating  the  average  potential 
of  the  grid  is  the  same  as  the  negative  end  of  the  filament;   in  this  case  no  change  in 
plate  current  occurs  when  the  grid  is  touched  and  so  no  noise  is  heard  in  the  phones. 


522  VACUUM  TUBES  AND  THEIR  OPERATION  [CHAP.  VI 

there  is  a  marked  difference  to  be  noticed ;  with  oscillations  the  two  clicks 
have  nearly  the  same  intensity,  but  with  no  oscillations  the  click  heard 
upon  removing  the  finger  from  the  grid  connection  is  much  softer  than 
the  one  heard  when  making  contact  with  the  grid.  When  the  tube  is 
not  oscillating  it  takes  an  appreciable  time  to  charge  the  grid  condenser 
to  its  normal  potential  and  the  accompanying  change  in  plate  current 
is  slow,  thus  giving  a  weak  sound;  the  larger  the  grid  condenser  and  the 
lower  the  filament  temperature,  the  longer  will  this  charging  time  be  and 
correspondingly  weaker  is  the  click  in  the  receivers. 

The  tests  for  the  oscillating  condition  can  then  be  summarized  as 
follows: 

Coupling  Test. — No  Grid  Condenser. — Distinct  sound  (plucking  string) 
when  critical  coupling  is  exceeded. 

With  Grid  Condenser. — The  click  occurring  when  critical  coupling  is 
exceeded  is  not  distinct  unless  the  grid  condenser  is  large  (several  milli- 
microfarads)  and  the  filament  temperature  subnormal. 

Finger  Test. — No  Grid  Condenser. — Two  distinct  clicks  when  tube 
is  oscillating  and  none  at  all  when  tube  is  not  oscillating. 

With  Grid  Condenser. — Two  distinct  clicks  of  nearly  equal  intensity 
if  tube  is  oscillating;  if  tube  is  not  oscillating  the  click  upon  touching  the 
grid  connection  is  more  pronounced  than  that  when  releasing  the  grid, 
the  distinction  being  more  pronounced  with  larger  grid  condensers. 

Peculiarities  of  Adjustment  of  Oscillating  Detectors. — When  first 
working  with  oscillating  detectors  certain  apparent  discrepancies  will  be 
encountered.  Thus  if  the  tuned  grid  circuit  uses  one  of  the  coils  of  a  loose 
coupler  and  the  other  coil  of  the  coupler,  or  a  section  of  it,  is  used  for  the 
tickler  coil,  it  may  be  found  that  when  the  coils  are  separated,  oscillations 
occur,  no  matter  which  way  the  tickler  coil  is  connected  in  the  plate  circuit. 
It  may  also  be  found  that  oscillations  occur  when  the  coils  are  quite  widely 
separated  and  that  as  the  coils  are  brought  nearer  together  the  oscilla- 
tions cease,  an  apparent  contradiction  to  the  analysis  previously  given. 

With  the  coils  arranged  as  shown  in  Fig.  132,  it  is  apparent  that  the 
magnetic  coupling  of  Li  and  Lz  is  weak,  but  it  may  well  be  that  the  two 

coils  of  the  coupler 
permit  enough  elec- 
•  TO  plate  trostatic  coupling  of 
the  plate  and  grid 
circuits  to  produce 
oscillations,  and  this 

FIG.  132.— If  an  ordinary  coupler  is  used  in  making  tests  for  even  if  the    connec- 
oscillations  some  peculiar  results  may  be  obtained.  tion     of     L\    is    re- 

versed.    Now  if  the 

sense  of  the  magnetic  coupling  of  LI  and  L?   is  incorrect  for  producing 
oscillations,  the  electrostatic  coupling  of  the  two  circuits  will  be  neutral- 


PECULIAR  NOISES  WITH  OSCILLATING  DETECTOR 


523 


ized  as  the  two  coils  are  brought  closer  together,  and  when  they  get 
close  enough,  the  coupling  due  to  both  effects  will  be  less  than  the 
critical  value  and  so  oscillations  will  stop.  In  case  the  tickler  coil  con- 
sists of  only  a  few  concentrated  turns  this  effect  will  not  be  noticed. 

When  the  coupling  of  plate  and  grid  circuits  is  accomplished  by  rotating 
one  coil  inside  the  other,  it  will  often  be  found  that  setting  the  coils  at 
right  angles  to  one  another,  which  of  course  makes  M  =  0,  will  not  stop 
oscillations  and  that  the  coils  must  be  rotated  considerably  past  the  90° 
point  before  the  oscillations  stop.  This  is  because  of  the  electrostatic 
coupling  introduced  by  the  proximity  of  the  two  coils;  enough  reversed 
magnetic  coupling  must  be  introduced  so  that  the  total  coupling,  induc- 
tive plus  capacitive,  is  less  than  the  critical  value  for  the  circuit.  This 
effect  is  mentioned,  and  analyzed  on  p.  504. 

Peculiar  Noises  Occurring  in  an  Oscillating  Detector  Circuit. — If 
the  oscillating  detector  circuit  has  no  condenser  in  series  with  the  grid 
its  behavior  is  very  regular,  but  if  a  grid  condenser  is  used  all  sorts  of 
queer  noises  may  be  heard  in  the  phones,  unless  the  adjustment  is  care- 
fully carried  out.  The  noise  may  vary  from  a  series  of  regular  "  clicks," 
separated  from  each  other  by  several  seconds,  to  a  high  shrill  signal ;  on 
carrying  out  further  adjustments,  the  note  may  become  so  high  as  to  be 
inaudible,  so  that  the  operator  has  no  convenient  way  of  telling  that  the 
action  of  the  tube  is  irregular  and  that  readjustment  is  required. 

The  condition  practically  always  occurs  as  a  result  of  too  tight  coupling 
of  the  tickler  coil,  too  high  a  resistance  for  the  grid  leak,  or  a  combination 
of  both.  The  noise  is  due  to  the  starting  and  stopping  of  oscillations,  the 
musical  pitch  having  nothing  to  do  with  the  frequency  of  oscillation,  but 
being  fixed  by  the  rapidity  with  which 
one  group  of  oscillations  follows  the 
next. 

The  oscillations  start,  thus  charging 
the  grid  condenser  and  reducing  the 
mean  potential  of  the  grid  and  so 
changing  the  Rp  of  the  tube;  but  the 
condition  for  oscillation  for  the  circuit 
given  in  Eq.  (101)  depends  upon  Rp, 
and  it  is  evident  from  inspection  of 
this  equation  that  if  RP  increases,  the 
value  of  M  required  for  oscillation  is 
increased.  In  Fig.  133  is  shown  the 
relation  between  Ep  and  Ip,  for  two 
values  of  Eog]  the  curve  OA  is  for 
Eog=Q,  and  the  curve  DB  is  for  Eog  at 
some  negative  value.  The  slope  of 
this  curve  serves  as  a  measure  of  R 


D  c 

Plate  voltage. 

FIG.  133. — When  oscillations  start,,  in 
a  circuit  using  a  condenser  in  series 
with  the  grid,  the  plate-current  curve 
may  change  from  OA  to  DB,  due  to 
the  decrease  in  average  potential  of 
the  grid,  when  oscillations  start. 


the  value  of   Rp   being  actually 


524  VACUUM  TUBES  AND  THEIR  OPERATION  [CHAP.  VI 

given  by  the  cotangent  of  the  slope,  when  the  scales  for  Ep  and  Iv  are 
the  same;  if  not  the  same,  the  value  of  Rp  obtained  by  measurement 
in  the  curve  must  be  multiplied  by  the  ratio  of  the  "  volts  per  inch  " 
of  this  graph  to  the  "  amperes  per  inch." 

Let  us  suppose  that  when  oscillations  start  the  normal  potential  of 
the  grid  is  zero,  the  plate  voltage  being  given  by  OC,  Fig.  133;  the  value 
of  Rp  is  then  tan  <f>,  and  M  is  adjusted  to  such  a  value  that  oscillations 
start.  The  grid  is  then  forced  negative  so  that  the  Ep  —  Ip  curve  changes 
from  OA  to  DB,  thus  increasing  the  value  of  RP  to  tan  </>',  and  so  increas- 
ing the  coupling  requirement,  as  given  by  Eq.  (101),  that  the  value 
of  M  is  not  sufficient  to  maintain  oscillations,  the  circuit  then  stops 
oscillating. 

During  the  oscillations,  however,  the  grid  condenser  has  become 
charged,  and  before  oscillations  can  again  start  the  charge  must  leak  off 
sufficiently  to  bring  the  plate  current  from  CB  to  CA,  Fig.  133.  The 
time  required  is  fixed  by  the  magnitude  of  the  charge  on  the  condenser 
and  the  time  constant  of  the  grid-condenser,  grid-leak  circuit.  The  adjust- 
ment might  be  such,  for  example,  that  90  per  cent  of  the  charge  in  the 

t 
condenser  must  leak  off  before  oscillations  again  start.     If  (1  —  e~^)  is 

to  be  0.90,  we  must  ha.ve  -^  =2.3;  if  then  C  =500  MM/  and  R  =2  megohms, 

KL 

we  have  t  =  2.3X5XlO-10X2xl06,=  .0023  second.  The  starting  and 
stopping  of  oscillations  in  the  circuit  would  then  occur  about  500  times 
a  second  and  a  musical  note  of  500  vibrations  a  second  would  be  heard 
in  the  telephone  receivers. 

If  the  leak  resistance  is  greater  in  value,  or  the  condenser  of  greater 
capacity,  the  note  will  be  of  lower  pitch,  and  it  will  be  higher  if  either 
the  leak  resistance  or  capacity  is  decreased.  When  the  terminals  of  the 
vacuum  tube  are  well  insulated  from  one  another  and  no  external  grid 
leak  resistance  is  used  it  is  possible  to  so  adjust  a  tube  circuit  that  the 
interval  between  successive  groups  of  oscillations  is  a  minute  or  more, 
thus  producing  a  series  of  clicks  in  the  telephone  receivers  separated  from 
each  other  by  that  interval  of  time. 

The  pitch  of  these  disturbing  noises  may  be  practically  always  sent 
beyond  the  audible  limit  by  lightly  touching  the  grid  connection  and 
filament  connection  of  the  oscillating  tube;  if  the  finger  and  thumb  making 
the  connection  are  pressed  down  too  tightly  the  leak  resistance  will  be 
lowered  to  such  an  extent  that  the  tube  will  stop  oscillating  altogether. 
The  pitch  of  the  note  may  be  varied  by  changing  either  the  plate  voltage 
or  filament  current,  both  of  these  having  influence  on  Rp  and  thus  on  the 
critical  value  of  the  coupling  M;  they  also  effect  to  some  extent  the  grid 
leak  resistance. 


REGENERATIVE   COUPLING  WITH  SPARK  SIGNALS  525 

The  squealing  noise  will  nearly  always  be  produced  if,  after  the  proper 
value  of  M  has  been  obtained  for  a  certain  setting  of  the  tuning  condenser 
C  (Fig.  123)  the  capacity  of  this  condenser  is  much  decreased.  Decreasing 
C  increases  co  and  so,  according  to  Eq.  (101),  makes  a  lower  value  of  M 
permissible ;  with  the  ordinary  detecting-tube  circuit,  having  grid  con- 
denser, it  is  practically  always  necessary  to  use  the  lowest  value  of  M 
compatible  with  the  requirements  of  Eq.  (101)  if  steady  oscillations  are 
to  be  produced.  A  value  of  M  much  greater  than  this  will  not  only  cut 
down  the  sensitiveness  of  the  tube  as  a  detector,  but  is  always  likely  to 
produce  noises. 

Use  of  Regenerative  Circuit  for  Spark  Reception. — A  tube  circuit 
arranged  with  "  tickler  "  or  other  form  of  coupling  for  the  detection  of 
continuous-wave  signals  is  also  adapted  for  the  reception  of  spark,  or 
damped-wave,  signals;  with  the  antenna  circuit  and  the  local  circuit  (Lz  —  C 
of  Fig.  127)  tuned  accurately  to  the  incoming  signal  the  tickler  coupling 
can  be  increased  to  a  value  slightly  less  than  that  required  for  producing 
oscillations.  The  intensity  of  the  signal,  by  using  a  suitable  value  of 
coupling,  can  be  increased  hundreds  of  times  over  the  value  it  would 
have  if  no  tickler  coupling  were  used. 

It  has  been  shown  that  the  effect  of  the  coupling  is  to  reduce  the 
resistance  of  the  L^  —  C  circuit  to  a  very  low  value  (Fig.  130)  so  that  a 
certain  e.m.f.  impressed  on  this  circuit,  from  the  antenna  circuit,  will 
produce  a  current  perhaps  100  times  as  great  as  would  normally  be  the 
case.  The  change  in  the  plate  current  (which  gives  the  signal  in  the 
phones)  is  proportional  to  the  square  of  the  voltage  impressed  on  the  grid, 
as  given  in  Eq.  (18),  and  so  will  increase  greatly  as  the  resistance  of  the 
L2  —  C  circuit  is  made  to  approach  zero  by  suitable  tickler  coupling.  If 
e.g.,  the  actual  resistance  of  L^  —  C  is  10  ohms  and  by  means  of  tickler 
coupling  the  effective  resistance  is  reduced  to  0.1  ohm,  the  current  in 
L2  —  C  is  increased  100  times,  the  voltage  impressed  on  the  grid 
is  increased  100  times,  and  the  signal  current,  A/p,  is  increased 
104  times. 

The  effect  on  the  signal  strength  as  the  mutual  inductance  between 
LI  and  Li  (Fig.  127)  varies  is  shown  in  Fig.  134;  as  M  is  increased  the 
signal  intensity  rapidly  increases,  retaining  its  normal  musical  quality, 
until  such  a  coupling  is  reached,  OA,  that  oscillations  start.  The  resulting 
noise  in  the  telephone  when  the  tube  is  oscillating,  is  of  "  scratchy  " 
quality  being  caused  by  a  kind  of  beat  phenomenon  between  continuous 
waves  locally  generated  and  the  incoming  damped  waves;  as  the  phase 
relations  between  the  successive  wave  trains  and  the  continuous  oscilla- 
tions of  the  tube  are  of  haphazard  values,  and  as  the  amplitude  of  the 
spark  signals  is  variable  throughout  each  wave-train,  the  resulting  vari- 
ation in  amplitude  of  the  plate  current  is  of  very  irregular  character,  thus 


526  VACUUM   TUBES  AND  THEIR  OPERATION  [CHAP.  VI 

producing  the  scratchy  note  for  couplings  indicated  by  the  dotted  line 
in  Fig.  134. 

Regenerative  Circuit  for  Short-wave  Spark  Reception. — For  short-wave 
reception,  say  less  than  400  meters,  probably  the  most  satisfactory  type 
of  circuit  is  one  which  uses  no  other  coupling  between  the  grid  and  plate 
circuits  than  that  due  to  the  capacity  coupling  in  the  tube  itself.  In 
this  scheme  the  "  tickler  "  coil  of  Fig.  127  is  replaced  by  a  small  vari- 
ometer, not  coupled  to  the  L^  —  C  circuit  at  all ;  the  required  amount  of 
inductance  in  this  variometer  varies  with  the  wave-length,  type  of  tube, 

etc.,  but  is    generally  less  than   1  milli- 
I  henry.     It  is  best  to  add  in  the  L^  —  C 

\  circuit    another    variometer    about    the 

'  same  as  that  used   in  the  plate  circuit, 

thus  making  it  possible  to  tune  the  closed 
circuit  with  very  small  value  of  C. 
«  The  L,2  —  C  circuit  is  carefully  tuned 

to  the  incoming  signal  and  the  regenera- 
£  tive  action  is  brought  to  its  maximum 

|  permissible  value  by  suitably   adjusting 

c  the  variometer  in  the  plate   circuit.     As 

*•          the  plate  inductance  is  increased,  a  slight 
increasing  M  further  adjustment  of   the    closed  tuned 

FIG.  134.— If  the  tickler  coil  is  used  circuit  is  generally  required  in  order  to 
when  receiving  spark  signals   (of  get  maximum  sensitiveness, 
sufficiently   low    decrement)    the         Behavior  of  a  Regenerative  Receiver 
signal   will   increase   very  rapidly  Regarding  Sound  of  Signal,    etc.— There 
as    tickler   is    increased   until  this 

passes  its  critical  value;  the  tube  are  man^  Cresting  phenomena  con- 
starts  to  oscillate  and  then  the  nected  with  the  adjustments  of  this  re- 
signal,  although  very  loud,  loses  generative  circuit  other  than  those  already 
its  characteristic  musical  note  and  mentioned.  When  M  is  made  just  great 
becomes  "mushy"  in  quality.  enough  to  produce  oscillations  (slightly 

greater  than  OA,  Fig.  134)  the  detecting 

efficiency  of  the  circuit  is  greatly  increased,  so  much  so  that  spark  signals 
so  weak  as  to  be  entirely  inaudible  with  tickler  coupling  just  less  than 
the  critical  value  become  quite  loud  when  oscillations  start.  In  this 
case  the  listening  operator  gets  no  clue  to  the  identity  of  the  sending 
station  from  the  spark  note  because  the  signal  is  inaudible  until  the 
tube  is  oscillating,  and  then  the  distinctive  spark  note  is  not  present. 

If  such  a  weak  signal  is  coming  in  and  the  closed  circuit  is  properly  tuned 
to  it  (with  tickler  coupling  about  equal  to  its  critical  value),  a  peculiar 
effect  is  produced  by  the  adjustment  of  the  antenna  circuit.  With  this 
circuit  much  detuned  of  course  the  signal  is  inaudible;  as  the  antenna 
loading  coil,  or  similar  adjustment,  is  increased  the  signal  becomes  audible 


BEHAVIOR  OF   REGENERATIVE   RECEIVER  527 

with  a  scratchy  quality  (tube  supposedly  oscillating) ;  as  this  adjustment 
is  continued  the  signal  increases  in  intensity  until  at  a  certain  value  of 
loading  it  disappears  completely;  on  continuing  the  adjustment,  however, 
the  signal  reappears  at  a  certain  point  and  gradually  decreases  as  the 
adjustment  is  further  carried  out.  Upon  investigation  it  will  be  found 
that  this  narrow  region  where  the  signal  is  inaudible  is  caused  by  the 
cessation  of  oscillations  in  the  tube  circuit.  The  antenna  circuit  introduces 
a  resistance  effect  into  the  oscillating  tube  circuit  which  varies  with  the 
relative  tuning  of  the  two,  being  a  maximum  when  the  antenna  and 
closed  circuit  are  tuned  alike;  hence  a  tickler  coupling  which  is  just 
sufficient  to  cause  oscillations  with  an  antenna  somewhat  mistuned  is 
insufficient  for  the  tuned  condition.  A  quantitative  idea  of  this  change 
of  resistance  of  the  oscillating  circuit,  due  to  variation  in  antenna  tuning 
is  given  in  Fig.  91,  Chapter  I,  p.  93. 

For  the  best  reception  of  the  signal  the  adjustment  of  the  antenna 
should  be  set  at  the  midpoint  of  the  silent  region  and  the  tickler  coupling 
increased  just  sufficient  to  produce  oscillations  for  this  condition. 

In  case  a  continuous-wave  signal  is  being  received,  the  following  effect  of 
the  antenna  tuning  on  the  reactance  of  the  oscillating  circuit  may  be  noted. 
With  antenna  and  closed  circuit  normally  adjusted,  a  certain  note  is  heard 
in  the  telephone;  this  note  may  be  observed  to  vary  over  a  considerable 
range  as  the  tuning  of  the  antenna  is  changed,  the  variation  in  note  being 
caused  by  the  change  in  the  effective  inductance  in  the  closed  oscillating 
circuit  by  the  reaction  of  the  antenna.  The  amount  of  change  in  note 
obtainable  depends  upon  the  coupling  between  antenna  and  closed  cir- 
cuit; some  idea  of  its  magnitude  may  be  had  by  inspection  of  Fig.  91, 
Chapter  I,  p.  93. 

Eqs.  (84)  and  (85),  p.  91,  permit  quantitative  prediction  of  the'amount 
of  change  in  resistance  and  reactance  of  the  oscillating  circuit,  as  affected 
by  the  antenna  circuit. 

Operation  of  Power  Tubes  in  Parallel  for  Greater  Power  Output. — 
Vacuum-tube  generators  or  converters  operate  very  well  in  parallel, 
remaining  synchronized  automatically;  l  the  proper  division  of  the  load 

1  An  interesting  demonstration  of  the  inherent  tendency  of  tube  circuits  to  syn- 
chronize with  each  other  is  easily  obtained.  If  a  small  power  tube  is  set  into  oscillation 
in  the  laboratory  and  an  autodyne  detector  circuit  in  the  same  room  is  used  for  listen- 
ing, it  will  be  found  that  as  the  beat  note  is  decreased  from  high  value  there  will  be 
a  certain  lowest  audible  note  obtainable.  Thus  perhaps  the  detector  adjustment  is 
such  as  to  give  a  beat  note  of  200;  upon  attempting  to  bring  this  detector  more  nearly 
into  synchronism  with  the  power  tube,  lowering  the  beat  note,  this  note  will  completely 
disappear,  and  it  will  seem  as  though  the  autodyne  had  stopped  oscillating,  but  it  will 
be  found  that  the  beat  note  has  disappeared  because  the  detector  tube  has  pulled  into 
synchronism  with  the  power  tube.  The  closer  the  two  circuits  are  together  the  higher 
will  be  the  lowest  beat  note  obtainable, 


528 


VACUUM   TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


may  be  most  easily  accomplished  by  variation  of  the  filament  currents. 
All  filaments  may  be  lighted  in  parallel  from  the  same  source,  but  each 
filament  should  have  its  own  rheostat;  it  is  also  best  to  have  an  ammeter 
in  series  with  each  plate  and  grid.  A  suitable  connection  scheme  is  shown 
in  Fig.  135;  the  same  scheme  of  connection  can  be  used  for  any  number 
of  tubes. 


FIG.  135. — Connection  of  several  power  tubes  for  parallel  operation. 

The  adjustments  of  the  circuit  must  of  course  be  changed  as  more 
tubes  are  put  into  operation,  because  the  effective  resistance  of  the  load 
must  equal  the  plate  circuit  resistance  of  the  battery  of  tubes  for  maxi- 
mum output,  and  the  combined  tube-circuit  resistance  varies  inversely 
as  the  number  in  operation. 

The  voltage  required  for  the  filament  of  the  ordinary  power  tube  is 
about  twenty;  it  is  limited  by  the  fact  that  too  much  power  must  not 


FIG.  136. — It  is  impossible  to  work  tubes  in  parallel,  with  their  filaments  in  series, 
because  of  the  greatly  different  filament  currents  resulting  in  the  different  tubes. 

be  used  in  the  filament  circuit,  yet  the  filament  current  must  be  fairly 
large  because  the  plate  current  must  not  be  more  than  about  15  per  cent 
of  the  filament  current,  and  this  plate  current  must  be  a  considerable 
fraction  of  an  ampere  unless  excessively  high  voltages  are  used. 

As  the  ordinary  electrical  power  supply  is  110  volts,  it  might  seem 
that  if  tubes  are  to  operate  in  a  group  several  filaments  might  be  con- 
nected in  series,  thus  saving  in  power  consumption;  thus  five  20- volt 
filaments  might  be  operated  on  a  110-volt  line  and  still  leave  enough  volt- 


OPERATION  OF  POWER  TUBES  IN  PARALLEL 


529 


age  for  a  control  rheostat.  But  such  a  connection  of  filaments  is  impos- 
sible. The  filament  current  of  each  tube  would  differ  from  that  of  the 
next  one  in  series  by  an  amount  equal  to  the  plate  current  of  that  tube 
as  shown  in  Fig.  136.  If  each  plate  current 
is  0.3  ampere,  the  currents  in  the  filament 
circuit  would  be  as  shown,  but  such  a  con- 
dition is  impossible  because  a  filament  which 
will  safely  carry  4.0  amperes  (tube  A)  would 
have  practically  no  electron  emission  with 
current  less  than  3.40  amperes,  so  that  tubes 
C  and  D  of  the  series  would  be  dead  in  so 
far  as  electron  current  is  concerned;  the 
plate  current  of  each  of  these  tubes  would 
be  zero  instead  of  0.3  ampere  as  shown. 
When  oscillations  start,  the  maximum  value 
of  plate  current  of  tube  A  would  be  about 


0.8  ampere,  thus  rendering  even  tube  B  more  Fia 


— The   filament   of   a 


power  tube  is  used  most  effi- 
ciently if  it  is  lighted  from  a 
small  alternating-current  trans- 
former as  shown  here. 


or  less  ineffective. 

If  alternating  current  is  available  for 
lighting  the  filaments  it  may  be  used  very 
advantageously;  the  voltage  of  the  power 

supply  may  be  reduced  by  a  transformer  to  any  value  desired  for 
the  filament;  the  plate  circuit,  instead  of  connecting  to  either  end 
of  the  filament  connects  to  the  center  point  of  the  secondary  of  the 

transformer  as  indi- 
cated in  Fig.  137. 
This  increases  the 
life  of  the  filament 
because  each  end  of 
the  filament,  in  turn, 
carries  the  larger 
curfent  instead  of 
one  end  being  con- 
tinously  loaded  more 
than  the  other,  as  is 

„  the  case  when   con- 
FIG.  138. — A  scheme  for  using   two   rectifier  tubes  A  and  B 

in  connection  with  transformer  7,  to  get  a  high,  continuous-  tmuous     current     IS 
voltage  supply  for  the  plate  circuit  of  oscillator  tube  C.         used  for  lighting  the 

filament. 

Alternating-current  Supply  for  Filament  Current,  Plate  Voltage.— It 
is  often  difficult  to  get  high-voltage  continuous-current  power  for  the  plate 
circuit  of  a  high-voltage  tube;  it  is  possible  to  use  a  rectified  alternating- 
current  supply  where  a  high-voltage  machine  is  not  available.  In  Fig. 


A.C. 

Supply 


530 


VACUUM  TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


138  is  shown  a  scheme  for  using  two  kenotrons  (rectifiers),  A  and  B,  con- 
nected to  a  high-voltage  winding  in  such  a  way  that  the  plate  of  the  three- 
electrode  generator  C  receives  unidirectional  pulses  which  serve  in  place 
of  a  continuous-current  supply.  By  the  use  of  suitable  condensers,  D, 
and  choke  coils,  E,  the  power  supplied  to  the  plate  of  C  may  be  made 
as  uniform  (free  from  pulsation)  as  may  be  desired. 

The  four  transformer  coils  shown,  F  the  primary,  G  and  H  low-volt- 
age secondaries  and  /,  high-voltage  secondary  will  all  be  wound  on  the 
same  core;  the  low-voltage  winding  H  must  be  protected  from  the  other 
windings  and  core  by  high-voltage  insulation  because  it  assumes  a  high 
positive  potential  as  soon  as  operation  of  the  set  begins.  If  the  voltage 
desired  in  the  plate  of  tube  C  is  2500  volts  the  winding  /  should  have  a 
voltage  rating  of  5000  or  6000  volts  (effective). 


\ 


FIG.  139. — Illustrating  the  action  of  the  rectifier  tubes,  in  connection  with  condensers 
D-D  (Fig.  138)  to  give  the  variable  unidirectional  voltage  a-b-c-d. 

Instead  of  using  several  condensers  and  choke  coils  to  smooth  out  the 
pulses  of  e.m.f.  supplied  to  the  plate  of  the  power  tube  a  single  condenser, 
of  sufficient  capacity,  might  be  used  without  choke  coils  The  required 
size  of  the  condenser  can  be  readily  calculated  if  we  assume  the  permissible 
variation  in  voltage  applied  to  the  plate. 

Let  us  suppose  the  voltage  furnished  by  one  half  of  transformer  I 
is  given  by  the  equation  e  =  Em  sin  ut  and  is  shown  in  Fig.  139  at  curve  1  ; 
this  voltage  is  operative  in  one  rectifier  circuit  and  the  voltage  operative 
in  the  other  rectifier  circuit  is  shown  at  curve  2.  The  average  voltage 
impressed  on  the  plate  of  the  power  tube  is  shown  by  the  dotted  line  V0, 
and  the  actual  voltage  is  shown  by  the  broken  line  a-b-c-d.  At  time  t\ 
the  condenser  D  (Fig.  138)  begins  to  charge  because  the  voltage  operating 
in  rectifier  A  circuit  becomes  larger  than  the  potential  difference  of  the 
condenser  plates.  Neglecting  the  voltage  required  to  cause  saturation 
current  to  flow  in  the  rectifier  (which  will  generally  be  small  compared 
to  the  voltage  V0  and  Em)  we  suppose  the  charging  current  of  the  condenser, 


ALTERNATING   CURRENT  SUPPLY   FOR   PLATE   CIRCUIT       531 

through  rectifier  AY  to  rise  at  once  to  its  maximum  possible  value,  i.e., 
saturation  current  of  the  rectifier,  Ic.  The  condenser  continues  to  charge 
at  a  uniform  rate  until  some  time  £2,  when  the  voltage  across  the  condenser, 
which  has  been  rising,  becomes  equal  to  the  voltage  of  curve  1;  at  this 
time  the  current  through  the  rectifier  suddenly  drops  to  zero. 

From  this  time  rectifier  A  is  idle  until  one  complete  cycle  later  than 
time  ti,  when  the  operation  is  repeated. 

From  time  fe  to  £3  the  condenser  is  discharging  through  the  plate  cir- 
cuit of  the  power  tube  the  voltage  falling  as  indicated  by  the  line  b-c. 
At  time  fe  rectifier  B  comes  into  play  and  the  condenser  voltage  is  again 
raised  along  the  line  c-d  and  from  time  U  until  rectifier  A  again  begins  its 
charging  cycle  the  condenser  voltage  again  falls. 

The  amount  of  potential  drop  from  6  to  c  is  evidently  fixed  by  the 
amount  of  current  taken  by  the  power  tube  and  the  capacity  of  the  con- 
denser used.  If  we  call  the  time  from  t\  to  fe,  which  is  the  time  the  con- 
denser is  charging,  6,  and  if  the  average  current  taken  by  the  plate  cir- 
cuit of  the  power  tube  is  70,  it  is  evident  that 


With  a  given  rectifier  (fixing  Ie)  it  is  evident  that  6  is  determined  at  once 
from  the  current,  7o,  required  for  the  power  tube.  If  V  is  the  maximum 
condenser  voltage,  at  time  fe,  and  V"  is  the  minimum  condenser  voltage 
at  time  fe  it  is  seen  that 


in  which  T  is  the  period  of  the  impressed  e.m.f.  If  the  specified  permis- 
sible fluctuation  in  condenser  voltage  is  given  this  equation  gives  the 
required  capacity  of  the  condenser.  If  the  fluctuation  is  expressed  as  a 
fractional  part  of  the  average  voltage  Fo,  that  is 


V'-V" 

~ 


-d\T     nV'-V" 
=C- 


From  this  relation  we  get  as  the  required  capacity  of  the  condenser,  after 
using  the  value  of  B  given  above 


in  which  /  is  the  frequency  of  the  alternating  voltage. 


532  VACUUM   TUBES  AND  THEIR  OPERATION  [CHAP.  VI 

From  this  equation  the  advantage  of  a  high-frequency  power  supply 
is  at  once  evident.  As  an  example  suppose  the  two  rectifiers  have  an 
emission  of  current  of  0.8  ampere,  the  frequency  of  power  supply  is  500 
cyles,  allowable  variation  of  plate  voltage  of  power  tube  to  be  ±5  per 
cent,  required  average  plate  voltage  2000  volts  and  required  plate  current 
of  0.2  ampere.  The  condenser  required  is,  from  Eq.  (102),  0.75  micro- 
farad. 

The  required  value  of  6  is 

0.2  7T 


By  reference  to  Fig.  139  it  is  evident  that  Em  is  approximately  given  by 
3  ;  in  the  above  example  0  =  68.5°  so 


sin 

JB»  =  2^=2150  volts. 

Actually  this  voltage  would  be  considerably  too  low;  we  have  neglected 
the  drop  of  voltage  in  the  rectifiers  which  would  probably  be  200  volts 
which  makes  the  required  value  of  Em  about  2350  volts.  As  this  voltage 
is  that  of  one-half  of  the  secondary  of  transformer  winding  7  (Fig.  138) 
it  is  evident  that  the  winding  should  give  a  maximum  voltage  of  4500  volts. 
If  we  consider  the  reactance  and  resistance  of  winding  7  other  slight 
corrections  would  be  required  making  it  advisable  perhaps  to  specify  a 
voltage  of  5000  (maximum)  for  this  transformer. 

It  may  sometimes  be  worth  while  to  consider  the  proper  values  of 
ratio  of  VQ  to  Em  from  the  standpoint  of  overall  efficiency.  Thus  the 
power  used  in  heating  filaments  A  and  B  (Fig.  138)  is  expended  throughout 
the  cycle,  whereas  we  have  assumed  the  emission  current  to  be  used  but 
a  small  fraction  of  the  cycle.  In  the  problem  worked  out  above  it  might 
pay  to  cut  down  the  amount  of  power  used  in  heating  the  filament,  thus 
cutting  down  7e,  making  6  larger.  Before  this  point  could  be  treated 
analytically  it  would  be  necessary  to  know  the  relation  between  emission 
current  and  required  filament  power.  At  present,  with  tungsten  filaments 
it  requires  from  50  to  100  watts  per  ampere  of  emission,  if  the  filament 
is  operated  at  such  a  temperature  that  its  life  may  be  1000  hours  or  more. 

For  average  conditions  a  value  of  0  of  -=  seems  right. 

Use  of  a  Separate  Exciter  for  a  Group  of  Tubes. — It  is  not  always 
possible  to  get  as  much  power  from  a  self-excited  tube  as  from  a  separately 
excited  one,  and  the  adjustment  for  such  a  condition  is  critical;  if  it  is 
used,  the  tube  may  stop  oscillating  when  a  slight  drop  in  plate  voltage 
or  filament  current  occurs.  This  is  a  dangerous  condition,  because  unless 


SEPARATELY  EXCITED   POWER  TUBES 


533 


the  operator  notices  at  once  that  the  tube  is  not  oscillating  the  plates 
will  rapidly  become  overheated  and  the  tube  perhaps  spoiled.  To  avoid 
this  contingency  a  separate  exciting  tube  may  be  used,  this  tube  furnish- 
ing only  enough  power  to  operate  its  own  circuit  and  supply  the  losses 
in  the  grid  circuits  of  the  group  of  power  tubes.  Such  a  scheme  is  shown 
in  Fig.  140;  the  exciter  tube  A  is  adjusted  with  tight  coupling  between 
Z/2  and  Li,  so  that  it  oscillates  under  any  condition  which  may  occur,  and 
the  power  tubes  M,  N,  etc.,  are  each  excited  by  a  common  connection 
to  tube  A.  By  adjustment  of  the  condensers  C\ — €2,  etc.,  the  output  of 
each  power  tube  may  be  controlled,  this  control  being  in  addition  to  that 


Load  Circuit 

FIG.  140. — When  many  tubes  are  to  operate  in  parallel  it  is  generally  best  to  excite  them 
from  a  separate  tube  A,  self -oscillating,  controlling  the  amount  of  excitation  by 
condensers  Ci  —  C2,  etc. 

afforded  by  the  filament  current.  The  frequency  of  the  exciter  circuit 
must  of  course  be  that  required  for  resonance  in  the  load  circuit  of  these 
power  tubes. 

In  case  the  individual  control  of  the  excitation  is  not  desired  a  common 
adjustable  condenser  may  be  inserted  in  the  exciter  lead  where  indicated 
by  the  dotted  lines  at  X;  this  condenser  should  have  a  reactance  about 
equal  to  the  impedance  of  the  combined  input  circuits  of  the  power  tubes. 

Although  the  largest  tubes  made  to-day  permit  a  power  consumption 
in  the  plates  of  not  more  than  250  watts,  thereby  limiting  the  power 
output  to  about  twice  this  amount,1  it  seems  likely  that  tubes  of  much 
greater  capacity  will  soon  be  obtainable;  water-cooled  plates  are  an 
obvious  necessity  and  a  steel  tube,  instead  of  glass,  with  continuous 
pumping  by  a  mercury-vapor  pump  during  use,  seem  to  be  likely 
developments. 

1  See  p.  539  et  seq.  for  tube  efficiency  analysis. 


534 


VACUUM  TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


Another  scheme  for  using  an  exciter  tube  for  maintaining  the  power 
tube  in  oscillation  is  shown  in  Fig.  141.  In  this  case  the  exciter  tube 
is  not  a  self -exciting  unit,  but  operates  in  conjunction  with  the  power 
tube;  the  frequency  of  output  is  determined  entirely  by  the  L  —  C  circuit 
of  the  power  tube. 

The  amount  of  excitation  furnished  to  the  grid  of  the  exciter  tube 
depends  upon  the  relative  magnitudes  of  €2  and  Cs;  ordinarily  63  should 
be  many  times  as  great  as  €2-  The  value  of  the  resistance  R  may  vary 
widely,  a  suitable  value  being  equal  to  the  resistance  of  the  plate-filament 
circuit  of  the  exciter  tube. 

This  arrangement  is  a  very  useful  one  if  it  is  desired  to  vary  the  fre- 
quency of  the  output  circuit  over  a  wide  range;  in  a  typical  case  the  fre- 
quency of  the  output  circuit  was  varied  (by  changing  L  and  C)  from  500 
to  300,000  cycles  per  second  without  changing  the  adjustment  of  the 


Power  tube 

FIG.  141. — A  scheme  for  using  an  untuned  exciter  tube;  this  scheme  is  a  good  one  if  the 
set  is  to  oscillate  with  very  wide  variations  in  the  values  of  L  and  C. 

exciter  tube  and  a  wider  range  could  have  been  covered  without  any 
other  adjustments  than  those  of  L  and  C,  had  it  been  so  desired. 

Special  Forms  of  Tubes — Dynatron — Pliodynatron. — In  a  special  form 
of  three-electrode  tube,  first  advocated  by  A.  W.  Hull  and  called  by  him 
the  dynatron  (see  Fig.  21,  p.  389,  for  picture  of  dynatron),  the  phenom- 
enon of  secondary  emission  is  utilized.  If  an  electron  traveling  at 
high  speed  collides  with  a  metallic  surface,  the  giving  up  of  its  energy 
at  the  surface  is  likely  to  "  jar  "  other  electrons  out  of  the  metal  at  the 
point  where  the  collision  occurs;  the  emission  of  the  electrons  from  this 
surface,  caused  by  the  colliding  electron,  is  called  secondary  emission. 
The  number  of  electrons  emitted  depends  upon  the  speed  of  the  colliding 
electron;  it  may  be  none  at  all  and  may  be  as  much  as  a  dozen  or  more. 

Ordinarily  these  electrons  due  to  secondary  emission  will  at  once 
re-enter  the  surface  from  which  they  have  been  emitted,  but,  if  there 
happens  to  be  in  the  vicinity  of  the  surface  an  electrode  of  higher  poten- 
tial, these  secondarily  emitted  electrons  will  not  re-enter  the  surface  from 


SIM'X'IAL  TYPES  OF  TUBES 


535 


which  they  came  but  will  go  to  the  higher  potential  electrode,  thus  causing 
electron  current  away  from  the  surface  to  which  the  first  electron  is 
traveling. 

The  number  of  electrons  taking  part  in  this  reversed  current  depends 
upon  the  number  caused  by  the  secondary  emission 
and  upon  the  potential  of  the  surface  attracting  them. 
Suppose  the  arrangement  of  electrodes  as  given  in 
Fig.  142;  the  grid  is  at  higher  potential  than  the 
plate  and  so  attracts  most  of  the  electrons  caused  by 
the  normal  thermal  emission  from  filament  F.  How- 
ever, some  of  these  electrons  will  go  through  the 
interstices  of  G  and  impinge  on  P,  causing  secondary 
emission  where  they  strike.  As  G  is  at  higher  po- 
tential than  P,  the  electrons  due  to  secondary  emis- 
sion are  likely  to  go  to  G  instead  of  re-entering  P. 

If  the  potential  of  G  is  held  constant  (contact  B 
remaining  fixed)  and  the  potential  of  P  is  gradually 
increased  from    zero    by    moving    contact  A  to    the 
happenings  will  be  about  as  shown  in  Fig.  143. 


FIG.  142. — Connection 
of  a  three-electrode 
tube  to  get  the 
characteristics  of  the 
dynatron. 


FIG.  143. — Curves  of  various  currents  occurring  in  the 
operation  of  the  dynatron. 


tron;     an    increasing    plate    potential 
current,  in   other  words,,  an   alternati 


right,  the  various 
Curve  0  —  A  shows  the 
electron  current  to  P 
due  to  emission  from  P; 
curve  0-B  shows  the 
amount  of  secondary 
emission  from  P,  due  to 
electrons  of  current  OA ; 
curve  C  shows  the  frac- 
tional part  of  the  second- 
ary emission  which  is  at- 
tracted to  G ;  curve  0-D 
shows  the  electron  cur- 
rent away  from  P  due 
to  secondary  emission, 
and  curve  OEFGH 
shows  the  actual  electron 
current  to  P,  all  of  these 
curves  being  plotted  for 
increasing  plate  poten- 
tial. 

The     peculiarity     of 
that  part   of  the   curve 
from  E  to  G  is  the  basis 
of  action  of  the   dyna- 
results    in    a    decrease    in    plate 
ir-current   test   of   the   resistance 


536 


VACUUM   TUBES  AND  THEIR  OPERATION  [CHAP.  VI 


of  the   plate-filament   circuit  in   this   region   of  operation   would   show 
a  negative  resistance. 

The  dynatron  has  thus  practically  the  same  characteristics  as  an 
ordinary  three-electrode  tube  with  the  regenerative  connection  of  plate 
and  grid  circuits,  and  it  may   be  used  for  similar 
purposes. 

The  current  curve  of  Fig.  143,  between  points  E 
and  G,  can  be  expressed  by  the  equation. 


(103) 


where 


i=  plate  current; 

i0  =  value  of  plate  current  obtained  by 
projecting  the  'curve  GFE  back 
to  v  =  o  as  shown  in  Fig.  143 ; 

r  =  internal    resistance    of   the    tube, 

determined   from   the   slope  of 
FIG   144.-Connection  the  QFE  curye 

of     three  -  electrode    m  .-,  f -.^       ,mn\         i 

tube  as  a  dynatron.   Transposing  the  terms  of  Eq.  (103)  we  have 

v=r(io  —  i) 

If  the  voltage  of  the  battery  B  (Fig.  144)  is  E  and  the  drop  across  the 
resistance  R  is  V,  then 


Then 


dV       R 


dE    R-r 


(104) 


As  R-r  may  be  made  small,  it  is  evident  that  a  small  increase  in  E,  the 
voltage  used  in  the  plate  circuit,  may  result  in  a  much  larger  change  in 
the  voltage  drop  across  R.  It  has  been  possible  to  regulate  the  tube  so 
that  an  increase  of  one  volt  in  E  has  resulted  in  a  change  of  the  potential 
difference  across  R  of  100  volts,  thus  giving  a  voltage  amplification  of 
100  times. 

The  dynatron  may  be  used  as  regenerative  detector,  oscillating  detector 
of  continuous  waves,  or  as  a  generator  of  alternating-current  power  just 
as  can  the  ordinary  three-electrode  tube;  it  is  not  evident,  however,  that 
it  has  any  advantage  over  the  three-electrode  tube  as  ordinarily  used. 

It  is  possible  to  add  a  fourth  electrode  to  a  dynatron  and  thus  make 
it  act  as  a  normal  three-electrode  tube  in  addition  to  the  effects  obtained 
from  secondary  emission.  A  possible  connection  of  such  a  tube  (called 
the  pliodynatron)  is  shown  in  Fig.  145.  By  suitably  adjusting  the  two 
e.m.f.'s  OB  and  OA,  the  circuit  may  be  made  to  oscillate  at  a  frequency 


SPECIAL   TYPES   OF  TUBES 


537 


FIG.  145. — Connections  of  the  pliodynatron. 


HOOO 


-50     —40     -30     -20      -10        0      +10      +20     +30    +40    +50     +60    +70    +80    +90    +100 
Grid  potential 

FIG.  146. — Dynatron  characteristics  in  an  ordinary  telephone  repeater  tube. 


538 


VACUUM   TUBES  AND   THEIR  OPERATION 


[CHAP,  vr 


determined  by  L-s  —  Cs;  so  adjusted  it  acts  as  an  amplifying  receiver 
for  continuous  waves;  with  slightly  different  voltage  OB  it  may  be  made 
to  act  as  an  efficient  detector  of  damped  waves. 

The  special  forms  of  plate  current  curve  for  the  dynatron  given  in 
Fig.  143,  may  be  duplicated  to  some  extent  by  any  three-electrode  tube; 
in  Figs.  146,  147,  and  148  are  shown  the  curves  of  grid  current  of  an  ordi- 


1000 
900 
800 
700 
600 
500 
400 
300 
200 
100 
0 

100 
200 
30f 
40C 


Amplif; 


ying  tube 


IU~ 1.15  amp 


75  v 


Its 


0  volts 


urves  of 


rrent 


olts 


for  vario  is  plate  V 


Stages 


ft 


150  v 


olt 


X 


/200  vo^ts 


-50      -40     —30     —20      -10         0       +10     f2i)      +30      +40     +50     +60      +70     +80     +90 

Grid  potential 
FIG.  147. — Dynatron  characteristics  in  an  ordinary  telephone  repeater  tube. 


nary  telephone  amplifying  tube  operated  outside  its  normal  range.  This 
tube  normally  operates  with  a  negative  grid,  but  by  carrying  the  grid 
through  sufficiently  high  positive  potentials  the  form  of  its  current  is  made 
to  resemble  that  of  the  dynatron  very  closely.  The  tube  was  not  pumped 
to  as  high  a  vacuum  as  are  the  dynatron  and  pliotron,  so  that  there  was 
more  gas  present  in  this  tube,  but  the  regularity  of  the  curves  and  the 
fact  that  they  could  be  duplicated  as  many  times  as  desired  shows  that 


THREB-ELECTRODE  TUBE  AS  POWER  CONVERTER 


539 


however  much  gas  there  was  present,  it  was  probably  playing  a  minor 
role  in  the  action  of  the  tube. 

Detailed  Study  of  the  Three-electrode  Tube  as  a  Power  Converter. — 
The  foregoing  analyses  of  the  conditions  for  oscillation  of  a  three-electrode 
tube  have  all  been  based  on  the  assumption  that  the  plate  current  in  the 
oscillatory  condition  could  be  sufficiently  well  represented  by  a  constant 
current  with  a  sine-wave  current  superimposed,  and  on  this  basis  we 
have  shown  that  the  theoretical  maximum  output  of  the  tube  was  one- 


1 

900 
830 
700 
6GO 
500 
400 
300 
230 
100 
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100 
200 

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1 

60     -50     -40      -30     -20      -10         0        +10      +20      +30     +40      +50      +60      +70      +80      +90     +100 
Grid  potential 

FIG.  148. — Dynatron  characteristics  in  an  ordinary  telephone  repeater  tube. 

half  of  the  input;  the  fact  was  also  mentioned  that  the  conditions  demanded 
for  this  efficiency  of  50  per  cent  could  not  be  realized,  so  that  we  were 
forced  to  conclude  that  the  maximum  efficiency  of  a  tube  generator  was 
about  40  per  cent. 

The  author  with  the  assistance  of  Mr.  H.  Trap  Friis  l  carried  out  a 

detailed  study  of  the  tube  generator  for  both  separate  and  self-excitation, 

and  it  was  found  that  the  efficiency  might  become  very  much  higher 

when  the  proper  adjustments  were  made;  part  of  the  results  of  this  study 

1  Proceedings  of  A.I.E.E.,  Vol.  38,  No.  10,  Oct.,  1919. 


540 


VACUUM  TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


will  be  given  here,  as  they  show  exactly  how  a  tube  functions.  The  nota- 
tion used  in  this  analysis  is  somewhat  different  from  that  used  so  far 
because  the  previous  symbols  are  not  applicable.  The  plate  current  can- 
not be  represented  by  Iov-\-Imp  sin  ut,  as  has  been  previously  assumed; 
it  consists  of  a  series  of  pulses  so  that  an  infinite  series*  of  sine  terms  would 
be  required  to  represent  the  alternating  component.  The  plate  voltage 
also  does  not  have  exactly  a  sinusoidal  variation.  We  therefore  represent 
the  instantaneous  value  of  the  actual  plate  voltage  by  ep,  grid  voltage 
by  e0j  plate  current  by  ip,  grid  current  by  ia,  etc.,  instead  of  representing 
each  by  a  constant  plus  a  sine  term. 

Oscillograms  were  taken  to  show  the  various  quantities  entering  into 
the  operation  of  the  tube  and  circuit,  the  frequency  of  the  alternating 
current  being  between  100  and  200  cycles;  later  the  circuit  constants 
were  diminished  sufficiently  to  raise  the  frequency  to  100,000  cycles,  to 

show    that    the    re- 

^ooooor^  suits     obtained     at 

the  lower  frequency 
(which  allowed  ac- 
curate oscillographic 
records  to  be  ob- 
tained) were  valid 
at  radio  frequencies. 
The  first  effect 
studied  was  the 
change  in  form  of 
ep  and  ip  as  the 
excitation  of  the 
grid  was  increased, 
using  a  separately 
excited  circuit  as 
indicated  in  Fig.  149. 

The  reactance  of  Ci  was  62  ohms  and  of  LI  was  8700  ohms;  the  value 
of  R  was  1000  ohms  and  the  resistance  of  LI  was  190  ohms.  The  MO  of 
the  tube  used  was  3.9. 

With  comparatively  low  values  of  Ec  and  Eg  a  record  was  taken  of 
eff,  ep,  and  ip,  and  is  given  in  Fig.  150;  it  is  seen  that  the  fluctuations  in 
ep  and  ip  were  nearly  sinusoidal  so  that  the  results  of  the  previous  analysis 
would  hold  good  for  this  condition.  Upon  increasing  eg  to  six  times 
its  value  the  forms  of  ev  and  ip  are  made  to  differ  widely  from  sine  forms, 
however,  as  shown  in  Fig.  151. 

An  interesting  point  is  shown  by  the  film;  the  value  of  R  used  was 
1000  ohms  and  this  is  the  value  which  gives,  for  this  tube,  maximum  out- 
put for  low  values  of  E8,  as  shown  in  Fig.  94.  This  value  1000  ohms 


-x^y- 

Continuous  c 
current  power  c 
supply  circuit  j-^ 

c 
c 

3 
0 

/       Plate 

P  / 

|{p                             II 
Filament                F                S  "a 

I""                            S  S 

w  iii             ^s 

FIG.  149. — Connection  of  power  tube  for  study  of  its 
characteristics. 


THREE-ELECTRODE   TUBE  AS  POWER  CONVERTER  541 

must  therefore  be  the  tube  resistance  Rp  for  the  low  value  of  Ev.  But 
with  large  excitation  used  in  Fig.  151  the  plate  current  evidently  fluctuated 
as  much  as  possible  (from  zero  to  saturation  current)  and  the  fluctuation 
in  ep  is  less  than  half  of  Eb,  indicating  that  R  should  be  more  than  doubled 
if  maximum  output  is  to  be  obtained  from  the  tube.  This  it  will  be  remem- 
bered has  been  predicted  as  necessary  when  ip  fluctuates  between  zero  and 
saturation  current,  and  ep  fluctuates  between  the  limiting  values  of  zero  and 
2  Eov.  With  a  resistance  load  of  the  kind  shown  in  Fig.  149  it  is  evident 
that  such  a  wide  variation  in  the  value  of  ep  is  impossible;  the  load  cir- 


FIG.  150. — Nearly  sinusoidal  variations  in  ep  and  ip  for  low  grid  excitation.     J£&  =  900 
h  =  .25,  #c  =  120,  Eg  =  50,  Frequency  =  140,  #  =  1000,  C  =  18.4  microfarads. 

cuit  must  contain  inductance  and  capacity  to  cause  ep  to  fluctuate  so 
widely.     This  point  is  taken  up  later  on  in  this  section. 

If  R  is  still  further  reduced  the  distortion  in  ep  and  ip  will  appear  with 
much  lower  values  of  Eg;  in  Fig.  152  is  shown  a  record  for  a  value  of 
Eg  of  100  volts  with  R  only  100  ohms.  The  fluctuation  in  ep  is  now 
hardly  noticeable  although  ip  fluctuates,  with  distorted  form,  from  zero 
to  saturation  current  as  before.  The  current  taken  by  the  grid  in  Figs. 
150  and  152  was  zero;  in  Fig.  151  the  grid  swings  positive  300  volts  so 
we  might  expect  a  large  grid  current,  but  it  is  shown  to  be  small.  This 
is  due  to  the  fact  that  the  plate  is  at  rather  high  potential  (650  volts) 
during  the  time  the  grid  is  positive,  so  that  but  few  electrons  go  to  the 
grid. 


542 


VACUUM  TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


Fig.  151  shows  also  the  fluctuation  of  h;  in  spite  of  the  large  induct- 
ance Li  (which  was  10  henries)  there  is  considerable  variation  in  h.    This 

must  of  course  always  be  the  case;  the  value  of  L\  ~  must  at  any  instant 

CM 

be  equal  to  the  difference  between  ED  and  ey. 


FIG.  151.  —  Distortions    occurring   with    higher    grid    excitations. 
Ec  =  120,  Eg  =  300,  /=  140,  R  =  1000,  C  =  18.4/x/. 


=  .34 


In  Fig.  153  are  shown  the  curves  of  ep,  ip,  and  eg  for  two  values  of 
R,  all  other  conditions  being  the  same;  it  may  be  seen  that  the  amount 
of  distortion  in  ip  is  reduced  as  the  value  of  H  is  increased.  In  getting 
these  two  films  the  value  of  Lj  was  kept  constant,  with  the  result  that 


THREE-ELECTRODE  TUBE  AS  POWER  CONVERTER 


543 


FIG 


152.—  -Witn  low  load  circuit  resistance  distortions  occur  for  even  low  grid  excitation. 
#6  =  900,  76  =  .34,  £c  =  120,  #?  =  100,/=140,  #  =  100,  C  = 


Fie;.  153. — Showing  effect  of  load  resistance  on  forms  of  voltage  and  current,  other  con- 
ditions constant.  For  both  films  Eb  =  900,  Ec  =  120,  ^  =  100  and /=  140.  For 
left-hand  film  7&  =  .295,  #  =  1000.  For  other  7&  =  .272,  #  =  2010. 


544 


VACUUM   TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


a  larger  percentage  of  the  generated  alternating  current  of  the  tube  went 
through  this  path,  with  the  higher  value  of  R,  instead  of  through  the  load 
circuit,  Ci  —  R. 

Attempts  were  then  made  to  see  what  adjustments  of  the  tube  and 
associated  circuits  gave  best  efficiency;  the  importance  of  high  efficiency 
will  be  at  once  appreciated  when  it  is  mentioned  that  a  given  tube  (the 
one  used  in  these  tests)  has  an  output  of  about  200  watts  in  normal  oper- 
ation whereas  if  the  efficiency  could  be  raised  to  90  per  cent,  the  safe 
output  would  increase  to  2250  watts. 

The  tests  carried  out  involved  an  adjustment  with  separate  excitation 
to  find  the  conditions  for  maximum  output  and  then  transferring  the  grid 
connection  to  a  proper  point  of  the  circuit  to  get  self-excitation,  recording 


FIG.  154. — Connection  of  the  power  tube  to  a  tuned  output  circuit,  showing  where  oscil- 
lograph vibrators  were  introduced  and  directions  of  current  assumed  as  positive 
(above  zero  line  in  oscillograms) . 

for  each  condition  the  forms  and  phases  of  currents  and  e.m.f.'s.  The 
tests  were  run  at  low  frequency  so  that  oscillograph  records  might  be 
obtained;  the  results  obtained  were  duplicated  later  in  a  high  frequency 
run. 

Fig.  154  shows  the  circuit  used;  simpler  ones  may  be  used,  but  the 
laboratory  apparatus  at  hand  was  best  suited  to  this  one.  The  diagram 
also  shows  where  the  oscillograph  vibrators  were  introduced  and  the 
direction  of  currents  assumed  as  positive;  if,  on  a  film,  a  current  is  shown 
below  its  zero  line,  it  was  flowing  in  the  opposite  direction  to  that  shown 
in  the  diagram.  If  the  frequency  of  the  exciting  voltage,  Eg,  is  chosen 
the  same  as  the  resonant  frequency  of  the  load  circuit 

i 

/=- 


CiC2  V 


THREE-ELECTRODE   TUBE  AS  POWER  CONVERTER 


545 


the  impedance  of  this 
circuit  between  the  two 
points  M  and  N,  where 
the  tube  is  attached,  will 
be  resistive  only,  its 
magnitude  being  equal 
1 


to 


ohms. 


The  quantities  to  be 
considered  are  shown 
conventionally  in  their 
proper  phases  in  Fig. 
155 ;  the  current  i\ ,  which 
flows  in  the  resonant 
load  circuit,  may  be 
several  times  as  large  as 
the  current  i,  furnished 
by  the  tube.  The  two 
important  things  in  this 
diagram  are  shown  in 
the  lower  part  of  the 
figure,  namely,  the  curves 
of  epip  and  of  epi.  These 
curves  give  the  power 
loss  on  the  plate  and  the 
power  supplied  by  the 
tube  to  the  load  circuit, 
respectively.  It  is  at 
once  evident  that 

Energy  loss  on  plate 

per  cycle  =  I     epipdt  = 
Jo 

Area  A. 

Energy  supplied  to 

r2* 

load  circuit  =  |     epidt  = 

Jo 
Area  C  —  Area  B. 

It  is  evidently  desirable 

to    make   the    latter   as 

large  as  possible  and  the 

former  as  small   as  pos-  pIG  155 —Showing  the  important  variables  to  be  studied 

sible,  if  the  tube  circuit  in  determining  tube  efficiency.- 


T  860  —  vv  — 
o            o 

-II     l] 

nr 

IF 

t- 

I 

_  a, 

•£-  L. 

1 

V 

u 

rO 

A      to 

u 

MI^T> 

U    LL) 

lo^vl 

1+  I 


Time 


546 


VACUUM   TUBES  AND   THEIli   OPKKATION 


[CHAP.  VI 


is  to  operate  efficiently.  Any  ordinary  scheme  of  analysis,  using  the 
relation  given  in  Eq.  (5),  p.  417,  must  fail  because  the  relation  does  not 
hold  good  for  those  values  of  ep  and  eg,  which  are  the  most  important 
ones  in  the  cycle  of  operation,  namely,  low  ep  with  positive  ev,  and 
very  high  values  of  ep  with  large  negative  ea. 

The  ordinary  so-called  static  characteristics  of  the  tube  used  are  given 
in  Fig.  156;   they  are  not  of  much  service  in  predicting  the  behavior  of 


200  400  GOO  800  1000  1200 

Plate  Voltage 

FIG.  156. — Static  characteristics  of  the  pliotron  used  in  making  the  tests. 


the  tube  when  the  output  is  forced  as  high  as  possible.  They  did  bring 
out  the  fact,  however,  that  the  filament  ammeter,  if  a  continuous-current 
instrument,  does  not  read  correctly  the  filament  current  when  the  tube 
is  generating  alternating-current  power.  The  ammeter  indicated  3.65 
amperes  when  getting  the  curves  of  Fig.  156  and  the  total  emission  for  such 
a  current  is  evidently  about  0.5  ampere.  Now  when  the  tube  was  oscillat- 


THREE-ELECTRODE   TUBE  AS   POWER  CONVERTER 


547 


ing,  the  filament  ammeter  reading  3.65  amperes,  the  total  emission  was 
about  0.8  ampere,  showing  that  the  filament  temperature  was  much  hotter 
than  when  not  oscillating.  Holding  the  voltage  across  the  filament  constant 
(approximately  the  condition  when  the  tube  is  oscillating)  the  set  of  curves 


Amp. 


FIG.  157. — This  set  of  curves  shows  how  the  filament  current  changed  as  the  plate 
voltage  was  increased;  even  with  3.75  amperes  in  that  end  of  the  filament  carrying 
the  larger  current  the  emission  was  only  .5  ampere,  whereas  when  oscillating  this 
same  tube  gave  an  emission  of  .8  ampere  with  an  indicated  filament  current  of  only 
3.65  amperes. 

given  in  Fig.  157  were  obtained.  The  grid  was  held  at  a  positive  potential 
of  100  volts  and  the  plate  voltage  suitably  varied.  The  electron  current 
to  the  plate  increases  the  filament  current  at  one  end  and  decreases  it 
at  the  other;  the  relative  values  of  increase  and  decrease  will  be  deter- 


548 


VACUUM  TUBES  AND  THEIR  OPERATION  [CHAP.  VI 


III 


I 
2 


.g 

'o 
> 

I 

o. 


'i 

1 


\ 


'3 


3  3 

»  g 


X 


mom 

«3=! 


V^ 


X 


\ 


i 


^ 


"V 


d  °9  ^ 


THREE-ELECTRODE  TUBE  AS   POWER  CONVERTER 


549 


mined  largely  by  the  resistance  used  in  series  with  the  filament  battery. 
It  can  be  seen  that  even  with  the  larger  filament  current  as  great  as  3.75 
amperes  the  emission  was  only  0.5  ampere. 

From  some  preliminary  oscillograph  records  we  knew  that  in  oper- 
ation the  total  emission  was  about  0.8  ampere  when  the  filament  ammeter 
read  3.65  amperes.  A  brief  test  showed  that  the  filament  current  required 


Amp. 

.8 


,=4.0  Amp. 


80 


120 


160 


200  240  280 

E6     Plate  Voltage 


320 


360    Volts 


FIG.  159. — Grid  and  plate  currents  for  various  fixed  grid  potentials  and  variable  plate 
voltage,  filament  current  at  4.0  amperes;  these  curves  were  obtained  by  extra- 
polation in  Fig.  158.  The  numbers  noted  on  the  individual  curves  signify  the  grid 
potential  (positive)  the  lower  set  of  curves  being  grid  current  and  upper  set  plate 
current. 

to  give  this  much  emission  was  4.00  amperes,  but  this  seemed  like  an 
excessive  current  at  which  to  carry  out  a  test,  so  we  got  the  characteristics 
required  from  extrapolation.  In  Fig.  158  is  shown  a  set  of  curves  show- 
ing the  variation  of  plate  and  grid  currents  for  various  filament  currents 
and  grid  and  plate  potentials,  they  being  extrapolated  for  the  higher 
filament  currents.  From  this  set  of  curves  the  results  given  in  Fig.  159 
were  obtained;  as  these  are  important  curves  they  were  verified  for  cor- 
rectness of  form  by  actually  getting  them  for  a  lower  filament  current. 


550 


VACUUM   TUBES  AND   THEIR  OPERATION  [CHAP.  VI 


These  are  given  in  Fig.  160  and  are  of  just  the  same  form  as  those  of  Fig. 
159. 

It  is  well  to  point  out  here  that  even  if  we  had  been  able  to  get  the 
curves  of  Fig.  159  with  a  filament  current  of  4.00  amperes  they  would  not 
have  given  the  proper  values  of  ip  and  ig  for  the  tube  in  operation.  While 
getting  these  static  characteristics  the  plate  and  grid  get  very  hot,  much 
hotter  than  when  the  tube  is  in  operation  as  a  generator.  The  emission 
from  the  filament  is  fixed  by  the  filament  temperature,  and  this  in  turn 
is  fixed  by  the  fil'ament  current  and  the  temperature  of  the  plate;  if  this 
is  hotter  when  getting  the  static  characteristics  than  when  the  tube  is 
generating,  the  values  of  iv  and  ig  obtained  would  probably  be  too  large. 


80 


120 


1GO  200          240 

E  b  Plate  Voltage 


280 


320 


SCO    Vo'tsl 


FIG.  160. — As  the  curves  of  Fig.  159  are  important,  and  they  were  obtained  by  extra- 
polation, they  were  verified  for  correctness  of  form  by  picking  off  from  Fig.  158  a 
similar  set  of  curves  for  a  filament  current  of  3.65  amperes;  evidently  these  curves 
are  of  the  same  form  as  those  of  Fig.  159. 

The  curves  of  Fig.  159,  in  connection  with  Fig.  155  enable  us  to  at 
once  give  the  minimum  potential  to  which  the  plate  should  drop  and  the 
maximum  positive  potential  for  the  grid.  In  order  to  make  the  area  A 

(Fig.  155)  small  the  plate  potential,  at  time  |,  should  be  as  low  as  possible. 

This  minimum  will  be  controlled,  however,  by  the  other  requirement 
that  the  area  C  should  be  large.  If,  during  the  time  when  ep  is  low,  ip 
does  not  have  its  maximum  possible  value  (saturation  current)  then  the 
positive  alternation  of  i  will  not  be  as  large  as  it  should  be  and  if  this  is 
not  large  the  power  input  to  the  load  circuit,  determined  principally  by 
the  area  of  C,  will  be  lower  than  its  proper  value. 


THREE-ELECTRODE  TUBE  AS  POWER  CONVERTER  551 


FIG.  161. — In  this  figure  various  forms  of  plate  current  have  been  assumed  and  (plate 
voltage  remaining  fixed  in  shape)  the  resulting  efficiencies  calculated. 


552  VACUUM   TUBES  AND  THEIR  OPERATION  [CHAP.  VI 

As  the  average  value  of  i  must  be  zero,  if  its  positive  loop  is  to  be  as 
large  as  possible,  and  the  area  of  A  to  be  kept  as  small  as  possible,  the 
conditions  should  evidently  be  so  adjusted  that,  at  minimum  plate  poten- 
tial, saturation  current  should  flow,  and  this  flow  should  last  for  a  short 
time  only.  During  the  rest  of  the  cycle  the  plate  current  should  be  zero. 

Fig.  161  shows  the  calculated  losses  on  the  plate  and  input  to  the 
load  circuit  for  four  different  forms  of  plate  current,  the  plate  voltage 
having  the  same  form  for  each.  It  will  be  seen  that  both  the  losses  and 
the  output  of  the  tube  are  greatest  for  the  sinusoidal  plate  current,  but 
the  efficiency  for  this  condition  is  only  39  per  cent;  as  the  form  of  plate 
current  approaches  a  short  pulse  the  efficiency  increases,  being  77  per 
cent  for  the  form  shown  in  curve  (d).  The  trapezoidal  form  shown  at 
(c)  resembles  very  closely  the  form  we  used;  the  test  actually  gave  about 
60  per  cent  efficiency. 

All  four  curves  are  drawn  with  the  maximum  plate  current  the  same, 
supposedly  the  saturation  current  for  the  filament  current  used ;  by  carry- 
ing out  other  constructions  it  will  be  evident  that  any  other  condition 
would  result  in  poorer  operation. 

By  now  referring  to  Figs.  155  and  159  it  may  be  seen  that  for  the  tube 
we  were  using  the  plate  potential  should  not  fall  lower  than  200  volts, 
that  at  this  time  the  grid  should  have  a  positive  potential  of  150  volts. 
With  greater  or  less  grid  potential,  the  plate  potential  being  200  volts, 
the  plate  current  would  be  less  than  saturation  value;  with  less  plate 

potential  the  current  (at  time  »,  Fig.  155),  would  be  less  than  saturation 

a 

value,  and  with  greater  voltage  than  200  volts  the  loss  on  the  plate  would 
be  greater  than  necessary. 

.  It  is  to  be  noted  that  the  efficiency  will  increase  for  all  the  cases  given 
in  Fig.  161,  if  the  voltage  of  the  power  supply,  Eb,  is  increased,  providing 
that  conditions  are  suitably  changed  to  have  the  same  minimum  plate 
voltage  as  given  in  Fig.  161.  This  is  shown  by  Fig.  162;  the  two  cases 
given  suppose  the  same  form  of  plate  current  and  same  minimum  value 
of  plate  voltage,  but  in  the  second  the  voltage  Eb  is  about  twice  as  large 
as  in  the  first  case.  It  is  seen  that  the  loss  on  the  plate  is  increased  only 
25  per  cent  whereas  the  input  to  the  load  circuit  has  been  more  than 
doubled.  The  higher  the  value  of  Eb  the  higher  is  the  efficiency,  the  limit 
being  fixed  by  the  safe  voltage  for  the  tube. 

In  the  tube  we  used  the  efficiency  did  not  rise  as  high  as  might  be 
expected,  due  to  the  fact  that  it  took  excessively  high  negative  potential 
on  the  grid  to  bring  the  plate  current  to  zero.  The  oscillograms  showed 
this  effect  so  a  static  characteristic  curve  was  taken  to  investigate  this 
point;  it  is  shown  in  Fig.  163.  If  Eq.  (5)  were  valid  for  this  tube,  a  neg- 
ative potential  of  260  volts  would  have  brought  the  plate  current  to  zero, 


THREE-ELECTRODE   TUBE  AS  POWER  CONVERTER  553 


FIG.  162.—  J  ej,ijdt  = 


I  epidt  = 


Efficiency  =  70%  Efficiency  =  79  % 

Assuming  a  fixed  form  of  plate  current,  and  fixed  minimum  of  plate  potential,  it  is  seen 
that  the  efficiency  rises  as  the  voltage  used  in  the  plate  circuit  (#&)  is  increased. 


554 


VACUUM   TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


whereas  it  took  about  1000  volts;  although  the  plate  current  is  small 
with  a  grid  negative  more  than  300  volts  this  small  current  has  a  marked 
effect  on  loss  of  power  on  the  plate,  because  of  the  very  high  plate  voltage 
during  that  part  of  the  cycle  when  this  small  current  is  flowing  to  the 
plate. 

Experimental  Proof  of  Foregoing  Theory. — To  test  the  validity  of 
the  ideas  presented  above  a  series  of  runs  were  made  with  the  tube,  using 
the  circuit  given  in  Fig.  154  and  the  results  therefrom  are  shown  in  Table 
I.  The  frequency  was  kept  at  the  resonant  value  for  the  output  circuit 
and  each  time  a  set  of  readings  was  taken  the  value  of  R  was  changed 
properly  to  maintain  the  current  in  the  oscillating  circuit  constant.  This 


Amp. 


6 

(3-13 

Q 


.05 


E,=1000  Volts 


It  =  3.65  Amp. 


-200 


-300 


-400 
Ec  Grid  Voltage 


-500 


FIG.  163. — The  tube  used  in  the  tests  did  not  have  a  constant  value  for  /x0;  theoretically 
a  negative  potential  of  260  volts  should  have  reduced  the  plate  current  to  zero. 
This  tube  would  have  required  about  1000  volts  (negative)  on  the  grid  to  completely 
cut  off  the  plate  current. 

was  necessary  in  order  to  keep  the  form  of  the  voltage  ep  constant  as  the 
values  of  Ec  and  Ea  were  varied.  While  it  was  not  thus  pointed  out 
in  discussing  the  current  forms  of  Figs.  161  and  162,  the  values  of  Ec 
and  Eg  are  the  factors  which  bring  about  the  change  of  current  form  as 
the  form  of  ep  is  maintained  constant.  The  form  of  current  shown  in 
(a)  Fig.  161  was  obtained  with  relatively  low  Ec  and  Eu,  the  value  of 
each  of  these  being  increased  for  the  succeeding  diagrams  of  the  figure. 

In  Fig.  164  are  shown  the  efficiency  curves  for  the  various  runs  of 
Table  I  and  on  the  curve  sheet  are  given  the  calculated  values  of  the 
maximum  positive  grid  potential  for  that  condition  in  each  run  which 
gave  maximum  efficiency,  as  indicated  at  a,  b,  c,  d,  etc.  For  the  com- 
paratively low  value  of  current  in  the  oscillating  circuit  which  obtained 


THREE-ELECTRODE  TUBE  AS   POWER  CONVETER 


555 


TABLE  I 

Eb  - 1000  volts.     Ci=2MF.     C2=3.9lMf\     ~=140.     L,  =9.8/7.     // =3.65  Amp. 


Eg 

/2 

Output 

—  Output 

Run. 

EC 

volts. 

effective 
volts. 

Input 
watts. 

effective 
amps. 

R 

ohms. 

RIS 

watts. 

Input 

% 

E 

120 

220 

334 

0.98 

149 

143 

42.8 

150 

220 

298 

1.00 

149 

149 

50.0 

180 

220 

214 

1.02 

119 

124 

51.5 

210 

220 

186 

1.00 

89 

89 

47.8 

250 

220 

119 

0.96 

42 

39 

32.8 

150 

260 

302 

1  00 

149 

149 

49.3 

180 

260 

273 

1.03 

149 

158 

58.0 

210 

260 

241 

0.99 

149 

149 

60.5 

240 

260 

197 

0.99 

119 

117 

59.5 

270 

260 

161 

0.96 

89 

82 

51.0 

150 

300 

302 

1.00 

149 

149 

49.3 

180 

300 

283 

1.02 

149 

155 

54.8 

210 

300 

261 

1.02 

149 

155 

60.0 

240 

300 

246 

1.00 

149 

149 

60.8 

270 

300 

212 

0.98 

134 

129 

60.8 

A 

180 

340 

291 

1.01 

149 

152 

52.3 

210 

340 

278 

1.03 

149 

158 

56.8 

240 

340 

265 

1.04 

149 

161 

60.8 

270 

340 

244 

1.01 

149 

152 

62.4 

•  B 

300 

340 

229 

0.99 

149 

146 

63.8 

330 

340 

186 

0.99 

119 

117 

63.0 

270 

400 

260 

1.02 

149 

155 

59.7 

300 

400 

250 

1.03 

149 

158 

66.3 

330 

400 

235 

1.02 

149 

155 

66.0 

360 

400 

222 

1.00 

149 

149 

67.3 

390 

400 

197 

0.96 

134 

124 

63.0 

420 

400 

150 

1.02 

89 

93 

61.8 

c 

450 

400 

126 

0.98 

74 

71 

56.3 

D 

410 

460 

228 

1.02 

149 

155 

68.0 

420 

500 

245 

.05 

149 

164 

67.0 

450 

500 

237 

.04 

149 

161 

68.0 

480 

500 

222 

.01 

149 

152 

68.6 

510 

500 

195 

.04 

119 

-  129 

66.2 

540 

500 

176 

.02 

104 

108 

61.5 

570 

500 

157 

.04 

89 

96 

61.2 

556 


VACUUM   TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


during  these  tests  the  form  of  plate  voltage  is  somewhat  different  from 
a  sine  wave,  and  the  variation  of  best  grid  potential  may  have  been  due 
to  this  cause.  The  increase  in  efficiency  with  increase  of  Eg  and  Ec  is 
as  would  be  expected  from  the  analysis  given  for  Fig.  161. 


FIG.  164. — Efficiency  curves  plotted  from  Table  I;  the  values  of  positive  grid  potential 
for  maximum  efficiency  in  each  run  is  calculated  and  recorded.  This  agrees  well 
with  the  predicted  "best  grid  potential." 

A  series  of  runs  was  then  carried  out  (results  given  in  Table  II)  to  study 
the  effect  of  varying  the  value  of  the  minimum  plate  voltage,  other  con- 
ditions remaining  the  same;  this  was  accomplished  by  varying  R,  thus 
cutting  down  the  value  of  the  oscillating  current  and  hence  the  variation 
of  voltage  across  the  condenser  Ci,  Fig.  154.  The  variation  of  potential 

TABLE  II 

£6=1000  volts.     Ci=2MF.     C2=3.91Mf.     ~=138.     Li  =9.8#.     I]  =3.65  Amp. 


Run. 

ep 
min. 
volts. 

EC 

volts. 

Eg 

effective 
volts. 

Input 
watts. 

/2 

effective 
amps. 

R 
ohms. 

Output 
=  RIt" 
watts. 

Output 

Input 

% 

A 

30 

270 

300 

134 

1.12 

37 

46.5 

34.7 

100 

270 

300 

179 

1.10 

85 

103 

57.5 

160 

270 

300 

204 

1.02 

117 

122 

59.8 

250 

270 

300 

217 

0.91 

149 

123 

56.8 

B 

490 

270 

300 

255 

0.60 

297 

107 

42.0 

THREE-ELECTRODE  TUBE  AS  POWER  CONVERTER 


557 


across  this  condenser,  it  will  be  noticed,  is  what  controls  the  fluctuation 
of  plate  voltage. 

The  value  of  mimimum  plate  voltage  can  be  calculated  by  subtracting 
from  Ei,  the  resistance  drop  through  LI  (which  was  very  small  for  most 
of  our  tests)  and  from  this  subtracting  the  maximum  value  of  the- alter- 
nating potential  drop  across  Ci.  These  calculations  were  made  and  the 
results  are  shown  in  the  curve  of  Fig.  165;  the  results  verify,  better  than 
might  be  expected,  the 
conclusions  reached  from 
theory.  With  the  excep- 
tion of  the  first  value  of 
ep  (min.)  the  calculated 
values  agreed  with  the 
values  measured  from  the 
films;  the  value  of  30  was 
obtained  by  measure- 
ment of  the  film,  the  cal- 
culated value  not  agree- 
ing very  well. 

For  various  of  the 
runs  given  in  Table  I 
oscillograms  were  taken; 
for  the  conditions  of  run 
A  the  curves  of  ep,  eg,  and 
ip  are  given  in  Fig.  166. 
From  this  film,  as  for 
the  succeeding  ones,  the. 
first  thing  to  be  noticed  FlG;  165-~ From  the  results  ^ven  in  Table  n  the  effi' 


60 


1  40 


200 


400 


Volts 


ciency  curve  shows  that  maximum  efficiency  occurs 
for  minimum  plate  potential  of  160  volts  the  proper 
value  predicted  from  Fig.  1&9. 


is  that  the  grid  voltage 
and  plate  voltage  are  just 
180°  out  of  phase,  show- 
ing that  the  load  circuit  was  resistive  only.  The  maximum  positive 
potential  of  the  grid  measures  on  the  film  296  volts  and  the  correspond- 
ing value  of  plate  potential  measures  220  volts.  By  reference  to  the  curves 
of  Fig.  159  it  may  be  seen  that  for  these  respective  voltages  a  large  part 
of  the  electron  current  is  drawn  to  the  grid,  resulting  in  the  peculiar 
double  humped  curve  of  plate  current.  The  maximum  negative  grid 
potential  was  650  volts,  but  even  this  was  not  sufficient  to  make  the  plate 
current  zero.  Its  values  follow,  as  exactly  can  be  measured,  the  values 
given  by  the  curve  of  Fig.  163. 

For  run  B  a  set  of  oscillograms  was  taken  to  show  all  of  the  quantities 
involved  in  the  operation  of  the  tube ;  it  required  five  oscillograph  records 
to  get  all  the  quantities  wanted.  These  five  films  were  combined  to  make 


558 


VACUUM   TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


the  record  shown  in  Fig.  167;  in  fitting  the  various  films  together  care 
was  taken  to  see  that  they  had  their  proper  respective  phases.  The 
white  line  drawn  vertically  through  all  the  records  gives  a  line  of  equi- 
phase. 

This  set  of  curves  gives  the  complete  story  of  the  circuit  and  tube. 
The  plate  current  is  very  nearly  the  form  shown  in  Fig.  162,  and  the  plate 
potential  is  nearly  of  the  form  shown  in  condition  (a)  of  the  same  figure. 
The  slight  depression  in  the  peak  value  ip  is  due  to  the  grid  taking  some 
current,  this  depression  coinciding  in  time  with  the  peak  of  grid  current. 
The  form  of  the  positive  alternation  of  the  i  curve  is  not  like  those  pre- 


FIG.  166. — Oscillogram  for  conditions  of  Run  A — Table  I;    evidently  the  minimum 

plate  potential  is  too  low. 

viously  given,  due  to  the  fact  that  it  has  been  assumed  that  h  was  con- 
stant whereas  it  actually  had  considerable  fluctuation,  as  shown  in  the 
record.  If  the  coil  used  for  LI  had  more  inductance  this  variation  in 
Ib  would  be  diminished;  we  had  only  10  henries  with  a  resistance  of  189 
ohms,  the  coil  being  air  core.  In  practice  an  iron  core  coil  of  greater 
inductance  would  be  used,  but  we  did  not  want  to  introduce  any  other 
sources  of  distortion  than  the  tube  itself. 

The  form  of  current  in  condenser  C\  differs  from  that  in  condenser 
€2  because  of  the  effect  of  i  which  will  practically  all  flow  through  Ci 
for  the  circuit  as  arranged. 

The  grid  current  has  just  the  form  and  magnitude  predictable  from 


THREE-ELECTRODE   TUBE   AS   POWER   CONVERTER 


559 


Fig.  159;  the  amount  of  current  taken  by  the  grid  in  this  test  and  the 
values  of  Ea  and  Ec  used  caused  a  loss  of  power  on  the  grid  (due  to 
bombardment)  of  about  10  watts. 


Area  A  =  590 
Area  8^180 
Area  0 1030 

Efficiency^ 

850 
850+590 


Eb=1040      I  b=  0.296     Ec=300     Eg=340   f=140 

Losses  not  caused  by  Tube=  70.5  Watts 

Eb  I  b- Losses  ^237  Watts  input 

R-- 149  Ohms    I2=  0.97     OutpuU  140  Watts 


FIG.  167. — Oscillogram  of  all  the  currents  and  voltages  for  Run  B — Table  I;  the  white 
line  represents  the  same  phase  on  all  films.  The  calculated  efficiency  from  the  epip 
and  epi  areas  agrees  well  with  the  calculated  efficiency. 

The  two  filament  currents,  ?'/  and  •&'/,  have  forms  which  might  be  pre- 
dicted from  curves  similar  to  those  given  in  Fig.  157;  in  that  end  of  the 
filament  carrying  the  larger  current  the  continuous  current  ammeter 
measuring  the  current  indicated  only  3.65  amperes,  whereas  the  current 


560 


VACUUM   TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


actually  went  as  high  as 
3.99  amperes  when  the 
plate  was  taking  its 
maximum  current.  The 
exact  amount  of  emis- 
sion from  the  filament 
when  the  tube  is  acting 
as  a  generator  cannot 
be  predicted  from  the 
static  characteristic; 
the  temperature  distri- 
bution in  the  filament 
which  exists  in  the  os- 
cillating condition  of 
the  tube  cannot  be 
duplicated  in  a  static 
test,  and  it  is  this  tem- 
perature distribution 
which  determines  the 
total  emission. 

The  drop  across  the 
condenser  €2  was  taken 
to  see  whether  or  not 
it  had  the  right  magni- 
tude and  phase  to  serve 
for  excitation  of  the 
grid  when  the  tube  was 
run  self-exciting;  the 
value  of  €2  had  been 
adjusted  with  this  point 
in  mind. 

The  scheme  of  get- 
ting the  efficiency  indi- 
cated in  Figs.  161  and 
162  was   tried   on   this 
record  of  ep,  ip,  and  i, 
the  power  curves  of  epip 
and  epi  being  shown  in 
Fig.  167;  the  value  ob- 
tained,    59    per    cent, 
FIG.  168. — Form  of  plate  current  curve  predicted  from  agrees   within  the  pre- 
Fig.  159;  it  agrees  well  with  the  form  actually  obtained  Q^gjon  of  the  test  with 
in  Fig"  167'  that   measured   by  the 


Amp 


Time 


THREE-ELECTRODE   TUBE  AS  POWER  CONVERTER 


561 


meters  in  the  test.  The  value  of  63.8  per  cent  given  in  Table  I  was  the 
value  obtained  when  the  oscillograph  circuits  were  not  connected,  the 
closing  of  the  circuits  changed  the  conditions  enough  to  drop  the  efficiency 
to  59.5  per  cent. 

Fig.  168  shows  the  form  of  ip  which  is  predicted  from  Fig.  159  after  the 
forms  and  magnitudes  of  ep  and  eg  have  been  assumed;  this  form  of  ip 
is  very  close  to  the  actual  form  given  in  the  oscillogram  of  Fig.  167. 

The  result  of  our  tests  and  analysis  have  then  shown  that  the  efficiency 
of  a  tube  as  a  converter  can  be  accurately  predicted  from  the  three  sets 
of  curves  given  in  Figs.  156,  159,  and  163  after  we  have  determined,  from 
the  curves  of  Fig.  159,  what  the  best  minimum  plate  potential  is  and 
also  what  the  maximum  positive  potential  of  the  grid  should  be. 


FIG.  169. — Arrangement  of  the  tube  circuit  for  self -excitation;   the  machine  Ec  main- 
tains the  grid  at  the  proper  average  potential. 


To  get  a  fair  efficiency  (60  per  cent  or  better)  the  value  of  /&  should 
not  be  greater  than  25  per  cent  of  the  saturation  current  of  the  tube; 
with  the  efficiency  known  and  the  safe  radiation  of  power  from  the  plate 
being  known  the  proper  value  of  Eb  is  fixed. 

Self-excited  Tube. — Using  the  circuit  and  constants  used  in  getting 
the  records  of  Fig.  167  an  attempt  was  made  to  run  the  tube  self-exciting 
by  changing  the  connections  slightly  as  shown  in  Fig.  169.  The  choke 
coil  L£  serves  to  prevent  the  grid  from  being  short-circuited  to  the  filament 
(for  the  a.c.  excitation)  through  the  machine  Ec.  The  voltage  for  exci- 
tation was  obtained  from  the  drop  across  the  condenser  €2,  the  insulating 
condenser  Cs  being  necessary  to  prevent  short-circuiting  the  machine 
Eb.  With  this  connection  the  grid  does  not  get  quite  as  much  excita- 
tion as  shown  by  the  curve  eCz  in  Fig.  167,  because  an  appreciable  part 


562 


VACUUM   TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


of  this  voltage  is  used  in  overcoming  the  reactance  drop  in  (3.  (In  this 
calculation  the  capacity  of  the  grid  circuit  of  the  tube  itself  must  be  con- 
sidered; in  some  of  the  Type  P  tubes  this  capacity  is  as  high  as  500  wf, 
when  the  load  circuit  has  its  proper  impedance  for  maximum  output — 
see  p.  442.) 

The  circuit  of  Fig.  169  refused  to  act  as  it  did  for  the  separate  excita- 
tion, giving  a  small  output  at  a  low  efficiency;  a  more  careful  exami- 
nation of  the  record  in  Fig.  167  gave  the  reason.  The  alternating  com- 
ponents of  eg  and  ep  must  be  exactly  180°  out  of  phase  if  the  maximum 
output  and  efficiency  are  to  obtain,  as  becomes  at  once  evident  if  the 
construction  of  Fig.  161  be  carried  out  for  any  other  than  the  180°  rela- 
tion. Measurement 
of  the  film  of  Fig. 
167  shows  ec2  to  be 
33°  out  of  the  180° 
phase  with  ep  and 
that  much  phase  dis- 
placement is  suffi- 
cient to  completely 
upset  the  conclusions 
so  far  reached.  It 
was  therefore  neces- 
sary to  change  the 
relative  phase  of  ep 

FIG.  170.— A  possible  arrangement  of  self-excitation,  in  which  and  6c*'  .A  Possible 
the  phase  of  the  voltage  impressed  on  the  grid  is  adjustable,  scheme  is  conven- 
tionally indicated  in 

Fig.  170;  a  rotating  field  is  produced  by  proper  connection  to  the  load 
circuit  and  a  rotatable  coil  placed  in  this  rotating  field  serves  for  the 
grid  excitation.  We  had  a  simpler  scheme  at  hand  so  did  not  try  this 
one. 

The  difference  in  phase  in  the  voltages  across  C\  and  C2  comes  from 
the  effect  of  the  current  i,  present  in  Ci  to  a  greater  extent  than  in  C2. 
By  making  the  effect  of  this  current  small  its  disturbing  effect  may  be 
reduced,  and  this  can  be  done  by  increasing  the  values  of  Ci  and  C2,  and 
decreasing  the  value  of  R,  the  value  of  L  being  properly  reduced  to  main- 
tain the  same  resonant  frequency.  The  increase  in  capacity  will  increase 
the  value  of  the  oscillatory  current  ii,  and  as  i  remains  constant  its  effect 
on  the  relative  phases  of  eCl  and  ec.2  becomes  proportionately  less  as  the 
capacity  is  increased. 

The  arrangement  of  apparatus  remaining  as  in  Fig  154,  the  constants 
were  readjusted  for  efficient  operation  and  a  set  of  readings  were  obtained 
as  follows:  Eb  =  900  volts,  Ec  =  230  volts,  E0  =310  volts,  Frequency  =  143, 


THREE-ELECTRODE  TUBE  AS  POWER  CONVERTER 


563 


FIG.  171. — Conditions  occurring  in  the  self -excited  tube;  the  plate  current  did  not 
drop  to  zero  as  it  should  do,  because  there  was  not  enough  negative  potential  on 
the  grid. 


564 


VACUUM  TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


FIG.  172. — In  this  case  of  the  self -exciting  tube  the  plate  voltage  did  not  fall  sufficiently 
low  to  give  best  efficiency;  it  measures  on  the  film  300  volts  where  as  Fig.  16o  shows 
the  proper  minimum  plate  potential  to  be  160  volts. 


THREE-ELECTRODE  TUBE  AS  POWER  CONVERTER  565 

LI  =9. 8  henries,  /&  =  0.321  ampere,  Ci=9.2  microfarads,  (72  =  19.4  micro- 
farads. The  resistance  of  the  load  circuit  was  7.80  ohms  and  the  oscil- 
latory current  produced  was  4.30  amperes,  giving  an  alternating  current 
output  of  143  watts.  The  input  to  the  tube  circuit  is  obtained  from  the 
product  Eblb  after  certain  losses,  not  chargeable  to  the  tube  circuit,  have 
been  deducted. 

The  condensers  C\  and  €2  each  consisted  of  two  condensers  connected 
in  series  because  of  the  high  potentials  occurring  in  the  circuit.  In  order 
to  make  the  two  individual  condensers  divide  the  voltage  Eb,  equally  it 
is  necessary  that  their  insulation  resistances  be  alike,  a  condition  seldom 


FIG.  173.— Separately  excited  tube— Eb  =  1040,  7&  =  .170,    #c=270,  #,,  =  300,  72=37. 
Input  =  106  watts.     Output  =  50,  Efficiency  =  47%. 

encountered.  That  condenser  having  the  higher  resistance  (the  better 
one)  will  take  practically  all  of  the  Eb  voltage  as  well  as  its  share  of  the 
alternating  voltage  of  the  circuit,  resulting  in  its  probable  breakdown. 
To  prevent  this  occurrence  leak  resistances  were  used  across  each  of  the 
condensers  making  up  Ci  and  €2,  the  leaks  each  being  21,000  ohms,  making 
the  leak  resistance  of  C\  and  €2  each  42,000  ohms.  Subtracting  the  I2R 
losses  in  these  leaks  as  well  as  the  I2R  losses  in  the  choke  coil  LI,  gives 
the  input  to  the  tube  circuit  229  watts;  the  efficiency  was  thus  62.7  per 
cent. 

Oscillograms  taken  of  the  currents  in  this  circuit  are  given  in  Fig.  171. 
It  is  evident  that  the  values  of  Eff  and  Ec  might  well  have  been  greater, 


566  VACUUM  TUBES  AND  THEIR  OPERATION  [CHAP.  VI 

resulting  in  a  higher  efficiency  because  of  the  resultant  smaller  minimum 
plate  current.  Although  the  plate  current  is  small  the  plate  voltage  is 
large  and  so  results  in  a  high  unnecessary  loss  on  the  plate. 

The  phase  of  ec.2  is  now  practically  coincident  with  that  of  Eg,  and  it 
should  therefore  serve  as  a  source  of  excitation.  The  circuit  did  not  give 
as  much  power,  however,  when-  made  self-exciting,  as  it  should,  so  the 
constants  were  changed  slightly  to  get  more  power.  As  finally  tested 
the  self-exciting  circuit  had  the  constants  and  performance  given  here- 
with: #&  =  1000  volts,  h  =0.335  ampere,  Ci  =7.36  microfarads,  C2  =  13.8 
microfarads,  L=  0.201  henry,  LI  =9.8  henries,  L2=9.0  henries,  #c 


FIG.  174. — Conditions  as  given  in  Run  B,  Table  II. 

volts,  72=8.0  ohms.  The  current  produced  in  the  oscillating  circuit  was 
4.40  amperes,  resulting  in  an  efficiency  of  57  per  cent. 

Fig.  172  shows  the  currents  and  voltages  in  this  self-exciting  circuit, 
and  it  is  at  once  evident  why  such  a  comparatively  low  efficiency  was 
obtained;  the  minimum  plate  voltage,  instead  of  being  160  volts,  as  it 
should  for  this  tube,  was  300  volts.  For  this  figure  the  curve  of  plate 
current  included  also  the  alternating  component  of  the  grid  current,  hence 
the  absence  of  the  depression  at  the  peak  value. 

The  current  through  the  plate-current  vibrator  reversed  during  part 
of  the  cycle,  due  to  the  fact  that  this  vibrator  carried  in  addition  to  the 
plate  and  grid  currents,  an  alternating  current  which  resulted  from  the 
voltage  across  the  condenser  €2  acting  through  the  reactance  of  coil  Lo  and 


THREE-ELECTRODE  TUBE  AS  POWER  CONVERTER  567 

condenser  CY2,  Fig.  169.  This  current  is  shown  as  ix  in  Fig.  172;  when 
the  plate  current  is  corrected  by  this  small  amount  it  is  seen  that  the  plate 
current  does  not  reverse,  as  we  know  it  cannot  with  the  conditions  as 
they  existed  in  this  test. 

Action  of  the  Tube  at  High  Frequency. — It  was  desired  to  showthat 
the  action  of  the  tube  was  just  the  same  at  high  frequency  as  at  the  low 
frequencies  used,  so  a  circuit  was  arranged  similar  to  that  of  Fig.  169, 
with  smaller  values  of  capacity  and  inductance.  The  choke  coils  LI 
and  Z/2  used  in  the  previous  tests  would  act  as  condensers  of  comparatively 
low  reactance  at  the  high  frequency  to  be  used  so  they  also  had  to  be 


FIG.  175. — Conditions  as  given  in  Run  E,  Table  I. 

changed.  The  constants  of  the  circuit  used  were:  #6  =  1000  volts,  h 
=  0.285  ampere,  Ci=.0144  farad,  C2  =  .0284  microfarad,  frequency 
=  98,500,  Li  =.023  henry,  L2=.016  henry,  Ec  =  240  volts,  72=6.16  ohms 
(high-frequency  determination).  There  were  no  leaks  used  with  the  con- 
densers in  this  circuit,  so  that  the  product  Ebh,  after  subtracting  the 
12R  loss  on  the  choke  coil  LI,  gives  the  input.  It  is  found  to  be  284 
watts,  and  as  the  output  to  the  load  circuit  was  160  watts  the  efficiency 
was  56.2  per  cent,  which  is  in  fair  agreement  with  the  results  obtained 
at  166  cycles. 

Figs.  173-177  are  shown  some  special  oscillograms  of  the  plate  current, 
plate  voltage,  and  grid  voltage,  all  for  the  separately  excited  tube  with 
the  circuit  shown  in  Fig.  154;  the  conditions  of  the  circuit  were  as  noted 
in  Tables  I  and  II. 


568  VACUUM  TUBES  AND  THEIR   OPERATION  [CHAP.  VI 

The  conditions  obtaining  when  Fig.  177  was  taken  show  the  best 
adjustments  for  efficiency  which  we  were  able  to  get  with  the  Type  P 
tube;  the  high  efficiency  was  obtained  without  unduly  decreasing  the 
output.  If  this  form  of  plate  current  could  be  maintained  and  the  value 
of  Eb  be  increased  to  3000  volts  the  calculated  efficiency  becomes  85 
per  cent;  this  is  probably  as  good  as  could  be  done  with  sine  wave 
shapes  of  ep  and  eg,  but  it  seems  as  though,  by  suitably  deforming  both 
of  them,  giving  them  both  flat  tops,  the  efficiency  could  be  considerably 
increased  over  this  value. 


FIG.  176.— Conditions  as  given  in  Run  C,  Table  I. 

Tests  similar  to  those  described  in  this  paper  were  carried  out  using 
a  much  smaller  tube,  that  styled  by  the  U.  S.  A.  Signal  Corps  type  VT-2. 
The  results  obtained  with  the  large  tube  were  duplicated  almost  exactly 
in  so  far  as  efficiency  was  concerned.  It  was  found  possible  to  so  adjust 
the  values  of  Ec  and  Es  that  the  tube  gave  an  output  of  6.3  watts  with 
an  efficiency  of  70  per  cent,  the  voltage  used  in  the  plate  circuit  being 
the  rated  value,  namely  300  volts.  It  was  found  possible  to  get  over 
7  watts  output  with  the  plate  loss  considerably  lower  than  its  safe  rated 
value;  if  the  plate  voltage  had  been  increased  to  perhaps  400  volts  the 
tube  output  might  have  been  raised  to  10  watts  while  still  having  the 
plate  loss  within  its  safe  value. 

These  tests  were  all  carried  out  with  a  separately  excited  tube;  with 
the  tube  self-excited  the  efficiency  was  not  obtained  higher  than  61  per 


THREE-ELECTRODE   TUBE  AS   POWER  CONVERTER  569 

cent,  with  a  plate  voltage  of  300.  This  run  gave  an  output  of  5.6  watts 
output  with  a  current  h  of  0.305  ampere;  the  frequency  was  400,000 
cycles,  the  value  of  R  was  53  ohms,  the  oscillating  current  0.325  ampere, 
Ci  and  €2  being  1360  and  770  micro-micro-farads,  respectively.  The 
value  of  EC  was  40  volts. 

With  the  conditions  of  a  self-excited  circuit  adjusted  for  the  best 
conditions  as  previously  outlined  difficulty  may  be  encountered  in  start- 
ing the  circuit  to  oscillate,  a  shock  of  some  kind  being  generally  required 
to  start  oscillations.  Because  of  this  possible  difficulty  it  may  be  the  best 


FIG.  177.— Best  conditions  for  high  efficiency.     Eb  =  1040,  h  =  -286,  Ec  =  410,  Eg  =  460, 


=  149,  Input  =  227  watts,  Output  =  155,  Efficiency  =  68 


practice  to  run  these  tubes  separately  excited,  using  one  tube  (so  adjusted 
that  it  oscillates  readily)  for  exciting  others  as  indicated  in  Figs.  140-141, 
pp.  533-534.  It  may  well  be  that  with  a  higher  resistance  in  the  oscil- 
lating circuit  more  output  can  be  obtained  from  two  tubes  if  one  only 
is  used  as  a  generator,  the  other  being  used  as  exciter  only.  Certainly 
if  more  than  two  tubes  are  to  be  used  it  will  be  well  to  use  one  as  exciter 
for  supplying  the  grid  voltage  for  the  others.  The  small  exciter  tube 
should  be  sot  with  coupling  much  greater  than  the  critical  value  and  it 
will  "  key  "  readily  and  quickly.  The  power  tube  excited  should  be 
arranged  with  sufficient  grid  bias  to  get  the  form  of  plate  current  shown 
on  page  553;  the  amount  of  excitation  imparted  to  the  grid  of  the  power 
$ube  must,  of  course,  also  be  properly  adjusted. 


570 


VACUUM  TUBES  AND  THEIR  OPERATION 


[CHAP.  VI 


Characteristics  of  the  Circuit  of  Fig.  122.— Using  the  circuit  shown  in 
Fig.  122,  a  series  of  runs  was  made  to  investigate  the  effect  of  changing 
the  constants  of  the  circuit  and  some  of  the  results  are  shown  in  Figs.  178 
and  179;  the  legends  and  diagrams  on  the  curve  sheets  make  them  self- 
explanatory.  For  these  tests  three  pliotrons  (type  P-30)  were  operated 
in  parallel,  all  grids  being  connected  together  as  also  were  the  plates;  the 
plate  current  recorded  on  the  curve  sheets  is  that  of  one  tube. 

It  may  be  seen,  from  Fig.  178,  curve  3,  for  example,  that  for  efficient 
coils  and  condensers  of  the  type  used  here  it  is  possible  to  get  as  much 
as  16,000  volt  amperes  from  one  tube,  with  only  800  volts  on  the  plate 
and  normal  filament  current.  The  behavior  of  the  tubes,  as  regards 


9    1000    123456789    2000 
Value  of  L,p  in  10~6  henries 
FIG.  178. — Amount  of  high-frequency  power  obtainable  from  three  Type  P  pliotrons  in 
parallel  and  effect  of  changes  in  Lg. 

stability,  conditions  for  maximum  output,  etc.,  agree  fairly  well  with  the 
theoretical  predictions. 

Characteristics  of  the  Three-electrode  Tube  as  an  Amplifier. — As  the 
voltage  impressed  on  the  input  circuit  of  a  tube  causes  a  change  in  the 
plate  current  which  may  be  flowing  through  an  inductance  or  resistance 
in  the  external  plate  circuit,  and  as  it  is  evident  that  the  drop  across  this 
external  circuit  may  be  many  times  greater  than  the  e.m.f.  impressed  on 
the  grid,  the  device  may  be  used  as  a  voltage  amplifier.  The  amplified 
voltage  in  the  output  circuit  will  have  very  nearly  the  same  form  as  the 


THREE-ELECTRODE  TUBE  AS  AMPLIFIER 


571 


input  voltage,  sufficiently  so  that  the  currents  due  to  speech  may  be 
amplified  many  times  (1000-10,000)  and  the  reproduction  of  the  voice 
be  almost  perfect.  The  circuits  used  in  amplifiers  and  arrangement  of 
apparatus  are  taken  up  in  a  later  chapter;  in  this  section  we  shall  con- 
sider only  the  amplifying  characteristics  of  the  tube  itself. 

As  noted  before  a  voltage  of  Emg  sin  oo£  introduced  in  the  input  circuit 
of  a  tube  is  equivalent  to  a  voltage  of  nvEmo  sin  wt  introduced  into  the  plate 
circuit,  this  voltage  causes  an  alternating  current  to  flow  in  the  plate  cir- 
cuit, the  magnitude  and  phase  of  which  depend  upon  the  external  impe- 


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^ 

> 

*>N. 

^ 

^> 

•-^ 

•> 

X 

*- 

/ 

C 

ur 

re 

-ir 

:1» 

bo 

R  = 

:33 

oh 

ms 

X 

>^ 

^ 

V 

4 

•• 

2 

61 

=  800 

R  = 

=  33j       % 

\ 

^> 

S 

\ 

^ 

/ 

•• 

; 

} 

/.i 

=  a 

30 

R: 

:55 

• 

V 

" 

^ 

' 

\ 

\ 

^ 

\ 

100      200     300      400     500      600      TOO     800     900    1000    1100     1200    1300    1400    1500    1600 
Value  of  Lpin  microhenries 

FIG.  179. — Showing  the  effect  of  varying  the  plate  circuit  inductance  with  fixed  value 
of  Lg.  Region  of  oscillation  indicated  by  solid  lines;  outside  these  limits  tubes 
refused  to  oscillate. 

dance  in  the  plate  circuit  and  the  resistance  of  the  tube  itself.     If  we  call 
the  alternating  component  of  the  plate  current  Ip  we  have  the  relation, 


(105) 


j 
P~RP+R' 


in  which  R  is  the  external  resistance  of  the  plate  circuit.  The  drop  across 
R  (which  is  the  only  available  part  of  the  amplified  voltage,  the  rest  being 
used  up  inside  the  tube  itself)  is  IVR  and  this  is  evidently  given  by 

T) 


572 


VACUUM   TUBES  AND  THEIR   OPERATION 


[CHAP.  VI 


From  this  we  get  the  actual  voltage  amplification  due  to  the  tube,  which 
is  designated  as  /x, 


R 


(106) 


This  factor  M  will  be  constant  (independent  of  the  magnitude  of  the 
input  voltage  Eg)  only  for  such  value  of  Ev  as  give  constant  Rp.  This 
can  be  seen  at  once  from  the  static  characteristic  of  a  tube,  showing  the 
relation  between  plate  current  and  grid  potential,  this  curve  to  be  taken 
with  the  proper  value  of  R  in  the  plate  circuit ;  throughout  that  part  of  this 
curve  which  gives  uniform  slope  the  factor  /i  is  constant  and  the  ampli- 


Valueof   (ep+/jL0eg) 


FIG.  180. — Two  tubes  having  different  plate-current  characteristics  as  indicated  in 
M  and  N  will  give  amplified  currents  having  more  or  less  distortion,  N  giving  more 
distortion  than  M . 

fication  is  distortionless,  a  very  necessary  feature  of  an  amplifier  used 
for  speech  amplification,  but  of  little  importance  for  ordinary  signal 
amplification. 

This  point  is  indicated  in  Fig.  180;  two  different  tubes  (or  different 
arrangements  of  the  same  tube)  might  have  characteristics  as  shown  at  M 
and  N  and  the  form  of  the  plate  current  produced  for  a  sine  wave  of  volt- 
age impressed  on  the  grid  as  shown  by  curves  m  and  n  in  the  same  figure. 

With  curve  N  the  value  of  -77^  is  greater   the   more   positive  the  grid 

arLg 

becomes,  resulting  in  a  lower  Rp;  from  Eq.  (106)  it  may  be  seen  that  for 
a  given  value  of  R  the  factor  /z  becomes  greater  the  smaller  RP.  A  sine 
wave  of  voltage  impressed  on  the  grid,  therefore,  does  not  produce  a  sine 


THREE-ELECTRODE  TUBE  AS  AMPLIFIER 


573 


wave  of  current  in  the  plate  circuit  and  so  will  not  produce  a  sine  wave 
of  voltage  across  a  resistance  in  the  plate  circuit. 


From  Eq.  (106)  it  is  evident  that  if  the  amplifying  power  of  a  tube 
is  to  be  efficiently  used  the  value  of  R  must  be  at  least  as  large  as  Rp  and 
should  really  be  much  larger.  In  Fig.  181  is  shown  the  measured  ampli- 


574* 


VACUUM   TUBES  AND   TIIE1II   OPERATION 


[CHAP.  VI 


fication  constant  of  the  Signal  Corps  VT-1  tube  taken  under  various 
conditions.  It  is  seen  that  the  factor  ju  increases  as  R  increases,  for  all 
conditions. 

Curve  1  was  taken  with  a  constant  "  B  "  battery  voltage;  under 
this  condition  the  plate  voltage  decreased  as  R  was  increased  due  to 
the  resistance  drop  in  R.  But  a  decreased  plate  voltage  resulted  in  an 
increase  in  Rp,  so  that  for  this  condition  as  R  was  increased,  it  approached 
Rp  very  slowly  due  to  the  increase  in  Rp  with  increase  in  R. 


Vol 


age 


lif 


pe 


tan 


Cur 


=-0.8 


=-i.q 


so 


10 


For 


lieu 


1.30 


:1BO 


40        60 


100      20       40   "   60       80      200     20 
External  Resistance  In  10 3  ohms 


80      300     20 


FlG.  182. — Showing  effect  on  the  amplifying  power  of  a  tube  of  holding  the  grid  at 
different  average  potentials,  making  the  grid  more  negative  increases  the  tube 
resistance,  hence  requiring  a  higher  external  resistance  to  get  the  same  amount  of 
amplification. 

Curve  2,  compared  to  curve  1,  shows  the  effect  on  //  of  increasing  the 
"  B  "  battery  voltage  sufficiently  to  compensate  for  the  IR  drop  in  the 
plate  circuit,  thus  maintaining  the  plate  voltage  constant;  it  is  seen  that 
the  increase  of  ju  with  R  is  much  more  rapid.  Curve  3  shows  the  effect 
of  maintaining  the  plate  potential  at  30  volts  instead  of  20  volts.  The 
alternating-current  resistance  of  the  plate  circuit  of  the  tube  Rp  was 
measured  for  curves  2  and  3  and  is  indicated  in  the  curves;  it  is  seen  for 
each  of  them  that  when  R  =  RP,  M  =  iMo  as  it  should  from  Eq.  (106). 


THREE-ELECTRODE   TUBE  AS  AMPLIFIER 


575 


In  using  a  tube  as  an  amplifier  it  is  customary  to  maintain  the  grid 
at  such  a  negative  potential  that,  for  any  probable  input  voltage,  the  grid 
will  not  become  positive;  maintaining  a  negative  grid  increases  the  value 
of  RPJ  so  that  for  a  given  R,  /JL  is  decreased.  This  effect  is  shown  in  Fig. 
182,  which  gives  the  behavior  of  a  tube  having  a  higher  value  of  //a  than 


28 
26 
24 
22 
20 
18 
16 

12 
10 
8 
6 
4 
2 
0 

A 

>-- 

^ 

TjJ 

pe 

D 

/\ 

^^ 

N 

!f 

=1. 

30 

i 

•S 

.  * 

^> 

^ 

\ 

7 

/ 

\ 

\ 

Ext 

;rn 

il  i 

esi 

sta 

ncfi 

in 

— 

us 

/ 

/ 

^ 

•\ 

\ 

e  c 

rci 

lit 

=  220,000 

ohi 

x 

. 

^ 

/ 

\ 

v 

s 

/ 

1 

/ 

, 

+•  — 

—^ 

^ 

\ 

\ 

\ 

1 

i 

/ 

/ 

\ 

f 

j 

\ 

\ 

\ 

\ 

I 

/ 

/ 

\ 

\ 

\ 

\ 

^ 

i 

1 

^ 

^  —  >, 

\ 

( 

V 

\ 

\ 

/ 

y 

I 

/ 

N^ 

\ 

\ 

\ 

\^ 

30 

0  v 

3lts 

in 

"B" 

bat 

ter 

y 

1 

/ 

i 

/ 

\ 

\ 

\ 

\ 

/ 

> 

i 

/ 

i. 

\ 

\ 

\ 

/ 

1 

1 

\ 

\ 

\ 

\ 

/ 

i 

i 

\ 

\ 

25 

0  v 

Olt! 

1 

/ 

\ 

\ 

\ 

/ 

\ 

i 

\ 

1 

1 

/ 

\ 

\ 

i 

< 

\ 

\ 

\ 

i  2C 

KJ  v 

olt 

/ 

\ 

\ 

1 

\ 

\ 

! 

\ 

f 

\ 

\ 

\ 

\ 

\ 

\ 

15( 

vc 

Its 

\ 

\ 

\ 

\ 

10 

0  v( 

)lts 

54           3           2-10+1          23          4           5 
Value  of    EC 

FIG.  183. — Variation  in  amplifying  power  with  different  grid  potentials  and  different 

plate  circuit  voltages. 


is  customary.  Fig  183  shows  the  variation  of  the  amplification  factor 
as  both  plate  circuit  voltage,  E^  and  grid  potential,  Ec,  were  varied. 
It  is  evident  that  this  tube  could  be  used  effectively  for  only  small  values 
of  input  voltage. 

If  the  plate  current  of  a  tube  is  expressed  by  the  relation, 


sn 


576 


VACUUM   TUBES  AND   THEIR  OPERATION  [CHAP.  VI 


1000 


900 


800 


700 


.1 

'o 


Char  veteristics  of  amplif yir  g  tube 


Curve  l 


<  I    o  \p     i  '  i 
L.30arap.  Ec= 

— ± — I.    I  .. 


E6*=130  volts 


=.66 


=197 


Type 


at  1000  cycles 


0      ohms 


50, 


100.000 


150,000 


200,000 


345678 
Volts  impressed  on  grid  (values  etfective.) 


10 


FHJ.  184. — The  quality  of  amplification  (distortionless  or  not)  is  shown  by  a  test  of  this 
kind.  The  tube  used  requires  an  external  resistance  in  series  with  the  plate  of  at 
least  150,000  ohms  to  givo  distortionless  amplification. 


THREE-ELECTRODE   TUBE  AS  AMPLIFIER  577 

we  get  after  expansion, 


sn  ut 

2AEmo2 
+juo2  —  ~-  cos 

The  first  term  gives  the  steady  value  of  plate  current  with  no  input  volt- 
age, the  second  the  true  amplification  current,  the  third  a  double-frequency 
distortion  current,  and  the  fourth  a  steady  increase  in  the  value  of  ip, 
while  Emg  sin  ut  is  acting.  The  third  term  has  the  same  coefficient  as 
the  fourth  and  the  fourth  term  will  register  on  a  direct  current  ammeter 
in  the  plate  circuit.  Hence  the  quality  of  amplification  of  a  tube  (distor- 
tionless or  not)  may  be  judged  by  the  indication  of  the  plate  ammeter 
as  the  input  voltage  is  impressed.  Fig.  184  shows  this  effect  and  also 
the  effect  of  added  resistance  in  the  plate  circuit  in  decreasing  the  distor- 
tion. With  150,000  ohms  added  in  the  plate  circuit,  this  tube  would 
give  essentially  distortionless  amplification  for  input  voltage  as  high  as 
5  volts. 

In  case  a  reactance  is  used  in  the  plate  circuit,  for  repeating,  instead 
of  resistance,  it  will  be  found  that  the  value  of  /x  is  greater  than  for  a 
corresponding  value  of  resistance.  Thus  if  an  inductive  reactance  (of 
negligible  resistance)  is  used  in  the  plate  circuit,  the  value  of  the  react- 
ance being  equal  to  the  tube  resistance,  a  value  of  /*  is  obtained  equal  to 
0.7  MO  instead  of  0.5  MO  as  was  obtained  for  resistance.  This  follows  at 
once  by  considering  the  voltage  relations  in  a  tube  circuit,  as  given  in 
Fig.  96,  p,  475. 


CHAPTER  VII 
CONTINUOUS-WAVE  TELEGRAPHY 

Advantage  of  Continuous-wave  Telegraphy. — Continuous-wave  teleg- 
raphy possesses  several  distinct  advantages  over  damped-wave  systems 
which  may  be  summarized  as  follows: 

1.  Greater  Selectivity. — This  advantage  is  due  primarily  to  the  fact 
that  energy  radiated  by  a  spark  transmitter  is  sent  out  in  damped-wave 
trains.     These  wave-trains,  striking  the  receiving  antenna,  induce  therein 
an  electromotive  force,  and  if  the  circuit  is  tuned  to  the  incoming  wave, 
maximum  current  and  signal  strength  are  obtained.     However,  even  if  the 
circuit  is  somewhat  de-tuned,  the  damped-wave  train  will  excite  the  circuit 
to  a  considerable  extent,  causing  it  to  oscillate  at  its  own  frequency,  as  well 
as  at  the  frequency  of  the  signal  wave.1     In  other  words  the  selectivity 
of  reception  of  a  spark  signal  is  fixed,  not  only  by  the  decrement  of  the 
receiving  circuit,  but  also  by  the  decrement  of  the  wave-train  itself,  which, 
of  course,  is  that  of  the  transmitting  station;    thus  more  or  less  inter- 
ference always  exists  between  spark  stations,  if  the   wave-lengths  are 
close  to  one  another. 

If  we  consider  the  effect  of  continuous  waves  at  the  receiving  station, 
the  conditions  will  be  somewhat  different.  The  incoming  energy  forces 
the  receiving  circuit  to  oscillate  at  its  own  signal  frequency,  except  at 
the  beginning,  when  the  forced  and  natural  oscillations  are  coexistent 
for  a  few  cycles.  Therefore  if  this  circuit  is  not  tuned  to  resonance  with 
the  incoming  signal  and  does  not  possess  abnormal  resistance  values 
(which  would  flatten  out  its  resonance  curve),  the  current  flowing  will 
be  very  small  and  the  signal  strength  extremely  weak,  under  all  conditions 
of  adjustment  except  that  of  resonance.  Thus  the  selectivity  is  good,  and 
the  station  will  receive  no  messages  except  those  for  which  it  is  tuned. 

2.  Increased   Range   of    Transmission. — This   follows   from   the   fact 
that  with  continuous-wave   transmission,  the  energy  is  radiated  at  and 
concentrated  into,  essentially  one  wave-length,  instead  of  being  spread 
over  a  number  of  wave-lengths,  as  indicated  by  the  energy  distribution 
curves  discussed  in  Chapter  V,  p.  326.     The  greater  the  amount  of  energy 
we  can  thus  concentrate  into  one  wave-length,  the  further  will  be  the 
distance  penetration  or  propagation  of  this  energy,  and  stations  may  be 

1  See  Chapter  IV,  p.  268. 
578 


ADVANTAGES  OF  CONTINUOUS- WAVE  TRANSMISSION          579 

reached  at  much  greater  distances  from  the  sending  station  than  with 
the  spark  transmitter.1  Also,  for  the  same  range,  less  power  is  required 
than  with  the  spark  transmitter,  and  the  transmission  efficiency  thus 
improved. 

3.  Antenna   Voltages  Decreased. — Since  the  energy  is  radiated  ~in  a 
continuous  stream,  when  a  signal  is  being  sent,  and  not  in  groups,  it  follows 
that  for  a  given  power  in  the  antenna  the  amplitude  of  the  oscillations 
need  not  be  so  great.     For  example,  if  we  assume  1000  sparks  per  second, 
a  decrement  of  .1,  and  a  300-meter  wave,  the  time  per  second  during  which 
energy  is  radiated  2  is: 

1000  X-^  X 10-6  =  .046  second 

=4.6  per  cent  of  the  total  time; 

whereas  with  continuous-wave  transmission  the  time  would  be  100  per  cent. 
It  is  therefore  obvious  that  if  much  power  is  to  be  radiated  by  the  damped 
wave-transmitter,  comparatively  high  oscillation  amplitudes  must  be 
used,  that  is,  the  energy  associated  with  a  group  of  waves,  for  a  given 
amount  of  energy  radiated  per  second,  must  be  high,  since  energy  is 
radiated  only  during  a  small  fraction  of  the  time.  Thus  a  given  antenna 
will  have  a  greater  possible  energy  radiation  on  continuous  waves,  since 
the  energy  may  be  radiated  continuously ;  an  advantage  of  thus  decreas- 
ing the  required  amplitude  of  oscillation  for  a  given  radiation  is  the  reduc- 
tion in  required  voltage,  thus  decreasing  the  construction  difficulties 
encountered  in  extremely  high-voltage  apparatus  and  antennae  (due  to 
corona  losses,  insulation  requirements,  etc.). 

4.  Adjustment  of  Signal  Note. — With  damped-wave  transmission  this 
characteristic  is  a  fixed  quantity  which  cannot  be  adjusted  by  the  receiving 
operator,  and  is  determined  entirely  by  the  transmitter  group  frequency. 
With  the  undamped-wave  receivers  described  below,  this  can  be  varied, 
over  wide  limits,  to  a  value  most  suitable  to  the  operator  for  distinguishing 
from  strays.     The  adjustability  of  the  note  of  the  received  signal  also 
serves  to  a  remarkable  degree  to  eliminate  interference  from  other  stations; 
because  of  this  feature  another  signal,  differing  in  frequency  from  the  true 
signal  by  perhaps  1  per  cent,  is  actually  inaudible. 

Summary. — The  above  advantages  combine  to  give  to  a  continuous- 
wave  transmitter  a  wonderful  degree  of  selectivity  and  efficiency  of  trans- 

1  The  statement  is  true  primarily  because  of  the  greater  sensibility  of  the  receiving 
circuit    adjusted  for  continuous-wave  reception.     The    attenuation  which  occurs  as  a 
wave  travels  over  the  surface  of  the  earth  is  probably  the  same  for  continuous,  as  for 
damped,  waves. 

2  On  the  assumption  that  radiation   ceases  when  the  current  in  the  antenna  has 
dropped  to  1  per  cent  of  its  original  value. 


580  CONTINUOUS-WAVE  TELEGRAPHY  [CHAP.  VII 

mission,  very  much  higher  than  could  be  obtained  with  the  damped- 
wave  type.  In  addition,  may  be  mentioned  the  very  important  part 
which  continuous  waves  have  played  in  the  development  of  radio  telephony 
(see  Chapter  VIII),  for  which  it  is  essential.  Because  of  these  advantages, 
it  is  probable  that  continuous-wave  telegraphy  will  ultimately  supersede 
and  replace  entirely  the  damped-wave  systems;  in  the  large  stations, 
this  change  already  has  been  made  or  is  being  made  at  the  present  time. 

High-frequency  Undamped-wave  Generators. — Continuous  high-fre- 
quency oscillations  may  be  produced  by  any  one  of  the  several  schemes 
described  below.  All  of  these  have  been  commercially  developed  and 
applied,  and  are  listed  in  the  order  of  their  importance  (this  relative  rating 
being  for  high-power  stations  only)  at  the  present  date  (1920).  It  is 
probable  that  the  first  three  means  of  generation  will  find  increasing 
development  in  the  future,  while  the  fourth  and  fifth  will  be  superseded 
by  one  form  of  the  first  three  methods.  The  development  and  impor- 
tance of  vacuum  tubes  as  generators  of  high-frequency  oscillations  has 
been  very  rapid  within  recent  years,  and  it  is  likely  that  this  source  of 
high-frequency  power  will  ultimately  replace  all  others. 

The  several  means  of  high-frequency  power  generation  are  as  follows: 

(1)  Poulsen  Arc; 

(2)  Alexanderson  Alternator; 

(3)  Goldschmidt  Alternator; 

(4)  Iron  in  saturated  cores; 

(5)  Marconi  Series  of  Spark  Gaps; 

(6)  Oscillating  Tubes. 

Poulsen  Arc. — A  great  deal  of  work  has  recently  been  done  in  an  effort 
to  determine  with  exactness  the  action  and  theory  of  this  type  of  generator, 
the  best  presentation  being  that  of  P.  O.  Pedersen  1  to  which  the  reader 
is  referred.  In  the  discussion  which  follows,  we  have  referred  largely 
to  his  paper  and  to  certain  earlier  theory  as  developed  by  Barkhausen, 
to  which  Pedersen  also  makes  reference.  Much  of  the  laboratory  work 
done  in  the  past  is  not  applicable  to  the  modern  arc  generator,  due  to  the 
wide  divergence  of  the  test  arc  and  the  arc  generator  as  designed  and 
constructed  for  commercial  service. 

Elementary  Theory. — Instability  of  the  Arc. — Consider  the  ordinary 
arc  circuit  indicated  in  Fig.  1  with  the  resistance  R  omitted  for  the  present. 
The  conduction  of  current  through  the  arc  is  simply  a  case  of  conduction 
through  an  ionized  gas,  in  this  case  vaporized  carbon  or  copper  at  a  very 
high  temperature.  Initially,  this  arc  stream  of  ionized  gas  is  not  present, 
so  that  to  start  the  current  flow  in  the  above  circuit,  it  is  necessary  to  bring 
the  two  electrodes  in  contact.  The  intense  heat  developed  by  the  current 
.  i  "On  the  Poulsen  Arc  and  Its  Theory,"  Proc.  I.R.E.,  Vol.  5,  p.  255,  1917. 


THE  OSCILLATING  ARC 


581 


Arc 


ordinary 
arc  has  to  have  a  sta- 
bilizing resistance  in 
series  with  it,  or  else 
it  is  inoperative. 


passing  through  the  point  of  contact  vaporizes  some  of  the  electrode 
material,  and  as  the  electrodes  are  separated  a  vapor  stream  or  arc  of 
ionized  gas  is  produced  which  forms  a  conducting  path  for  the  current. 
The  ionization  is  assisted  by  the  high  temperature  of  the  arc  and  the 
bombardment  of  the  negative  electrode  (cathode) 
by  the  positive  ions  this  dissociating  the  electrode 
into  positive  ions  and  electrons,  the  latter  then  being 
attracted  to  the  positive  electrode  (anode). 

As  is  the  case  for  pratically  all  gaseous  con- 
ductors, the  resistance  of  the  arc  decreases  as  the 
current  increases.  This  will  be  apparent  when  it  FlG-  ['" 
is  recalled  that  the  resistance  of  the  arc  depends  on 
its  state  of  ionization  which,  in  turn,  depends  on 
the  heating  or  vaporizing  forces  which  act  on  the 
electrodes,  caused  by  the  current  flowing  through 

the  circuit.  Stated  briefly,  the  more  current  we  pass,  the  more  ionized 
vapor  we  have,  and  the  more  ionized  vapor,  the  "  fatter  "  the  arc  and  the 
lower  the  resistance.  If  the  resistance  decreases  with  current  fast  enough, 
the  IR  drop  will  decrease,  even  if  the  current  increases,  and  this  is  always 

the  case  in  the  actual  arc.  The  current 
and  voltage  relations  of  such  a  con- 
ductor would  appear  as  shown  in  the 
curve  of  Fig.  2,  known  as  the  "  static 
characteristic  "  of  the  arc;  this  name 
arises  from  the  fact  that  it  is  obtained 
from  a  series  of  fixed  (static)  current 
values  together  with  the  corresponding 
voltages. 

Thus,  if  an  arc  were  connected 
directly  across  a  constant-potential 
^PP^  a  short-circuit  condition  might 
t>e  immediately  attained,  the  voltage 
impressed  always  being  above  the  value 
required  for  equilibrium  and  the  current  thus  continually  increasing  to 
make  IR  =  E.  Since  R  is  very  small  for  a  large  current,  the  condition 
would  be  equivalent  to  a  short-circuit.  On  the  other  hand,  if  the  volt- 
age impressed  corresponded  to  a,  Fig.  2,  and  the  current  started  to 
decrease  below  the  value  6,  then  the  arc  current  would  continually 
decrease  until  the  arc  was  extinguished. 

Stabilizing  Effect  of  Resistance.  —  The  above  phenomenon  represents 
an  unstable  condition,  in  which  the  IR  drop  decreases  automatically  with 
increase  in  current.  A  stable  circuit  is  one  in  which  the  IR  drop  increases 
with  current,  and  to  stabilize  the  arc  it  is  necessary  to  add  additional 


FIG.  2.-Relation  of  current  and  volt- 
age  across  an  ordinary  arc. 


582 


CONTINUOUS-WAVE   TELEGRAPHY 


[CHAP.  VII 


A  =  EArc+IRA 
B  =  EArc+IRB 


resistance  R  in  the  circuit,  as  indicated  in  Fig.  1.  This  resistance  is  the 
familiar  "  ballast  "  resistance  used  on  all  arc  lamps,  and  the  conditions 
now  existing  in  the  circuit  are  shown  in  Fig.  3,  an  inspection  of  which 

will  indicate  how  the  circuit  has 
been  stabilized. 

Considering  curve  A,  the  opera- 
tion is  stable  for  all  currents 
greater  than  /,  and  is  unstable  for 
currents  below  this  value.  Thus, 
on  the  stable  portion  of  the  curve, 
a  decrease  of  voltage  results  in  a 
decrease  of  current,  and  thus  a 
decreased  IR  drop  across  the  re- 
sistance. The  voltage  across  the 
arc  therefore  rises,  and  initial  con- 
ditions are  restored.  The  current 


I  Arc 


in 


FIG.  3.— Showing  the  "drops"  occurring   m 

the  arc  equipped  with  ballast  resistance;  value  may  be  controlled  by  varying 
sufficient  series  resistance  must  be  used  the  terminal  voltage,  as  shown  by 
to  make  the  resistance  drop  across  the  the  two  current  values  a  and  b  on 
combination  of  resistance  and  arc  in  series  the  characteristic  curve  A,  or  by 
increase  with  the  current.  changing  the  amount  of  ballast 

resistance  used,  as  shown  by  the 

current  values  a  and  a'  for  two  different  characteristics  A  and  B  for 
the  same  terminal  voltage.  If  impressed  voltage  is  reduced  to  the 
minimum  value  (Ef  for  curve  B)  then  the  arc  may  operate  or  may  go 
out.  This  point  is  therefore  called  the  point  of  "  indifferent  "  stability. 

The  function  of  the  ballast  resistance  is 
thus  to  stabilize  the  operation  of  the  arc 
for  slow  changes  of  voltage.  Commercial 
arc  generators  have  this  resistance  short- 
circuited  when  operating  steadily,  to  in- 
crease the  efficiency,  the  inductance  and 

inherent  resistance  of  the  circuit  being  FIG.  4. — If  a  circuit  of  L  and  C  in 
sufficient  to  stabilize  the  circuit. 

Effect  of  Inductance — Choke  Coils. — If 
a  very  high  inductance  is  inserted  in  the 
circuit  as  shown  at  L'  (Fig.  4)  very  quick 
changes  of  generator  current  are  minimized 
and  prevented  to  a  large  extent.  Thus  if 

a  sudden  increase  of  generator  voltage  occurred,  the  current  would  tend 
to  increase,  and  would  increase  slightly,  setting  up  a  counter  e.m.f.  of  self- 
induction  in  L',  which  would  minimize  the  variation  of  current.  It  is 
important  to  note  that  the  inductance,  in  order  to  be  effective,  requires 


series  is  shunted  around  an  arc 
supplied  from  a  continuous-cur- 
rent generator  through  choke 
coil  L',  an  alternating  current 
will  flow  in  the  circuit  made  up 
of  L,  C,  R,  and  arc  in  series. 


THE  OSCILLATING  ARC  583 

a  variation  in  the  current  flowing  through  it,  and  the  arc  supply  is  there- 
fore not  strictly  a  constant-current  source.  This  variation  may  be  made 
extremely  small,  however,  by  using  large  inductance  values. 

A  Simple  Explanation  of  the  Operation  of  the  Oscillating  Arc. — If  a 
condenser,  in  series  with  an  inductance,  is  connected  to  a  source  of  electric 
energy,  of  voltage  E,  the  current  which  flows  after  closing  the  switch  is 
an  oscillatory  one,1  its  frequency  being  fixed  by  the  natural  period  of  the 
oscillatory  circuit  and  its  magnitude  depending  upon  the  voltage  E, 
and  the  ratio  C/L.  This  oscillatory  current  dies  away  due  to  the  damping, 
and  the  condenser  is  finally  charged  to  a  potential  difference  E,  and  there 
is  no  current  in  the  circuit. 

Suppose  an  arc,  connected  as  in  Fig.  4,  is  burning  steadily  (switch  in 
the  oscillatory  circuit  being  open),  with  a  difference  of  voltage  across  the 
two  electrodes  equal  to  E.  When  the  switch  is  closed  the  current  flowing 
in  the  L,  C,  R  circuit  is  given  by  2 


Now  by  inspection  of  Fig.  4  it  is  evident  that  this  current  must  be 
robbed  from  the  arc,  because  the  value  of  Z/  is  always  chosen  large  enough 
to  prevent  rapid  variations  of  current  from  the  generator.  Hence  when 
the  current  i  starts  to  flow  the  arc  current  starts  to  decrease,  being  always 
equal  to  IQ  —  i.  But  we  have  seen  that  it  is  a  characteristic  of  the  arc  that 
when  its  current  decreases  the  voltage  across  it  increases;  hence  Eq.  (1) 
does  not  correctly  represent  the  current  into  the  condenser,  unless  E  is 
made  to  depend  on  i  for  its  value.  Actually  the  current  is  greater  than 
indicated  by  Eq.  (1),  because  of  the  increase  in  E  during  the  time  i  is 
flowing  in  the  direction  indicated  in  Fig.  4. 

The  increase  in  E  during  the  first  alternation  is  not  great,  because 
the  amount  of  current  taken  by  the  condenser  is  only  a  small  fraction  of 
the  arc  current.  Thus  if  the  arc  is  burning  with  50  volts  across  the  gap 
and  a  current  of  10  amperes  is  flowing,  the  decrease  in  current  upon  first 
closing  the  switch  (Fig.  4)  will  probably  be  less  than  10  per  cent  of  the 

arc  current.    The  value  of  */^4  used  in  the  oscillating  circuit  should  not 

be  less  than  about  50;  the  normal  value  is  perhaps  200.  This  value  sub- 
stituted in  Eq.  (1)  shows  that  during  the  first  alternation  of  the  oscillatory 
state  the  maximum  value  of  condenser  current  will  be  less  than  1  ampere. 
The  condenser  will  charge  up  to  a  voltage  about  twice  that  of  the  arc  3 
and  then  start  to  discharge;  the  current  during  discharge  adds  to  the 

1  For  analysis  of  this  action  see  Chapter  IV,  p.  249. 

2  Eq.  (11),  p.  208;  see  also  Fig.  39,  p.  251. 

3  See  Chapter  IV,  p.  251. 


584 


CONTINUOUS-WAVE  TELEGRAPHY 


[CHAP.  VII 


current  through  the  arc  and  thus  gives  it  greater  than  normal  value. 
This  results  in  a  decrease  in  voltage  across  the  arc,  thus  tending  to  facilitate 
the  discharge  of  the  condenser,  thus  producing  a  greater  discharge  current 
than  would  have  occurred  if  the  arc  voltage  had  held  constant. 

It  will  thus  be  seen  that  the  voltage-current  characteristic  of  the  arc 
tends  to  give  a  greater  current  in  the  condenser  during  both  the  charge 
and  discharge  periods,  than  would  occur  if  the  arc  voltage  were  independent 
of  the  current  through  the  arc. 

Now  the  current  flowing  into  the  oscillatory  circuit  is  supplied  when 
the  arc"  voltage  is  higher  than  normal  and  the  current  flows  out  of  the 
oscillatory  circuit  (against  the  influence  of  the  arc  voltage)  when  the  arc 
voltage  is  less  than  normal.  As  energy  is  being  supplied  to  the  oscillatory 


Arc 
voltage 


Current  in 

oscillatory 

circuit 


Curves  A 


V  *  25  volts 

Average  arc  voltage,  perhaps  300  volts 


Curves  A  &  B  are  not  to  same  scale 

FIG.  5. — A  simple  explanation  of  the  oscillating  arc  can  be  obtained  from  these  curves; 
curves  A  show  the  start  of  oscillations  and  curves  B  give  the  conditions  when  the 
oscillations  have  reached  the  steady  state. 


circuit  during  the  charge  and  extracted  during  the  discharge,  from  the 
conditions  just  cited  it  is  evident  that  more  energy  is  supplied  to  the  oscil- 
latory circuit  from  the  arc  supply  circuit  during  the  charge  than  is  given  up 
to  the  arc  during  the  discharge.  Unless  too  great  a  resistance  is  present 
in  the  oscillatory  circuit  this  action  results  in  a  building  up  of  the  current 
in  the  oscillatory  circuit,  and  this  building  up  will  increase  until  the  maxi- 
mum value  of  the  oscillatory  current  is  practically  equal  to  the  generator 
current,  IQ. 

This  action  is  shown  by  curves  A  of  Fig.  (5),  the  curves  of  which 
are  nearly  self-explanatory;  the  current  in  the  oscillatory  circuit  is  reck- 
oned positive  when  it  is  flowing  in  the  direction  indicated  in  Fig.  4. 


THE  OSCILLATING  ARC  585 

The  lower  curve  of  Fig.  5  is  the  product  of  the  current  i  and  the  voltage 
acting  on  the  oscillatory  circuit.  Area  A  gives  the  energy  supplied  to 
the  oscillatory  circuit  by  the  arc  during  the  first  alternation,  and  area 
B  gives  the  energy  supplied  by  the  oscillatory  circuit  to  the  arc  during 
the  second  alternation.  The  difference,  A-B,  gives  the  energy  supplied 
to  the  oscillatory  circuit  during  the  complete  cycle,  and  if  this  is  greater 
than  the  PR  loss  in  the  oscillatory  circuit  during  the  cycle  the  oscil- 
latory current  will  continue  to  increase  until  some  other  factor  controls  the 
action. 

The  excess  of  area  A  over  area  B  depends  upon  the  arc  characteristic, 
being  greater  as  the  characteristic  curve  (Fig.  2)  becomes  steeper;  as  to 
whether  or  not  the  excess  is  sufficient  to  build  up  oscillations  depends 
upon  the  resistance  of  the  oscillatory  circuit.  These  two  factors  control 
completely  the  operation  of  the  arc;  it  must  be  remembered,  however, 
that  the  relation  between  arc  voltage  and  arc  current  used  in  plotting 
Fig.  5  must  be  determined  from  the  oscillatory  state  because  the  static 
characteristic  gives  too  great  a  difference  in  areas  A  and  B.  The  vari- 
ation between  the  static  characteristic  and  dynamic  characteristic  increases 
with  frequency,  in  such  a  way  that  at  high  frequency  (say  500,000  cycles 
per  second)  the  difference  between  areas  A  and  B  is  not  sufficient  to  pro- 
duce much  oscillatory  power. 

A  simple  arrangement  of  apparatus  which  has  nearly  the  same  action 
as  the  arc  is  shown  in  Fig.  6.  A  source  of  e.m.f.  is  connected  to  a  resist- 
ance R  which  is  fitted  with  a  sliding 
contact,  B.  Between  the  lower  point  of 
the  resistance  R  and  the  contact  B  is 
connected  an  oscillatory  circuit  consisting 
of  L  and  C  in  series. 

Suppose  that,  with  B  in  the  middle  of 
R,  switch  S  is  closed;  current  will  im- 
mediately start  to  flow  as  indicated  by  i,  „ 

'  1  IG.  6. — A  simple  circuit  which  may 
charging  condenser  C.    Now  as  C   starts      be  made  to  operate  the  same  M 

to  charge  contact   B  is  moved  up  on   R,       an  oscillating  arc. 
thereby  increasing  the  voltage  impressed 

on  the  L-C  circuit.  The  motion  of  B  is  so  regulated  that  it  reaches  B'  in 
an  interval  just  equal  to  one-quarter  of  the  natural  period  of  L-C]  it 
then  starts  to  move  down  on  R  and  reaches  point  B"  in  an  interval 
equal  to  one-half  of  the  natural  period  of  L-C.  Thereafter  the  contact 
oscillates  between  B'  and  B",  making  a  complete  cycle  in  a  time  equal 
to  the  natural  period  of  L-C. 

Such  an  arrangement  will  result  in  the  building  up  of  a  large  oscillating 
current  in  the  L-C  circuit,  the  magnitude  being  limited  only  by  the  volt- 
age E  and  the  resistance  of  the  oscillatory  circuit. 


586  CONTINUOUS-WAVE  TELEGRAPHY  [CHAP.  VII 

Types  of  Oscillation.  —  The  types  of  oscillation  which  may  be  gener- 
ated have  been  arbitrarily  designated  on  the  basis  of  the  minimum  arc 
current  value  as  follows: 

Type     I.  -Minimum  current  is  greater  than  zero. 
Type    II.  Minimum  current  is  equal  to  zero. 
Type  III.  Type  II  with  immediate  re-ignition,  resulting  in  pro- 
duction of  trains  of  damped  oscillations. 

Type  I  Oscillations.  —  In  this  type  of  oscillation  the  operation  is 
essentially  as  given  above  in  the  simple  explanation  of  arc  action.  The 
amount  of  alternating-current  power  generated  is  not  as  great  as  the 
device  is  capable  of  delivering,  and  the  efficiency  of  conversion  is  com- 
paratively low,  probably  less  than  40  per  cent.  The  action  of  the  arc 
with  this  type  of  oscillation  is  very  steady,  however. 

Type  II  Oscillations.  —  With  type  II  oscillations  the  arc  current 
goes  to  zero,  as  a  minimum  value  for  an  appreciable  part  of  the  cycle. 
In  this  case  the  maximum  value  of  the  radio  frequency  current  is  some- 
what" greater  than  the  value  of  the  essentially  constant  direct  current 
flowing  through  the  arc,  or 


Under  this  condition  the  arc  is  extinguished  and  no  current  flows 
across  it  for  a  small  interval  of  the  time  of  each  charging  alternation. 
During  this  internal  the  steady  direct  current  flows  into  the  condenser, 
however,  charging  it  to  the  same  polarity  and  potential  as  at  the  beginning 
of  the  preceding  discharge  cycle.  The  time  required  to  charge  the  con- 
denser and  amount  of  charge  depend  largely  on  the  state  of  ionization 
of  the  arc.  If  the  ignition  voltage  is  low,  the  amount  of  this  charge  will 
be  decreased,  and  the  amplitude  of  the  radio  frequency  oscillation  will 
be  correspondingly  decreased.  This  is  the  case  if  the  arc  is  not  deionized 
rapidly  enough,  or  if  the  electrode  separation  is  made  too  small. 

The  curves  of  current  and  voltage  for  this  case  would  be  (according 
to  accepted  authorities)  approximately  as  shown  in  Fig  7.1  During  the 
interval  from  a  to  b  constant  current  (from  d.c.  supply)  is  flowing  in  the 
oscillatory  circuit  and  thus  the  drop  across  the  L  of  the  oscillatory  circuit 
is  zero.  Therefore  E^  =  Ec  and  since  the  condenser  current  is  constant, 

J  TjJ 

—  —  -  =  K}  or  voltage  curve  must  be  a  straight  line  during  this  interval. 
at 

These  characteristics  hold  only  if  the  arc  is  comparatively  long,  much 
longer  than  is  normally  used  in  the  commercial  arc,  to  which  they  are 
therefore  not  applicable.    The  greater  distance  between  electrodes  entails 
1  Zenneck,  "Wireless  Telegraphy,"  pp.  234-236. 


THE   OSCILLATING  ARC 


587 


Arc  Current=I(L.c)t  Genera  tor  Current 


a  decreased  efficiency  due  primarily  to  the  higher  voltage  required  to  keep 
the  arc  ignited.  The  arc  is  also  more  apt  to  blow  out.  The  greater  igni- 
tion voltage  required  causes  a  corresponding  increase  in  the  time  of  charg- 
ing, which  is  not  conducive  to  a  constant-frequency  generation.  It  should 
be  noted  that  the  arc  separation  cannot  be  made  too  small,  however,  as 
with  this  condition  the  arc  current  tends  to  remain  constant  in  value 
and  (the  static  characteristic  being  very  flat  in  this  region)  but  little  vari- 
ation of  the  voltage  across  the 
arc  occurs.  Thus  the  periodic 
charge  and  discharge  of  the 
shunting  condenser  does  not 
take  place  with  much  vigor. 
The  arc  therefore  requires  a 
certain  minimum  length  to  be 
active. 

Type    in    Oscillations.— 
The  third  form  of  oscillation 
represents  an  abnormal  oper- 
ating condition,  such  as  may 
exist  with  the  gap  too  short. 
The  maximum  amplitude  of  the 
radio  frequency  current  in  this  FIG.  7. — Action  of  the  arc  when  the  arc  current  re- 
case  also  is  greater  than    the     mains  zero  for  an  appreciable  fraction  of  a  cycle, 
steady  d.c.  current  and  as  a 

consequence  the  arc  current  goes  to  zero.  The  arc,  however,  due  to  its 
ionized  condition,  and  the  high  voltage  across  it  at  that  instant,  immediately 
reignites,  and  the  condenser  current  flows  through  the  arc  without  interrup- 
tion (practically).  The  voltage  across  the  arc  thus  has  no  opportunity  to 
rise,  and  comparatively  small  charging  potential  is  impressed  on  the 
condenser  by  the  supply  circuit.  The  discharge  is  therefore  similar  to 
the  discharge  which  occurs  in  the  closed  circuit  of  a  spark  transmitter, 
the  oscillations  decreasing  until  the  energy  initially  stored  has  been  dis- 
sipated in  the  circuit.  As  the  current  decreases,  the  voltage  (a.c.)  also 
decreases,  until  it  reaches  a  value  when  it  is  no  longer  able  to  reignite 
the  arc.  The  arc  is  then  extinguished  and  the  supply  circuit  again  feeds 
into  the  condenser  circuit,  charging  the  condenser  until  the  ignition  volt- 
age is  reached,  whereupon  discharge  occurs  and  the  above  events  are 
repeated. 

The  result  is  a  series  of  damped  high-frequency  wave-trains,  exactly 
similar  to  those  produced  by  the  spark  transmitter,  but  the  group  frequency 
is  very  much  greater,  since  the  interval  between  trains  is  determined  by  the 
time  required  for  the  supply  potential  to  charge  the  condenser  up  to  the 
ignition  voltage  value,  which  time  is  very  short. 


588 


CONTINUOUS-WAVE   TELEGRAPHY 


[CHAP.  VII 


The  characteristics  of  this  type  of  oscillation  are  indicated  in  Fig. 
8.1  During  the  interval  between  two  groups  of  oscillations  the  voltage 
across  the  arc  is  shown  as  uniformly  increasing  from  a  small  to  a  high 
value,  but  as  the  arc  is  extinguished  during  this  interval,  it  is  evident 
that  this  can  only  occur  if  the  d.c.  supply  current  is  decreasing  more  and 
more  rapidly  during  this  interval.  While  this  is  not  apparent  in  Zenneck's 
figure,  it  is  evident  that  such  must  be  the  case  if  the  explanation  is  to  hold 
good. 

Normal  Poulsen  Arc. — It  is  important  to  note  that  the  three  classes 
of  oscillations  described  above  do  not  in  any  case  exactly  apply  to  the 
operation  of  the  modern  Poulsen  arc.  Present  generators,  of  all  capacities 


Arc  Current=I(L.C)+Generator  Current 


FIG.  8. — Supposed  action  of  an  oscillatory  arc,  the  length  of  which  is  much  less  than 

normal. 

up  to  1000  kw.  (input)  utilize  what  has  been  designated  as  the  "  normal 
Poulsen  arc."  In  this  arc  the  ratio  of  direct  current  in  the  supply  circuit 
to  the  radio  frequency  current  (effective  value)  is  always  equal  to  the 
A/2,  or: 

Idc  =  V2lac 

where  Iac  is  the  effective  value  of  the  current  in  the  oscillatory  circuit. 

The  normal  arc  therefore  represents  the  division  limit  between  oscil- 
lations of  type  I  and  type  II,  its  characteristics  being  somewhat  similar 
to  those  of  type  I,  as  shown  in  Fig.  9.2 

Professor  Pedersen  in  his  paper  previously  referred  to  emphasizes 
the  importance  of  the  extinction  voltage  on  the  characteristics  of  the  nor- 
mal arc.  As  the  arc  current  approaches  the  zero  value,  the  arc  voltage 
suddenly  rises,  as  shown  in  the  above  figure.  The  arc  must  be  able  to 
develop  this  voltage  if  operation  is  to  be  efficient.  Previous  theory  has 

iZerineck,   "Wireless  Telegraphy,"  p.  237.    See  also  Rein-Wirtz   "Radio  tele- 
graphisches  Practicum  "  3rd  edition,  p.  32. 
2  Ibid.,  p.  236. 


THE   OSCILLATING  ARC 


Arc 
Current 


Arc  Current=I(L.cfGenerator  Current 


r 


(lenerator 
Current 


neglected  this  portion  of  the  characteristic,  principally  because  investi- 
gators worked  with  comparatively  long  arcs,  for  which  the  preceding 
explanation  (Fig.  7)  is  adequate,  as  the  extinction  voltage  in  this  case 
is  very  small  compared  to  the  ignition  value. 

It  seems  to  the  author  that  none  of  these  curves  (Figs.  7,  8  and  9) 
represents  the  conditions  as  well  as  that  given  in  Fig.  5.  It  is  to  be  noticed 
that  if  the  action  shown  in  Fig.  5  is  continued  for  many  cycles  the  difference 
between  the  arc  voltage  during  charging  of  the  oscillatory  circuit  condenser 
and  that  during  discharge  continually  increases;  this  is  indicated  by 
curves  B  of  Fig.  5,  which 
represents  the  condition 
perhaps  100  cycles  after 
the  oscillations  start. 

It  is  to  be  noted  that 
here  the  current  has  reached 
a  steady  value  (fixed  am- 
plitude) and  that  the  arc 
voltage  pulsates  between 
perhaps  25  volts  and  a 
very  high  value,  that  corre- 
sponding to  practically  zero 
current  in  Fig.  2.  Fig.  5 
brings  out  a  relation  sel-  FlG-  9-— Voltage  and  currents  for  the  "normal"  arc. 
dom  mentioned  by  writers, 

that  the  reading  of  a  continuous-current  voltmeter  across  the  arc  is  about 
50  volts  before  oscillations  begin  but  immediately  jumps  to  300  or  more 
when  oscillations  start;  in  fact  the  reading  may  be  as  much  as  perhaps 
500  volts  if  a  sufficiently  high-voltage  power  supply  is  used.  A  c.c.  volt- 
meter reads  average  values,  hence  the  change  in  reading  from  50  volts 
to  300  volts  indicates  that  the  maximum  voltage  across  the  arc  may  be 
1000  or  more;  as  the  duration  of  this  high  voltage  is  only  a  small  frac- 
tion of  a  cycle  its  value  may  be  three  or  four  times  the  average  value, 
i.e.,  the  reading  of  the  continuous-current  voltmeter  across  the  arc. 

Practical  Construction  of  the  Arc  Generator  or  Converter. — To  increase 
the  power,  efficiency,  and  constancy  of  frequency  of  the  arc  generator,  sev- 
eral special  devices  are  employed.  These  devices  are  the  result  of  extended 
investigations  carried  out  by  V.  Poulsen,  and  their  application  has  been 
primarily  responsible  for  the  rapid  development  and  commercial  success 
of  this  type  of  generator.  Previous  to  this  time  many  investigators  had 
utilized  the  fundamental  arc  circuit,  but  had  not  succeeded  in  obtaining 
sufficient  high-frequency  energy  to  permit  the  operation  being  considered 
a  practical  success.  Poulsen's  investigations  offered  the  first  solution 
and  demonstrated  that  the  simple  arrangement  of  Fig.  4  would  give 


590  CONTINUOUS-WAVE  TELEGRAPHY  [CHAP.  VII 

undamped  oscillations  at  constant  radio  frequencies  and  sufficient  energy 
for  the  purposes  of  radio  telegraphy  and  telephony  if  modified  as  follows: 

1.  The  arc  is  caused  to  take  place  in  hydrogen  or  a  gas  rich  in  hydrogen. 

2.  The  positive  electrode  is  kept  as  cool  as  possible,  and  therefore  is 
constructed  of  some  material  having  a  high  heat  conductivity,  usually  cop- 
per, cooled  by  circulating  water.    The  negative  electrode  is  of  carbon  and  is 
rotated  slowly  on  its  axis  while  the  arc  is  in  operation,  to  improve  the 
regularity  of  the  oscillations. 

3.  The  arc  is  acted  upon  by  a  transverse  magnetic  field,  which  assists 
in  the  rapid  deionization  (scavenging)  of  the  gases  in  the  arc.     The  electro 

magnets  supplying  this  magnetic 
field  are  sometimes  connected  direct- 
ly in  the  supply  circuit  as  indicated 
in  Fig.  10. 

The  strength  of  this  field  affects 
the  characteristics  of  the  arc  to  a 
FIG  10  -The  ordinary  Poulsen  arc  burns  in  considerable  extent,   and  if  not  of 
a  hydrogen  vapor,  in  a  transverse  mag-   . ,  ,         .      ~   .  , 

netic  field  and  has  a  water-cooled  anode.  the  COrrect  value>  ^efficiency  and 
Resistance  R'  is  cut  out  when  the  arc  is  inconstancy  of  oscillation  result, 
oscillating.  As  expressed  by  Professor  Pedersen : 

"  The  arc  should  burn  in  the  weak- 
est field  in  which  it  works  normally,  only  igniting  once  a  period,  and 
always  on  the  electrode  edges.  Both  stronger  and  weaker  fields  require 
excessive  supply  voltage.  This  is  therefore  the  most  suitable  field 
intensity — the  one  giving  the  highest  efficiency  and  the  most  constant 
behavior  of  the  arc." 

If  the  field  is  made  too  strong,  the  increase  in  resistance,  due  to  the 
stretching  out  of  the  arc  as  it  is  being  extinguished,  causes  the  extinction 
voltage  (the  potential  across  the  arc  at  the  instant  the  arc  current  has 
fallen  to  zero)  to  reach  excessive  values.  This  excessive  voltage  may 
cause  a  reignition  of  the  arc  across  a  shorter  path  and  interfere  with  the 
constancy  of  the  oscillations. 

If  the  field  is  too  weak,  the  conditions  for  successive  arcs  (in  successive 
cycles)  are  not  constant,  due  to  the  fact  that  ignition  does  not  take  place 
from  the  same  point  of  each  electrode,  but  from  the  points  where  the  preced- 
ing arc  existed  at  the  instant  of  being  extinguished.  The  arc  length  thus 
grows  successively  longer  and  longer  until  the  arc  can  no  longer  ignite 
across  the  longer  distance.2  Ignition  then  takes  place  between  the  elec- 
trode tips  again  and  the  process  is  repeated.  This  also  causes  a  varia- 
tion in  the  frequency  as  the  conditions  for  successive  arcs  are  not  constant 
(arc  resistance,  charging  period,  etc.).  Since  the  proper  action  of  the 

2  The  reader  is  referred  to  the  photographs  in  Pedersen's  paper  for  evidence  of  the 
correctness  of  these  statements. 


THE  OSCILLATING  ARC  591 

field  consists  in  blowing  out  the  arc  and  allowing  a  new  arc  to  form  at  the 
beginning  of  the  next  period,  it  is  evident  that  its  intensity  will  depend 
on  the  frequency  to  be  generated.  Pedersen  has  found  the  proper  field 
intensity  to  be  approximately  proportional  to  the  frequency.  Thus  with 
an  arc  drawing  about  20  amperes  from  the  supply  line,  and  an  oscillatory 
circuit  with  a  ratio  of  VL/C  about  300,  Pedersen  found  the  most  suitable 
field  strength  to  be  given  by  the  relation  (H + 400)  X=  5000,  in  which  H 
is  in  gausses  and  X  in  kilometers.  With  a  hydrogen  atmosphere  it  seemed 
that  a  field  about  one-fifth  as  large  as  this  was  proper. 

Action  of  the  Gaseous  Atmosphere. — The  hydrogen  or  coal  gas  in 
which  the  arc  usually  operates  assists  in  cooling  the  electrodes,  and  thus 
when  the  arc  current  falls  to  zero,  the  cooling  action  of  the  gas  promotes 
a  rapid  increase  in  the  arc  resistance  (deionization) .  It  also  affects  the 
static  characteristic,  making  it  steeper  than  in  air,  as  shown  in  Fig.  26, 
page  141. 

The  reason  for  the  hydrogen  atmosphere  thus  steepening  the  curve 
is  not  known,  but  the  effect  of  this  increase  in  slope  upon  the  arc  operation 
is  evidently  to  cause  the  arc  voltage  variation  (which  in  turn  acts  to 
charge  the  condenser)  to  be  more  sensitive  and  of  greater  amplitude  for 
a  given  arc  current  variation.  The  radio  frequency  energy  input  is  thus 
increased. 

The  foregoing  features  of  construction  are  embodied  in  all  modern 
arc  generators.  Fig.  11  illustrates  a  500  kw.  arc  (input  rating),  which 
is  much  less  than  the  maximum  capacity  to  which  generators  of  this 
type  have  been  built  up  to  the  present  time. 

Generators  of  1000  kw.  capacity  are  of  the  same  general  construction, 
but  somewhat  larger  in  size.  The  arc  chamber  is  equipped  with  a  water- 
cooled  jacket  to  assist  in  cooling  the  chamber,  while  the  copper  anode 
has  circulating  water  supplied  to  it  by  means  of  flexible  pipe  connections. 
The  negative  electrode  is  usually  of  carbon,  although  graphite  is  being 
largely  used  for  the  higher  capacity  arcs.  The  anode,  as  shown  in  the 
figure,  is  equipped  with  hand  wheels  to  permit  the  accurate  adjustment 
of  the  gap  length.  The  smaller  wheels  shown  are  used  for  clamping  the 
electrode  into  its  proper  position.  The  enormous  size  of  magnetic  circuit 
apparently  required  for  these  large  capacity  generators  is  indicated  in 
Fig.  11  as  well  as  in  Fig.  12,  which  shows  the  generator  with  the  electrodes 
and  arc  chambers  removed;  the  circuit  shown  in  the  latter  figure  is  for 
a  500  kw.  arc,  the  upper  pole  piece  having  been  removed. 

Arc  generators  are  most  efficiently  used  at  the  longer  wave-lengths 
and  are  therefore  usually  operated  at  3000  meters  or  above,  6000  meters 
being  the  wave-length  generally  used.  In  some  cases  the  wave-length 
is  as  high  as  18,000  meters.  The  capacities  range  from  100  kw.  or  less 
up  to  1000  kw.;  350  kw.  arcs  are  generally  used  for  high-power  land 


592 


CONTINUOUS-WAVE  TELEGRAPHY 


[CHAP.  VII 


stations.     Small-capacity  arcs,  with  a  capacity   of  20-30  kw.,  have  been 
in  successful  use  on  board  ship.     The  usual  wave-length  is  4000  meters, 


FIG.  11. — A  500  kw.  Poulsen  arc  converter;  over  the  operator's  head  is  the  anode  ter- 
minal and  on  the  right  is  shown  the  pipe  for  carrying  off  the  exhaust  gases  from 
the  arc  chamber.  (Proc.  I.  R.  E.  Vol.  7.,  No.  5). 


FIG.  12. — Magnetic  field  structure  for  a  500  kw.  converter;  the  proper  form  of  pole 
piece  has  been  the  subject  of  considerable  study.     (Proc.  I.  R.  E.  Vol.  7.,  No.  5.) 

and  the  sets  have  a  transmission  range  of  perhaps  2000  miles  in  the  day- 
time.    Just    recently  small  arcs  (2  kw.  input)  have  been  constructed, 


THE  HIGH-FREQUENCY  ALTERNATOR  593 

which  when  fed  from  a  GOO- volt  line  seem  to  operate  satisfactorily  for 
wave-lengths  as  short  as  800  meters. 

High-frequency  Alternator. — The  generation  of  high-frequency  cur- 
rents by  means  of  machines  similar  in  their  principles  of  construction 
to  the  huge  alternators  which  supply  the  modern  central-station"  Isads, 
has  doubtless  occurred  to  the  student.  The  extremely  high  frequencies 
required,  however,  necessitate  machines  of  special  design  which  require 
a  high  grade  of  engineering  skill  in  their  construction.  Alternators  for 
supplying  loads  of  commercial  frequency  may  be  any  one  of  the  three 
following  types : 

I.  The  armature  is  the  rotating  element,  the  d.c.  field  being  stationary. 
This  arrangement  is  similar  to  that  employed  on  all  d.c.  generators  but 
is  rarely  used  on  alternators,  particularly  the  large  sizes. 

II.  The  field  rotates  with  respect  to  the  armature,  which  is  fixed  in 
position.     This  construction  possesses  several  advantages  over  type  I, 
particularly  due  to  the  lesser  insulation  requirements  of  the  field  winding 
and  its  greater  simplicity  as  compared  to  the  armature  winding.     This 
construction  is  universal  on  all  modern  alternators. 

III.  Both  the  field  and  armature  windings  are  stationary  in  space, 
the  flux  linking  the  armature  winding  being  periodically  varied  by  means 
of  an  inductor,  revolving  in  the  air  gap.     This  inductor  is  essentially  a 
disk  whose  periphery  has  been  divided  into  sections,  alternate  sections 
possessing  a  high  magnetic  reluctance,  while  the  intermediate  sections, 
which  are  made  of  steel,  possess  a  relatively  low  reluctance.     This  type 
is  practically  unused  in  the  low-frequency  machines  of  commercial  engineer- 
ing, but  possesses  several  inherent  advantages  which  make  it  the  most 
satisfactory  of  the  alternators  designed  for  high-frequency  generation. 
Since  both  windings  are  fixed,  in  position,  their  proper  insulation  is  much 
simplified.     Very  serious  difficulty  is  encountered  when  it  is  attempted 
to  place  an  insulated  winding  on  the  revolving  member  (rotor) ,  due  to  the 
high  peripheral  speeds  and  consequently  high  centrifugal  stresses  involved. 

Design  of  the  High-frequency  Alternator. — That  a  special  construction 
and  design  is  required  may  be  seen  from  the  following:  If  we  consider 
a  machine  of  the  inductor  type  having  a  maximum  permissible  speed  of 
20,000  r.p.m.  and  a  required  frequency  of  100,000  cycles  per  second,  the 
rotor  diameter  being  assumed  30  centimeters,  the  distance  through  which 
a  point  on  the  rotor  moves  in  generating  one  cycle  is 

20,000 


7rX30X; 


60     =0.31  cm. 


100,000 

Therefore,  in  this  small  space  we  must  have  a  section  of  high  reluctance 
(for  instance,  bronze)  and  a  section  of  low  reluctance  (steel)  so  that  a 


594 


CONTINUOUS-WAVE  TELEGRAPHY 


[CHAP.  VII 


Cast  steel  yoke 


Field  coils 


Armature 

coils  around 

poles  N  and  S 


complete  cycle  of  flux  variation  from  minimum  to  maximum  and  back  to 
minimum  occurs  while  the  inductor  moves  through  this  space.  Special 
precautions  in  design  and  materials  used  must  be  observed  if  the  hysteresis 
and  eddy  current  losses  are  to  be  minimized,  as  these  become  very  large 
at  the  higher  frequencies. 

Construction.  —  The  construction  of  the  Alexanderson  high-frequency 
alternators  (first  suggested,  and  first  ones  built  by  R.  A.  Fessenden),  is 
indicated  in  Fig.  13. 

The  pole  pieces  BB  are  threaded  into  th^  yoke  A  as  indicated,  the 
air  gaps  being  thus  accurately  adjustable.  The  pole  tips  NS  are  finely 

laminated  to  reduce  eddy  current  and 
hysteresis  losses  and  are  slotted  to 
receive  the  armature  winding.  The 
field  windings  WW  are  installed  as 
shown,  and  with  a  steady  direct  cur- 
rent flowing  through  them,  set  up  a 
flux  as  indicated  in  the  diagram.  It 
is  evident  that  the  reluctance  of  this 
circuit  will  vary  as  the  inductor  R  ro- 
tates between  the  two  faces  of  the  air 
gap.  This  inductor  is  properly  de- 
signed for  the  high  stresses  which  exist 
when  it  is  operated  at  its  rated  speed 
of  20,000  r.p.m.  The  rim  velocity 
under  this  condition  is  about  300 
meters  per  second  and  the  centrifugal 
force  at  the  periphery  is  68,000  times 
the  weight  of  metal  there. 

A  developed  view  of  the  winding  and  rotor  is  shown  in  Fig.  14.  If 
we  consider  the  loop  formed  by  conductors  6-7,  the  flux  linking  it  will 
be  a  maximum  with  the  inductor  in  the  position  shown.  As  the 
inductor  moves  to  the  right,  the  tooth  e  is  replaced  with  a  non-magnetic 
insert  and  the  flux  decreases  to  a  minimum  value.  Then  as  the  inductor 
continues  to  move  to  the  right  the  tooth  d  enters  the  loop  6-7  and  the 
flux  increases  again  to  a  maximum.  The  variation  of  flux  and  correspond- 

ing induced  voltage  ( 

that  a  complete  cycle  is  generated  while  the  rotor  travels  a  dis- 
tance represented  by  the  tooth  pitch  (distance  of  a  point  on  a 
tooth  to  similar  point  on  adjacent  tooth).  The  frequency  is  thus 
equal  to  the  number  of  inductor  teeth  multiplied  by  the  revolutions 
per  second. 

The  effective  number  of  poles  for  this  type  of  machine  is  evidently 


I 

FIG.  13. — Simplified  cross-section  of  an 
Alexanderson  alternator. 


E 


~)  i 


is  indicated  on  the  figure.     It  will  be  noted 


THE  ALEXANDERSON  ALTERNATOR 


595 


twice  the  number  of  inductor  teeth  or  spokes.     Thus  to  generate  100,000 
cycles  we  would  require 

f        1  00  000 

N  =  -J—=  0^7~7 
rps     20,000 

60 


=300  spokes  on  the  inductor 


An  examination  of  the  winding  indicates  that  loops  2-3,  10-11,  etc., 
pass  through  the  same  flux  variations  as  loop  6-7,  and  as  these  loops 
are  all  connected  in  series  the  voltage  will  add  up  around  the  periphery. 
The  same  analysis  holds  for  loops  4-5,  8-9,  12-1,  etc.  The  windings  are 
brought  out  to  separate  terminals  and  may  thus  be  connected  in  series 


FIG.  14.— Developed  view  of  the  winding  and  rotor  of  the  machine  shown  in  Fig.  13. 

or  parallel,  whichever  may  be  most  suitable  for  the  conditions  involved. 
It  should  be  remembered  that  two  similar  windings  are  placed  in  the 
pole  tip  on  the  near  side  of  the  air  gap,  which  are  not  shown  in  the  figure. 
Thus  the  operator  has  four  or  more  separate  windings  which  he  may  con- 
nect in  any  arrangement  most  desirable  for  his  conditions.  On  the  alter- 
nator at  the  New  Brunswick  station,  each  coil  has  its  terminals  brought 
out,  there  being  64  such  coils. 

On  the  normal  inductor  generator,  the  number  of  armature  slots  is 
always  equal  to  the  effective  number  of  poles.  In  the  Alexanderson 
machine  the  number  of  armature  slots  may  be  two-thirds  the  number  of 
poles.  This  is  a  distinct  advantage,  as  more  space  and  more  thorough 
insulation  is  thus  permitted  for  the  winding.  Thus  in  the  figure,  we  have 
between  the  lines  xx,  twelve  armature  slots  and  nine  inductor  spokes, 


590  CONTINUOUS-WAVE   TELEGRAPHY  [CHAP.  VII 

which  represent  eighteen  effective  poles,  or  the  armature  slots  are  two- 
thirds  the  effective  poles. 


The  greater  the  flux  variation  (-7-)  the  greater  will  be  the  generated 

voltage.  By  decreasing  the  air  gap  the  effect  of  the  inductor  on  the  flux 
becomes  more  pronounced  and  thus  the  generated  voltages  increase. 
On  a  certain  machine,  with  a  minimum  permissible  air  gap  of  .004  inch 
(for  each  of  the  two  gaps),  the  voltage  generated  was  nearly  300  volts. 
With  the  air  gaps  increased  to  .015  inch  each,  the  voltage  decreased  to 
150.  (Eccles.)  Similarly,  the  output  capacity  increases  as  the  air  gap  is 
decreased  and  vice  versa. 

The  highest  frequency  for  which  these  machines  have  been  constructed 
at  the  present  time  (1920)  is  200,000  cycles  per  second  with  a  capacity 
of  about  1  kw.  Machines  of  50  kw.  and  greater  have  been  constructed, 
the  frequency,  however,  being  lower  for  these  higher  capacity  machines, 
usually  about  50,000  cycles.  A  2-kw.,  100,000-cycle  generator  is  indicated 
in  Fig.  15,  showing  the  driving  motor,  normally  operating  at  2000  r.p.m., 
connected  through  special  1  :  10  gears  to  drive  the  alternator  shaft  at 
20,000  r.p.m.  This  general  arrangement  is  followed  on  all  alternators  of 
this  type,  the  gear  ratio  decreasing  as  the  capacity  increases.  On  some 
machines  the  driving  motor  is  connected  to  the  low-speed  gear  shaft  by 
means  of  a  chain  connection.  A  view  of  a  piece  of  one  armature  of  a 
2-kw.,  100,000-cycle  machine  is  shown  in  Fig.  15A. 

As  might  well  be  supposed,  the  high-speed  machines  are  not  as  reliable 
in  operation  or  as  easy  to  maintain  as  a  low-frequency  machine  of  the  same 
power.  The  bearings  of  the  machine  shown  in  Fig.  15  are  flexibly  fastened 
to  the  tied  plate  of  the  machine  so  that  as  the  armature  shaft  expands 
each  bearing  will  move  away  from  the  rotor  disk  equally,  thus  maintain- 
ing the  two  air  gaps  equal.  Forced  oil  feed  must  be  used  for  the  bearings 
and  for  the  larger  machines,  pipes  carrying  cooling  water  are  liberally 
distributed  throughout  the  structure  of  the  machine. 

The  high  peripheral  speed  of  the  disk  results  in  a  very  rapid  circulation 
of  air  through  the  two  air  gaps,  causing  considerable  noise  and  power 
consumption.  The  small  machine  shown  in  Fig.  15  requires  about  7  h.p. 
to  turn  the  disk  at  rated  speed,  the  machine  not  being  loaded. 

These  high-frequency  inductor  alternators  require  suitable  tuning 
condensers  to  neutralize  their  internal  reactance  before  they  can  deliver 
appreciable  power;  a  small  200,000-cycle  machine  will  scarcely  deflect 
a  voltmeter  across  its  terminals  unless  a  proper  condenser  is  connected 
across  the  armature  terminals. 

Connection  to  the  Antenna. — The  armature  winding  may  be  directly 
connected  to  the  antenna  as  shown  in  Fig.  16a,  or  it  may  be  inductively 
coupled  as  shown  in  Fig.  166,  by  using  an  oscillation  transformer.  In 


THE   ALEXANDERSON   ALTERNATOR 


597 


either  case  the  antenna  circuit  must  be  tuned  to  the  frequency  of  the 
alternator  if  maximum  output  is  to  be  obtained.     If  the  2-kw.  100,000- 


High  frequency 
generator, 
0,000  rp.m.  jf 


Rockh 


Driving 

motor  2,000  rp.m. 
r 


Oil  pipes  for  bearings 


FIG.  15. — View  of  a  small  100,000  cycle  Alexanderson  alternator. 


Windings  in  face 
of  armature 


Steel  Ring 

for  holding  Arma 


Core 


FIG.  15A. — A  view  of  a  section  of  one  armature  of  the  machine  in  Fig.  15. 

cycle  machine  is  considered,  its  reactance  at  this  frequency  with  normal 
air-gap,  may  be  taken  as  5.4  ohms  or 


L  = 


5.4 


2rX  100,000 


598  CONTINUOUS-WAVE   TELEGRAPHY  [CHAP.  VII 

Thus  the  antenna  capacity  (Fig.  16a)  must  be  such  that 
3000  =  1885  VLC  =  1885  >/8J38C 

or  C=0.3  microfarad.  It  is  evident  that  the  direct  connected  scheme 
(16a)  could  not  be  used  unless  a  suitable  loading  inductance  (Z/)  were 
added,  as  antennae  are  not  built  with  such  a  high  capacity.  The  arrange- 
ment utilizing  an  oscillation  transformer  (Fig.  166)  would  most  probably 
be  used  in  any  case.  The  maximum  continuous  load  of  this  machine 
is  30  amperes  at  70  volts,  or  the  equivalent  antenna  circuit  resistance 

as  measured  at  the  terminals  of  the  generator  must  thus  be  —  =2.3  ohms. 

oO 

Application. — At  this  time  the  Alexanderson  alternator  is  rapidly 
increasing  in  importance  and  application,  particularly  the  lower-frequency 

machines  (20,000-50,000 
cycles)  of  large  capacity. 
The  inherent  disadvan- 
tages of  this  type  of  gen- 
erator due  to  the  high 
speeds  and  complications 
attendant  thereto,  such 
as  lubrication,  etc.,  ap- 
parently prevent  it  from 

representing  a  practical 

FIG.  16. — Two  schemes  for  connecting  a  high-frequency  „  . 

generator  to  an  antenna;  that  shown  in  (6)   is  gener-  means  of  generation  on 
ally  used.  board  ship,  or  for  small- 

power     installations     or 

portable  field  service.  For  high-power  land  stations,  however,  engaged 
in  transoceanic  and  transcontinental  service,  it  will  probably  be  increas- 
ingly successful  in  application  and  performance.  It  is  also  adaptable  to 
the  requirements  of  radio  telephony.  (See  Chapter  VIII.)  The  most 
successful  station  utilizing  this  type  of  generator  is  located  at  New 
Brunswick,  N.  J.,  where  a  200-kw.  set  is  installed.  This  equipment  is 
shown  in  Fig.  17.  For  a  further  description  of  this  machine  and  station 
the  reader  is  referred  to  a  paper  by  E.  F.  W.  Alexanderson.1 

One  of  the  chief  difficulties  in  the  operation  of  a  high-frequency  alter- 
nator is  the  accurate  control  of  its  speed.  An  almost  imperceptible 
change  in  alternator  speed  will  result  in  the  pitch  of  the  signal  note  at  the 
receiving  station  changing  several  octaves.  That  the  Alexanderson 
generators  are  controlled  in  speed  to  better  than  0.1  per  cent  can  be  told 
at  once  by  noting  the  constancy  of  pitch  of  the  signal  received  from  the 

1  "  Transatlantic  Radio  Communication,"  Proc.  A.  I.  E.  E.,  Oct.,1919. 


THE  GOLDSCHMIDT  ALTERNATOR 


599 


/I /ex an  ^£y  son  £OQ  /fW  a//cr  na  /o  /• 


New  Brunswick  station.  An  ingenious  arrangement  of  relays  operate  on 
the  driving  motor  so  as  to  make  its  speed  essentially  constant. 

The  Goldschmidt  Alternator. — Theory. — This  generator,  first  brougnt 
out  in  commercial  form  by  Dr.  R.  Goldschmidt,  is  based  on  principles 
which  are  radically  different  from  those  involved  in  the  Alexanderson 
machine.  These  are: 

1.  The  magnetic  field  produced 
by  an   alternating  current  of  fre- 
quency  n,  may  be    considered  as 
consisting  of  two  component  fields, 
the  magnitude   of   each    of    these 
fields  being  one-half  the  magnitude 
of  the  resultant  total  field  and  con- 
sidered as  rotating  in  opposite  direc- 
tions at  frequency  n. 

This  is  simply  the  theory  of  con- 
jugate vectors  and  is  illustrated  in 
Fig.  18.  Fig.  18A  represents  the 
normal  derivation  of  a  sine  curve 
from  a  rotating  vector  while  Fig. 
18B  utilizes  the  principles  of  con- 
jugate vectors;  the  horizontal 
components  of  $'  and  </>"  neutralize 
one  another,  while  the  resultant 
vertical  component  is  at  all  times 
as  indicated  by  the  sine  curve  to 
the  right.  Similarly,  the  current 
/  could  be  represented  in  the  same 
manner.  The  construction  illus- 
trates graphically  the  principle 
stated  above. 

2.  If  a  coil  (rotor)    is  revolved 
in  this   alternating  magnetic    field 
at  synchronous  speed,  it  is  appar- 
ent from  the    foregoing   that   the 
component  fields  will  induce  e.rri.f.'s 
of  different  frequencies,  since  they 
are  rotating  in  opposite  directions. 
If  we  assume  the  coil   to   revolve 
in    a    counter-clockwise    direction, 

flux  4>'  will  rotate  with  it,  thus  cutting  no  conductors  and  generating  no 
e.m.f.  in  the  coil.  The  other  component  $"  is  moving  against  the  rota- 
tion of  the  coil.  Thus  the  frequency  will  be  twice  what  it  would  be  if 


FIG.  17.  Views  of  the  high-powered  Alexan- 
derson  generator  installed  at  New  Bruns- 
wick; over  the  alternator  (in  the  lower 
view)  may  be  seen  the  oscillation  trans- 
formers which  connect  the  generator  to 
the  antenna. 


600 


CONTINUOUS-WAVE  TELEGRAPHY 


[CHAP.  VII 


the  coil  were  standing  still.     Reviewing  the  above,  two  frequencies  may 
be  considered  as  being  generated  in  the  coil,  viz., 

fi=N—Nr  (produced  by  <£') 
fi  =N-\-Nr  (produced  by  <j>") 

since  Nr=N, 

this  becomes  J\  =  0 

f2=2N 


0  ^ 

18-A-Normal  Construction 


0  +  <t> 


<t>  =  0+0" 


18-B  Construction 

by  means  of  Conjugate 

-Vectors 


pIG  ig  —  A  stationary,  pulsating,  magnetic  field  may  be  represented  by  two  rotating 
fields  each  constant  in  strength,  rotating  in  opposite  directions.  Each  rotating 
field  has  one  half  the  strength  of  the  stationary  pulsating  field. 

In  these  expressions  N  is  the  frequency  of  the  alternating  field,  while 
Nr  is  the  rotational  speed  of  the  coil  expressed  in  cycles  per  second.  There- 
fore, if  the  terminals  of  the  rotating  coil  are  connected  together,  a  current 
will  flow  in  the  circuit  whose  frequency  is  2N,  and  a  doubling  of  the  initial 
frequency  N  has  been  obtained.  It  is  evident  that  this  double-frequency 
current  could  be  led  to  a  second  fixed  coil,  with  a  revolving  coil  placed 
in  the  influence  of  its  magnetic  field  and  a  further  doubling  of  frequency 
would  result,  if  the  coil  is  rotated  at  a  frequency  2N.  If  the  speed  of 
rotation  is  Nr  as  for  the  first  case,  the  frequencies  would  be 


f2=N+NT=2N+N=3N 


THE  GOLDSCHMIDT  ALTERNATOR  601 

A  practical  example  of  these  effects  is  found  in  the  double-frequency 
component  which  appears  in  the  d.c.  field  circuit  of  a  single-phase  alter- 
nator when  the  machine  is  carrying  load.  This  is  illustrated  by  the  ondo- 
graph  record  shown  in  Fig.  19,  in  which  the  60-cycle  armature  e.m.f .  and 
the  120-cycle  (2N)  e.m.f.  induced  in  a  search  coil  on  the  pole  are  both 
shown.  The  field  winding  revolves  at  synchronous  speed  in  an  alternating 


ARMATURE  REACTION 

IN  A 
SINGLE-PHASE  ALTERNATOR 


Ondograph.Record 


A=Terminal  E.M.F.  of 

Armature 
B=  E.M.F.  Induced  in 

Search  Coil  on  Pole 

shoe 


FIG.  19.  —  Ondograph  record  from  a  single-phase  alternator;  curve  B,  obtained  from  a 
search  coil  on  the  pole  face  shows  a  frequency  twice  as  great  as  that  generated  in 
the  armature. 

field  produced  by  the  current  in  the  armature  winding.     We  thus  have,  as 
for  the  first  case  cited  above. 


It  has  already  been  indicated  how  additional  increases  in  frequency 
might  be  obtained  by  using  a  number  of  machines  (consisting  of  a  fixed 
and  movable  coil)  connected  in  cascade.  However,  instead  of  having 
the  rotor  currents  excite  a  distant  stator,  it  is  more  practical  and  econom- 
ical to  have  it  react  back  on  its  own  stator.  The  fundamental  connections 
would  then  be  as  shown  in  Fig.  20. 

Connections  for  Increasing  Frequencies  in  the  One  Machine.  —  The 
source  of  power,  A,  supplies  current  of  frequency  N  to  the  stator 
winding  S  and  the  rotor  winding  R  rotates  in  this  field  at  synchronous 

speed   (in  r.p.m.  =  -  ^  —  =  —  ).     There  will  thus  be  induced  in  R  an 
\  no.  of  poles/ 

e.m.f.  of  frequency  N—N=Q  and  an  e.m.f.  of  frequency  N+N=2N. 
If  the  terminals  are  joined  by  a  low-impedance  path,  a  current  of  this 
frequency  will  flow  in  the  rotor  circuit.  Associated  with  this  current  is 


602  CONTINUOUS-WAVE   TELEGRAPHY  [CHAP.  VII 

a  magnetic  field  whose  frequency  is  27V.  Recalling  that  we  may  represent 
this  field  by  two  oppositely  rotating  fields,  whose  frequency  is  2N,  it  is 
evident  that  one  component  (the  one  revolving  in  the  same  direction  as 
the  rotor)  will  cut  the  stator  at  a  frequency  2  7V+  N  =3  N,  while  the  other 
component  will  cut  it  at  a  frequency  2N—  N  =  N,  corresponding  e.m.f.'s 
being  induced  in  the  stator  circuit.  If  the  terminals  of  the  stator  coil 

Higher  Frequency"  b(?    J°med     ^     a     SUltable     cirCuit>    CUr' 

rents  of  these  frequencies  will  flow. 
Furthermore,  the  field  set  up  by  the 
triple-frequency  current  will  induce 
in  the  rotor  e.m.f.'s  of  frequency 
37V-7V=27V  and  3  TV -f  TV  =4  TV,  and 
currents  of  these  frequencies  will  flow 
in  the  rotor  circuit.  In  turn,  the 
current  of  frequency  =4  N,  will  in- 
duce in  the  stator  e.m.f.'s  of  frequency 

FIG.  20.— Conventional  diagram  of  ro-  4  N  ~  N  =  3  N  and  4  N+  N  =  5  N.    Thus, 
tor  coil  R,  and  tuned  stator  circuit  if  we  assume  an  initial  supply  frequency 
S-C,  supplied  with  magnetizing  cur-  to  the  stator  of  10,000,  we  have  trans- 
rent  through  choke  coil.  formed  it  by  means  of  so-called  "  elec- 
trical reflections  "  outlined  above,  into 

a  frequency  of  57V  =  50,000,  which  may  be  employed  for  radio-telegraph 
and  radio-phone  transmission. 

These  several  e.m.f.'s  may  be  tabulated  as  follows: 

Stator  Rotor 

N  2ATandO 

3  TV  and  N  ±Na,ud2N 
5TVand3TV 

If,  instead  of  supplying  alternating  current  to  the  stator  winding, 
we  employ  direct  current,  the  results  are,  similarly: 

Stator  Rotor 

0  N 

27V  and  0  37V  and  N 

4  TV  and  27V 

This  is  the  usual  arrangement  for  commercial  machines,  the  source 
of  supply  being  a  storage  battery  or  d.c.  generator. 

Application  of  Tuned  Circuits. — In  discussing  the  reflection  of  frequen- 
cies we  have  indicated  the  coil  circuits  as  being  completed  in  the  rotor 
by  a  short-circuiting  resistance  while  the  stator  circuit  is  completed  by 
a  condenser.  Since  the  coils  themselves  possess  considerable  impedance 
at  the  high  frequencies  involved,  this  must  be  compensated  for  by  suitable 


THE  GOLDSCHMIDT  ALTERNATOR 


603 


capacities,  so  that  the  circuit  may  be  in  resonance  for  the  frequency  of 
the  induced  e.m.f.,  i.e., 

1 


Choke  coil 


l_ 


g: — WBSP 1 

3  ifp 

J 


27T/C' 

By  thus  employing  tuned  circuits,  the  magnitude  of  the  current  flow  pro- 
duced will  be  a  maximum  and  is  limited  only  by  the  effective  resistance 
of  the  circuit.  This  ef- 
fective resistance  includes 
the  losses  due  to  hystere- 
sis and  eddy  currents  as 
well  as  dielectric  losses. 

Since  e.m.f.'s  of  sev- 
eral frequencies  are  con- 
cerned, circuits  must  be 
available  which  are  tuned 
to  each  of  these  frequen- 
cies. Fig.  21  indicates 
the  arrangement  em- 
ployed by  Goldschmidt, 
for  a  quadrupling  of  the 

generated  frequency  di-  FlG-  21- — In  orcler  to  get  currents  °f  appreciable  ampli- 
,  tudes  of  the  various  frequencies  generated  in  a  "re- 

flection" type  machine  the  rotor  and  stator  must  be 
plied  to  the  stator.  supplied  with  suitably  tuned   circuits,  one  for  each 

The  rotor  R  revolves       frequency  generated, 
at  the  required  speed  in 

the  d.c.  field  produced  by  the  stator  winding  S,  supplied  by  means  of 
the  storage  battery  B.  There  is  thus  induced  in  R  an  e.m.f.  of  fre- 
quency N,  the  value  of  which  is  given  by 


N 


NpXRPM 
120 


where  Np  =  the  number  of  poles. 


This  e.m.f.  will  cause  a  current  of  corresponding  frequency  to  flow  in  the 
circuit  R,  Ci,  Li,  C"i,  the  values  of  the  capacities  and  LI  being  adjusted 
so  that  the  circuit  is  tuned  to  this  frequency.  Ci  compensates  for  the 
inductance  of  the  rotor,  while  L\  and  C'\  compensate  each  other,  and  the 
drop  across  them  is  thus  very  small.  This  current  induces  an  e.m.f.  of 
frequencies  2  TV  and  0  in  the  stator  circuit  S,  £2,  £2,  €'2,  in  which  the  values 
of  €2,  L2  and  €'2  are  adjusted  to  resonance  for  the  frequency  2N.  €2 
compensates  for  the  inductance  of  the  stator  winding,  while  L%  and  €'2 
compensate  each  other,  and  therefore  practically  no  drop  exists  across 
this  portion  of  the  circuit.  The  double-frequency  current  induces  an 
e.m.f.  of  frequencies  3N  and  N  in  the  rotor,  and  triple-frequency  current 


604  CONTINUOUS-WAVE   TELEGRAPHY  [CHAP.  VII 

flows  in  the  circuit  R,  Ci,  €3,  which  is  tuned  to  resonance  for  this  frequency. 
Practically  no  current  of  frequency  N  will  pass  through  Cs,  since  LI,  C"i, 
represents  almost  a  short  circuit  path  across  €3  for  this  frequency. 

The  triple-frequency  current  flowing  in  the  rotor  circuit  R,  Ci,  Cs, 
induces  in  the  stator  e.m.f  .'s  of  frequencies  4Af  and  2N,  and  currents  of  cor- 
responding frequencies  flow  in  the  circuits  S,  €2,  CA  and  S,  €2,  Z/2 ,  €'2, 
respectively,  each  of  which  are  tuned  to  resonance.  The  condenser  CA 
represents  the  antenna  through  which  we  thus  have  a  current  flowing 
whose  frequency  is  four  times  the  frequency  (N)  of  the  current  initially 
generated.  If  it  were  desired  to  utilize  the  triple-frequency  current,  the 
antenna  would  be  connected  to  the  rotor  in  place  of  Cs,  while  L^.  and  €'2 
could  be  omitted  from  the  stator  circuit.  By  suitably  arranging  other 
circuits  higher  frequencies  could  be  obtained  but  such  an  arrangement  is 
not  employed  to  any  extent  commercially,  as  the  quadruple-frequency 
machine  is  more  efficient  and  fulfills  all  requirements. 

For  the  complete  Goldschmidt  machine  as  described  in  the  preceding 
discussion,  we  may  tabulate  the  generated  frequencies,  as  before — 

Stator  Rotor 

0  N 

27VandO  3AT  and  N 

4N  and  2N 

An  exact  analysis  of  all  the  actions  in  this  machine  is  complicated 
and  would  be  out  of  place  here.  The  amplitudes  of  the  various  frequencies, 
it  must  be  pointed  out,  however,  are  not  the  same;  for  all  e.m.f. 's  of  zero 
frequency  the  amplitude  is  zero,  while  the  other  amplitudes  depend  for 
their  values  upon  the  tightness  of  the  magnetic  coupling  between  the  rotor 
and  stator  circuits. 

A  fairly  good  idea  of  this  reflecting  action  may  be  obtained  by  exami- 
nation of  the  cut  in  Fig.  22  which  shows  the  stator  and  rotor  currents 
of  a  single-phase  induction  motor  excited  by  a  60-cycle  supply  and  running 
near  synchronous  speed.  The  rotor  current  evidently  shows  the  two 
frequencies  (/+/')  and  (/  —  /'),  /  being  the  impressed  frequency  and  /' 
the  frequency  of  rotation.  The  rotor  circuit  and  stator  circuit  were 
not  tuned,  otherwise  more  frequencies  might  have  been  accentuated, 
and  the  stator  current  would,  for  example,  show  /  -f2/'  and  /  —  2/' 
frequencies. 

In  Fig.  22  is  shown  the  effect  of  running  the  rotor  at  practically 
synchronous  speed.  Here  the  amplitude  of  the  differential  frequency 
(/—/')  is  so  small  that  the  film  does  not  show  it,  although  it  can  be  seen 
from  the  film  that  the  rotor  frequency  is  slightly  more  than  twice  the 
Stator  frequency. 


THE  GOLDSCHMIDT  ALTERNATOR 


605 


FIG.  22. — Rotor  and  stator  e.m.f.'s  of  a  single-phase  induction  motor.  The  rotor  e.m.f. 
may  be  separated  into  its  two  components  as  shown  by  the  dashed  line.  One  fre- 
quency is  equal  to  that  impressed  on  the  stator  plus  the  frequency  of  rotation 
and  the  other  frequency  is  the  difference  of  the  two. 


FIG.  23. — When  the  rotor  was  run  at  practically  synchronous  speed  the  amplitude  of 
the  differential  frequency  was  practically  zero,  leaving  in  the  rotor  only  the  additive 
frequency. 


606 


CONTINUOUS-WAVE  TELEGRAPHY 


[CHAP.  VII 


Construction.— If  we  assume  a  required  frequency  of  40,000  cycles 
per  second,  and  a  frequency  transformation  ratio  of  4,  the  initial  frequency 
generated  is  10,000.  From  the  general  equation  for  frequency 

.No.  of  poles  Xr.p.m. 
120 

it  is  readily  seen  that  a  large  number  of  poles  will  be  necessary, 
ing  a  maximum  desirable  speed  of  3000  r.p.m.,  we  have 


Assum- 


No.  of  poles  = 


120X10,000 
3000 


=400. 


Considering  a  maximum  safe  peripheral  speed  of  200  meters  per  second, 
we  obtain  1.25  meters  as  the  maximum  diameter  permissible  for  the  rotor. 
This  gives  a  circumference  of  400  cm.,  and  thus  the  space  available  per 
pole  is  1  cm.  The  windings  are  therefore  laid  out  similar  to  the  armature 
winding  of  the  Alexanderson  machine,  and  consist  on  both  rotor  and 
stator  (the  windings  are  identical)  of  the  simple  zig-zag  winding  shown 
in  Fig.  24.  The  windings  are  split  up  into  sections  which  can  be  connected 


fc    1  CTT  .^ 


FIG.  24. — Developed  winding  of  a  Goldschmidt  alternator. 

in  series  or  parallel  arrangement  to  secure  the  most  suitable  voltage  for 
the  resistance  of  the  antenna  used.  The  conductor  is  made  up  of  a  number 
of  very  fine  strands,  about  No.  40  A.  W.  G.,  each  insulated  individually 
to  reduce  skin  effect. 

To  reduce  the  iron  losses,  the  rotor  and  stator  are  constructed  of  veiy 
thin  laminations  of  high-resistance  iron.  These  laminations  are  .05  milli- 
meter in  thickness  and  are  seps&rajted  by  paper  about  .03  millimeter  thick. 
When  the  assembled  material  i$  compressed  the  volume  of  paper  is  more 
than  one-third  the  total  volume..  To  further  decrease  the  iron  losses, 
the  iron  is  worked  at  low  densities. 

It  is  evident  from  the  foregoing  discussion  on  the  action  of  this  machine, 
that  the  air  gap  must  be  made  as  small  as  possible- so  that  the  magnetic 
leakage  between  the  two  windings  shall  be  a  minimum,  since  the  induced 
voltages  decrease  for  each  succeeding  reflection,  this  decrease  being  fixed 
by  the  amount  of  magnetic  leakage  and  the  losses.  Excessive  magnetic 
leakage  also  tends  to  prevent  neutralization  of  the  intermediate  currents 


THE   GOLDSCHMIDT  ALTERNATOR  607 

and  thus  additional  losses  are  caused  which  may  be  minimized  by  reducing 
the  gap. 

On  the  largest  machines  we  thus  find  extremely  small  air  gaps,  being 
about  .08  cm.  on  a  100  kw.  machine  (normal  rating).  The  rotor  of 
this  machine  weighs  about  5  tons  and  is  1.25  meters  in  diameter,  which 
indicates  the  extreme  precision  and  care  required  for  the  proper  construc- 
tion of  this  type  of  generator.  Trouble  may  be  experienced  if  the  rotor 
expands  under  the  effects  of  temperature  rise  produced  by  continuous 
operation.  This  will  cause  an  increasing  output  (almost  inversely  pro- 
portional to  the  gap  length)  as  the  gap  decreases  until  the  rotor  suddenly 
makes  contact  with  the  stator  and  jams  tight,  resulting  in  the  destruction 
of  the  machine. 

It  is  also  important  that  the  rotor  and  stator  slots  be  strictly  parallel 
to  the  shaft  and  to  each  other.  That  is,  there  should  be  no  skewing,  as 
otherwise  the  e.m.f.'s  induced  throughout  the  length  of  one  conductor  of 
the  winding  will  not  be  in  the  same  phase,  and  a  decreased  voltage  (and 
thus  a  decreased  output)  results.  A  divergence  of  1  millimeter  in  1  meter 
length  would  cause  a  decrease  of  20  per  cent  in  the  total  output. 

Typical  Installation. — The  largest  alternators  of  this  type  have  a 
maximum  output  of  200  kw.  with  a  normal  output  of  100  kw.,  one  of 
which  is  located  at  Hanover,  Germany,  the  other  at  Tuckerton,  N.  J. 
These  machines  are  of  the  four-reflection  type,  with  direct-current  supply 
to  the  stator  and  having  400  poles.  For  an  output  frequency  of  50,000, 
which  means  an  initial  frequency  of  12,500,  the  motor  drives  the  generator 
at  3750  r.p.m.  This  motor  is  rated  at  4000  r.p.m.,  250  h.p.,  220  volts, 
and  is  supplied  from  two  direct-current  generators  in  Ward  Leonard  con- 
nection, to  secure  the  necessary  flexibility  of  speed  control  and  ease  of 
starting.  The  generator  is  directly  connected  to  this  motor  by  means 
of  a  flexible  coupling. 

The  antenna  at  the  Hanover  Station  consists  of  a  double-cone  system, 
the  aerial  wires  being  supported  by  a  single  steel  tower  250  meters  high. 
The  aerial  system  is  made  up  of  36  bronze  cables  of  8  mm.  diameter,  the 
outer  ends  of  these  cables  being  attached  through  insulators  to  poles 
12  meters  high  which  are  arranged  in  a  circle  around  the  tower,  the  radius 
of  this  circle  being  about  450  meters.  The  tower  is  insulated  at  the  base 
and  half  way  up  by  means  of  heavy  glass  insulators  and  is  supported  by 
steel  guy  wires,  sectioned  by  insulators. 

Frequency  Transformation. — The  design  and  construction  of  such 
alternators  as  described  above,  which  provide  at  their  terminals,  e.m.f.'s 
of  frequency  sufficiently  high  to  be  used  directly  for  radio-transmission, 
requires  the  highest  type  of  engineering  skill  if  the  many  complex  problems 
involved  in  their  construction  are  to  be  solved  successfully.  Alternators  of 
somewhat  lower  frequency,  however,  say  10,000  cycles  per  second,  can  be 


CONTINUOUS-WAVE  TELEGRAPHY  [CHAP.  VII 

built  with  comparative  ease  with  consequent  reduction  in  initial  cost, 
and  increased  reliability  of  operation.  Therefore  instead  of  using  the 
high-frequency  alternator  directly  supplying  the  antenna  circuit,  we  may 
substitute  a  lower-frequency  machine,  and  step-up  the  frequency  to  the 
required  value  by  means  of  a  frequency  changer  or  transformer.  Efficient 
frequency  transformation  thus  presents  a  means  for  supplying  undamped 
radio-frequency  current,  and  the  action  of  some  of  the  various  frequency 
changers  which  have  been  proposed  for  this  purpose  are  therefore  of 
interest. 

Types  of  Frequency  Changers. — Frequency  changers  may  be  static, 
constructed  similarly  to  the  ordinary  modern  power  transformer,  or  may 
contain  a  revolving  element.  In  the  latter  type,  utilizing  one  rotor 
winding  and  one  stator  winding,  the  frequency  is  raised  by  electrical 
reflections,  four,  five,  or  even  higher  transformations  being  accomplished. 
This  type  is  illustrated  by  the  Goldschmidt  machine  as  described  above, 
which  may  thus  be  considered  as  a  generator  and  frequency  changer  in 
one,  as  it  generates  a  current  of  frequency  N,  and  this  initial  frequency  is 
then  transformed  to  some  higher  frequency  at  the  output  terminals. 

The  simplest  type  of  frequency  changer  utilizing  a  rotating  element 
is  illustrated  by  the  large-capacity  frequency  changers  used  for  the  inter- 
change of  power  between  systems  of  different  frequencies  as  for  instance, 
a  25  and  a  62J  cycles  system.  The  machine  consists  of  two  rotors  and 
two  stators,  the  rotors  being  mounted  on  a  common  shaft,  the  one  element 
Dperating  as  a  synchronous  motor  and  the  other  as  an  alternator,  and 
vice  versa,  depending  on  the  direction  of  energy  flow.  By  means  of  appa- 
ratus of  this  type  it  is  thus  possible  to  transform  a  commercial  frequency 
supply  of  25  cycles  to  a  frequency  of  10,000,  or  less,  which  may  be  further 
transformed  by  one  of  the  static  transformers  described  below. 

Many  forms  of  the  static  type  of  frequency  changer  have  been  sug- 
gested, differing  mainly  in  the  manner  of  their  connections,  and  the  number 
of  frequency  transformations.  Thus  there  are  frequency  doublers  and 
triplers,  which  may  be  further  connected  in  cascade,  resulting  in  additional 
increase  of  frequency.  Fundamentally,  nearly  all  of  them  operate  on 
the  same  phenomenon,  namely,  the  asymmetrical  variation  of  flux  with 
magnetizing  force  in  saturated  iron  cores.  The  explanations  to  be  given 
below  will  consider  only  this  feature  of  the  circuit  although  a  rigid  analysis 
would  undoubtedly  require  an  investigation  of  the  variation  in  resistance 
throughout  the  cycle,  as  well  as  these  peculiar  flux  chancres. 

Tory  Frequency  Tripler. — In  the  Joly  frequency  tripler  illustrated  in 
Fig.  25.  The  primaries  are  joined  in  series,  and  the  turns  and  core  dimen- 
sions in  the  two  transformers  are  so  proportioned  that  B  is  saturated  at 
about  one-half  the  current  .value  required  to  saturate  A.  Thus,  if  we 
assume  a  sine  wave  of  voltage  E  supplied  by  the  alternator,  we  can  plot 


STATIC  FREQUENCY  CHANGERS 


609 


this  voltage  and  the  total  flux  <£,  which  must  be  developed  in  the  two 
transformers    to    develop    the 
required  c.e.m.f.,  as  shown  in 
Fig.  26  A. 

Since   the   total   flux  <j>  is 
a  maximum  when  the  primary 


current   is   a   maximum,    the        Alternator 
component  fluxes,  which  exist 
in  each  transformer,  and  which 
add  up  to  give  this  total  flux, 
must  each  be  a  maximum  at 
this   instant.     Since  B  satur-  FlG-  25-— Use  of  two  saturated  cores  to  triple  the 
ates    at    about    one-half   the    s  frequency, 

current  value  required  for  A, 

we  can  plot  the  component  fluxes  as  shown  in   Fig.   26 B.     The   pri- 
mary current,  which  has  not  been  indicated,  is  approximately  sinusoidal 

in  form.  The  two  fluxes  <£o  and  $&, 
by  their  variation  cause  e.m.f. 's  Ea2 
and  EM  to  be  induced  in  their 
respective  secondary  windings,  the 
wave  form  of  these  e.m.f.'s  being 
indicated  in  Fig.  26C. 

The  two  secondary  windings  are 
so  connected  together  that  the  volt- 
age across  the  load  circuit  (L  —  C, 
Fig.  25)  is  obtained  by  taking  the 
difference  of  Ea2  and  Ew',  in  Fig. 
26 D  this  line  voltage  (Ea2  —  Eb<i)  is 
shown  and  it  is  evident  that  the 
e.m.f.  is  principally  a  triple-fre- 
quency one.  The  load  circuit, 
which  includes  the  radiating  antenna 
and  its  loading  coil  (if  any),  must 
be  tuned  to  this  triple-frequency 
e.m.f.,  if  an  appreciable  output  is  to 
be  obtained. 

Frequency  Doublet. — An  arrange- 
ment for  doubling  the  frequency  first 
suggested  by  Epstein  in  1902  and  sub- 
FIG.  26.— Analysis  of  action  of  the  ar-  sequently  developed  by  Joly  and  Val- 
rangement  of  Fig.  25.  louri,  is  indicated  in  Fig.  27.     Both 

transformers  are  identical,  and  each 
is  equipped  with  a  tertiary  circuit,  supplied  from  the  storage  battery  B . 


V*" 


-E, 


610 


CONTINUOUS-WAVE   TELEGRAPHY 


[CHAP.  VII 


The  steady  current  flowing  through  these  windings  is  adjusted  to  bring 
the  transformer  fluxes  just  to  the  point  where  saturation  occurs,  i.e.,  at 
the  knee  of  the  curve  as  indicated  in  curve  A,  Fig.  27.  If  the  two  primaries, 
in  series,  are  connected  to  an  a.c.  supply,  it  may  readily  be  seen  from 
the  figures,  that  on  a  positive  half  cycle  the  flux  in  T\  (wherein  the  m.m.f. 
of  the  primary  winding  assists  the  d.c.  winding),  will  change  very  little, 
while  the  flux  in  TV  will  decrease  considerably,  since  the  primary  m.m.f. 
opposes  the  m.m.f.  of  the  d.c.  winding.  On  the  negative  half  cycle,  the 
reverse  is  true.  These  conditions  are  indicated  in  Fig.  28,  A  and  B.  It 
should  be  noted  that  an  asymmetrical  variation  of  flux  thus  occurs  in  each 
transformer,  the  flux  of  one  transformer  having  a  large  variation  during 
one  alternation  while  the  flux  of  the  other  transformer  changes  only  slightly 
and  on  the  next  alternation,  these  conditions  are  reversed.  These  fluxes 


FIG.  27. — Use  of  two  saturated  cores  for  frequency  doubling. 

exist  in  separate  cores  and  do  not  combine  to  form  a  double  frequency 
flux.  The  e.m.f.'s  which  they  induce  in  their  respective  secondary  wind- 
ings are  indicated  in  Fig.  28C,  and  since  the  secondaries  have  been  connected 
reversed  with  respect  to  each  other,  the  difference  of  the  voltages  must 
be  taken  to  obtain  their  resultant.  This  is  indicated  in  Fig.  28ZX 

This  method  for  obtaining  a  doubling  of  the  initial  frequency  has 
found  some  commercial  application  to  high-frequency  work,  having  been 
developed  by  Count  von  Arco  for  the  Telefunken  Company,  and  known 
as  the  Joly-Arc  System.  It  is  employed  at  the  U.  S.  Radio  Station  at 
Sayville,  Long  Island,  for  doubling  an  initial  frequency  of  ^OOO.1 

PlohTs  Frequency  Doublet. — An  interesting  circuit,  applying  these 
principles,  as  suggested  by  Plohl,  is  indicated  in  Fig.  29.  The  action  of 
this  circuit  will  be  evident  from  the  connections  and  the  curves  shown 

1  Bucher,  "Practical  Wireless  Telegraphy,"  p.  273. 


STATIC   FREQUENCY   CHANGERS 


611 


in  Fig.  30.  Essentially,  the  chokers  Ri  and  Rz  act  as  magnetic  valves, 
each  absorbing  the  impressed  e.m.f.  almost  completely  on  alternating 
half  cycles,  while  offering  very  little  impedance,  due  to  saturation  effects, 
during  the  other  half  cycle.  Thus  a  flux  will  alternately  be  produced 
by  PI  and  P%  and  since  they 
are  wound  in  reverse  relation- 
ship, this  flux  will  always  be  in 
the  same  direction,  through  the 
core  of  T  as  shown  in  Fig. 
30C.  A  double-frequency  volt- 
age is  thus  induced  in  the 
secondary  winding,  as  indicated 
in  Fig.  SOD. 

Taylor's  Frequency  Tripler. 
— An  arrangement  for  tripling 
the  initial  frequency  of  a  three- 
phase  supply,  as  developed  by 
A.  M.  Taylor,  is  indicated  in 
Fig.  31. 

The  three  chokers  Ri,  R2, 
and  Rs  are  saturated  early  in 
the  cycle,  at  a  relatively  low 
value  of  current,  while  the  core 
of  the  transformer  T  remains 
unsaturated  at  all  times.  Con- 
sidering one  of  the  elements, 
for  instance  that  between  a 
and  b,  and  assuming  a  sine 
wave  of  voltage,  the  voltage 
and  flux  conditions  which  must 
exist  are  as  indicated  in  Fig. 
32A.  (Fig.  31A  indicates  the 
circuit  detail  under  analysis.) 
As  the  primary  current  increas- 
es, a  point  is  reached  where 
the  choker  becomes  saturated.  FIG.  28.— Analysis  of  the  action  of  the  arrange- 
When  this  occurs,  the  imped-  ment  of  Fi&-  27-  The  flux  *TZ  'm  curves  B 
ance  of  the  circuit  decreases  ^^wn  m  reversed  phase. 

materially,  and  the  primary  current  increases  rapidly,  as  indicated  by  the 
current  curve  (Fig.  325) .  This  causes  very  little  change  in  the  choker  flux, 
which  has  already  reached  saturation,  but  does  cause  a  variation  in  the 
transformer  flux.  The  transformer  flux,  although  varying  proportion- 
ately to  the  primary  current  7,  does  not  reach  large  amplitudes,  since 


612 


CONTINUOUS-WAVE   TELEGRAPHY 


[CHAP.  VII 


FIG.  29. — Another  type  of  frequency  doubler. 


FIG.  30.— Curves  showing  action  of  appa- 
ratus shown  in  Fig.  29. 


most  of  the  flux  required  to  produce 
the  proper  sine  wave  of  counter 
e.m.f.  is  already  existent  in  the  core 
of  the  choker.  The  choker  and  trans- 
former flux  must  add  to  give  a  result- 
ant equal  to  the  sine  wave  of  flux 
shown  in  Fig.  32 A,  based  on  the 
assumed  sine  voltage.  The  trans- 
former flux  will  induce  in  the  second- 
ary a  voltage  the  form  of  which  is 
shown  in  32C.  A  similar  e.m.f.  wave 
will  be  induced  by  each  of  the  other 
two  phases  in  exactly  the  same  way 
as  outlined  above. 

The  voltages  e&c  and  eca  will 
differ  in  phase  from  eai>  by  120° 
and  240°  (electrical  degrees),  respect- 
ively, as  the  primary  supply  volt- 
ages Eab,  Ebc,  Eca  differ  in  phase 
from  one  another  by  this  amount. 
These  three  induced  voltages  eab, 
d>c,  eca,  exist  simultaneously  in  the 
secondary  winding  of  T  and  thus  add 
up  to  give  the  resultant  triple-fre- 
quency voltage  indicated  in  32 D. 
It  would  be  possible  to  employ  nine 
chokers,  and  a  nine-phase  supply, 
to  produce  a  nine-fold  transform^ 


STATIC   FREQUENCY  CHANGERS 


613 


tion,  if  this  were  desirable.  In  this  case  a  sine- wave  alternator  could 
not  be  used,  due  to  interference  effects  in  the  high-frequency  circuits,  and 
a  machine  of  special  design  would  be  required. 

Losses  of  Static  Frequency  Changers. — The  above  methods  of 
frequency  transformation  which  utilize  static  transformers  possess  the 
disadvantage  of  excessive  iron  losses,  even  though  special  precautions 
are  taken  in  the  construction  of  the  iron  cores,  as  at  the  higher  frequencies 
these  losses  are  very  large;  dielectric  losses  in  the  insulation  may  also 
be  excessive.  Probably  the  most  practical  would  be  the  Joly  arrange- 
ment for  doubling  the  frequency,  using  two  of  these  doublers  in  cascade 
to  quadruple  the  frequency,  and  making  the  delivered  energy  thus  suit- 


FIG.  31. — A  frequency  tripler,  working  from  a  three  phase  supply. 

able  to  the  requirements  of  radio  telegraphy  and  telephony.  With  every 
arrangement  it  is  highly  important  that  the  secondary  circuit  be  tuned 
to  the  desired  upper  harmonic,  as  otherwise  the  higher-frequency  current 
will  be  relatively  small  and  current  of  fundamental  frequency  will  prob- 
ably predominate. 

The  "Wabbling  Neutral"  as  a  Means  of  Tripling  the  Alternator 
Frequency. — It  is  a  well-known  fact  that  the  line  currents  of  a  3-phase 
system  are  120°  out  of  phase  and  their  algebraic  sum  is  equal  to  zero. 
Their  third  harmonics  differ  therefore  by  3X120°,  or  360°,  i.e.,  a  complete 
period,  and  are  in  phase  with  each  other.  Since,  in  all  cases,  the  instan- 
taneous (algebraic)  sum  of  the  alternator  currents  must  be  zero,1  it  is 
evidently  impossible  for  the  line  currents  to  contain  third  harmonics.  If 
we  impress  a  sine  wave  of  voltage  on  three  Y-connected  transformers 

1  Delta-connected  load  assumed,  or  if  Y-connected,  the  neutral  point  of  the  load  is 
supposed  ungrounded. 


614 


CONTINUOUS-WAVE  TELEGRAPHY 


[CHAP.  VII 


(their  secondaries  being 
open-circuited,  and  hence 
not  shown  in  Fig.  33  as 
they  can  have  no  effect 
when  open),  the  third  har- 
monic component,  which 
normally  predominates  in 
the  exciting  current  of  an 
iron-core  transformer,  is 
suppressed,  and  the  mag- 
netizing current  is  a  sine 
wave. 

The  line  voltages  are 
sine  waves,  but  the  voltage 
to  neutral  must  contain  a 
strong  third  harmonic,  due 
to  the  suppression  of  the 
third  harmonic  component 
in  the  exciting  current, 
which  must  be  present  if 
the  c.e.m.f.  is  to  be  a  sine 
wave.  Therefore,  the  wave 
of  magnetization  cannot  be 
of  sine  form,  but  will  be 
flat  topped  (somewhat  as 
indicated  in  Fig.  34,  curves 
1,  2,  and  3)  due  to  the  satu- 
ration of  the  iron.  The  in- 
duced e.m.f.'s  will  thus 
have  the  wave  form  indi- 
cated, and  may  be  resolved  FlG  32.— Curves  of  flux  and  e.m.f.  explaining  the 
into  their  fundamental  and  action  of  the  apparatus  shown  in  Fig.  31. 


To  Xlftee 

Phase 
Alternator 


FIG.  33. — The  "wabbling  neutral"  scheme  of  tripling  frequency;  the  center  point  of  3 
F-connected  iron  core  coils  is  connected  to  the  antenna  arid  the  center  point  of 
3  F-connected  air  core  coils  is  connected  to  ground.  The  three-phase  power 
supply  is  otherwise  ungrounded. 


STATIC   FREQUENCY  CHANGERS 


615 


third  harmonic  components  as 
noted  that  the  third  harmonic 
phase.  Thus  the  potential  of 


i-o 


/     3-0 


shown  in  curves  4,  5,  and  6.     It  will  be 
components  in  all  three  phases  are  in 
point  0,  Fig.  33,  will  fluctuate  at  triple 
frequency  as  shown  in  curve  7  of 
Fig.   34.      This    triple    frequency 
e.m.f.  may  be  impressed  on  an  an- 
tenna circuit  as  shown  in  Fig.  33. 

The  voltages  indicated  in  the 
above  curves  exist  across  the 
transformer  windings,  and  add  up 
to  give  a  sine  wave  of  c. e.m.f.  at 
the  line  terminals.  This  is  shown 
in  curve  8,  wherein  the  third  har- 
monic potentials  neutralize  one 
another,  only  the  fundamental 
components  combining.  This 
curve  is  evidently  a  sine  wave, 
which  is  as  it  should  be,  if  it  is  to 

t     neutralize  the   impressed  voltage, 

which  has  been  assumed  as  a  sine 
wave. 


r\  r\ 


L/ 


\J\  \J 

\ 
\ 


r\ 


i    \   2-0   ; 

r\'  r\  \r\  r\> 


f 


rV 

\  / 

\  / 

v  y 

t"    >  '~N  " 

/      \  /       ^ 

N  3-0  '  v 


r\^  \r\f    r\' 

1  \        /N          \       /          A 


r\  r 

^ 


vy  / 
\      / 


vy\  v_/ 

\ 
\ 


FIG.  34.— Curves  of  flux  and  e.m.f.  to  analyze  the  action  of  the  wabbling  neutral;  in 
curves.  8  the  voltage  forms  e0—  i  and  e$—  3  are  shown  without  their  third  harmonics, 
these  being  shown  separately  on  the  X  axis. 

In  Fig.  35  is  shown  an  oscillograph  record  of  this  scheme  of  frequency 
conversion;  three  transformer  primaries  (secondaries  open)  were  connected 
in  Y  to  a  three-phase  power  line  and  another  Y  connection  was  made 


616 


CONTINUOUS-WAVE  TELEGRAPHY 


[CHAP.  VII 


with  three  air-core  coils.  The  two  neutrals  were  then  connected  together 
and  the  resulting  current  in  the  connection  was  nearly  a  pure  sine  wave 
of  triple  frequency. 

Application  of  Rectifier  Elements  to  Frequency  Changers. — Another 
type  of  frequency  changer  is  that  utilizing  a  rectifying  element  in  the  pri- 
mary circuit.  The  action  is  due  fundamentally  to  the  fact  that  the  flux 
in  the  iron  core  is  always  set  up  in  the  same  direction,  regardless  of  reversal 
of  the  supply  current.  Fig.  36  indicates  a  typical  connection,  while 
37  indicates  the  voltage  and  flux  relations  obtained. 


FIG.  35. — Oscillogram  showing  the  third  harmonic  obtainable  from  the  curcuit  of 

Fig.  33. 

Fig.  38  indicates  an  arrangement  utilized  by  Zenneck  and  others. 
This  operates  exactly  similar  to  the  arrangement  of  Fig.  36,  but  makes 
use  of  four  valves  to  secure  unidirectional  current  through  the  one  primary 
winding.  Current  is  permitted  to  flow  only  in  the  direction  indicated 
by  the  arrows  in  the  valve  elements;  an  inspection  of  the  figure  will  indi- 
cate their  operation.  Fig.  37  is  also  applicable  to  the  operation  of  this 
circuit. 

Marconi  Multi-gap  Generator. — By  properly  timing  the  discharge 
periods  of  related  spark  circuits,  each  circuit  acting  inductively  on  a 
common  secondary  circuit,  undamped  high-frequency  oscillations  may 
be  obtained  in  the  secondary  circuit.  This  principle  has  been  utilized 
by  Marconi  in  the  construction  of  a  multi-gap  generator,  the  connections 
of  which  are  indicated  in  Fig.  39. 


MARCONI   MULTI-GAP  GENERATOR 


617 


The  synchronous  gaps  D\,  D2)  D$,  etc.,  are  all  rigidly  keyed  to  the  same 
shaft,  but  are  displaced  properly  with  respect  to  one 
another  so  that  the  discharge  in  the  several  circuits 
occurs  at  different  intervals.  The  result  is  graphically 
illustrated  by  the  curves  shown  in  Fig.  40.  It  is  essential, 
if  efficient  operation  is  to  be  obtained,  that  the  several 
circuits  are  discharged  in  proper  sequence  and  at  exactly 
the  right  instant,  so  that  the  component  oscillations 
acting  on  the  common  antenna  circuit  will  produce  a 
constant  amplitude  high-frequency  current  as  shown. 
This  is  accomplished  by  the  proper  displacement  of 
the  several  disk  discharges  on  the  shaft  and  is  also 
insured  by  means  of  an  auxiliary  disk  resembling  a  toothed 
wheel,  which  acts  as  a  "  trigger  "  to  cause  the  main  dis- 
charge to  occur  at  exactly  the  proper  instant.  This  is 
not  shown  in  the  diagram. 

It  is  evident  that  the  speed  of  rotation  of  the  discharger  disks  is  fixed 
by  the  radio  frequency  generated  and  for  this  reason  the  generator  is 

particularly  adapted  to  long  wave-lengths. 
If  we  assume  a  generator  with  ten  disks, 
each  having  40  studs,  and  the  shaft 
revolved  at  50  r.p.s.  the  interval  between 
two  condenser  discharges  is 


FIG.  36.— A  fre- 
quency doubler 
using  iron  core 
and  rectifiers. 


/A  \. 


t 


\. 


50X40X10    20,000  SeCOnd< 

The  radio  frequency  is,  therefore,  as- 
suming the  discharges  to  occur  at  one- 
cycle  intervals,  equal  to  20,000  and  the 
wave-length  15,000  meters.  Similarly  if 
the  successive  discharges  occur  at  inter- 
vals of  every  other  cycle,  the  frequency 
may  be  40,000,  corresponding  to  a  wave- 
length of  7500  meters. 

This  generator  is  not  used  to  any 
great  extent,  and  a  very  brief  treatment 
only,  which  is  not  complete,  has  there- 
fore been  given. 

Oscillating  Tubes. — Within  the  last  few 
years  many  improvements  in  the  design 
and  construction  of  vacuum  tubes  have 

been  made  and  their  applications  are  continually  growing  more  varied  and 
important.    At  the  present  time,  however,  the  power  obtainable  from  oscil- 


FIG.  37. — Voltage  and  flux  relations 
for  the  circuit  of  Fig.  36. 


618 


CONTINUOUS-WAVE  TELEGRAPHY 


[CHAP.  VII 


lating  tube  circuits,  as  described  in  Chapter  VI,  is  comparatively  small. 

Their  greatest  field  of  use  has  therefore  been  confined  to  the  reception  of 

undamped  wave  signals  (see  p.  483),  and  to  small  power  transmitting 
sets  (of  perhaps  1  kw.  high-frequency  output),  such 
as  might  be  employed  for  military  service  in  the 
field,  or  any  other  service  where  light  weight  and 
small  space  requirements  are  primary  considera- 
tions. 

To  secure  the  large  amount  of  power  required 
for  long-distance  transmission,  it  is  necessary  at 
the  present  time  to  connect  a  number  of  the 
tubes  in  parallel,  and  adjust  the  several  circuits 
so  that  they  operate  properly.  The  limitation 
in  output  of  one  tube  is  due  primarily  to  the 

FIG.  38. — By  using  four  inability  of  the  tube  to  radiate  the  large  amount 
rectifiers     the     double  of  nea^  wnicn  is   necessarily  generated  within  the 


primary  coil  of  Fig.  36 
may  be  replaced  by  a 
single  coil. 


tube  itself.     As  improvements  in  design  and  con- 


struction occur,  under  the  extensive  developments 
which  are  now  being  carried  on,  it  may  be  expected 
that  the  rating  of  tubes  will  continually  increase,  so  that  eventually  this 
device  may  replace  the  present  forms  of  undamped  wave  generators. 
Oscillating  tubes  possess  several  advantages  over  all  other  high-frequency 
generators,  principally:  ease  of  adjustment  and  reliability  of  operation, 


_:=- JfrD.C. 

I  ^  ^    Generators 
-=-   L    in  Series    C, 


FIG.  39. — Marconi's  "multi-gap"  scheme  for  generating  undamped  waves  from  a  series 

of  spark  discharges. 

small  space  requirements,  simplicity  of  construction  and  relatively  high 
efficiency. 

Some  progress  along  the  lines  indicated  above  may  already  be  recorded. 
Large  tubes  have  been  constructed  having  an  input  rating  of  500  watts 


VACUUM   TUBE   GENERATOR 


619 


and  greater,  while  in  England  ti  steel  tube  equipped  with  a  water-cooled 
plate  and  rated  at  5  kw.  has  been  developed.1  The  plate  voltage  of  these 
high-power  tubes  is  in  the  neighborhood  of  5000  to  10000  volts,  the  plate 
current  having  a  normal  value  of  perhaps  0.25  ampere.  The  plates  become 
very  hot,  while  the  tube  is  in  service,  in  some  cases  approaching  incandes- 
cence, and  special  metals  are  there- 
fore required  in  its  construction, 
tungsten  usually  being  used. 

In  rating  the  tube  by  its  energy 
input,  as  has  been  done  above,  the 
filament  circuit  supply  has  not  been 
included.  It  should  be  noted  that 
the  external  oscillating  circuit  con- 
nected to  the  tube  must  take  its 
proper  share  of  this  input  energy, 
or  too  much  energy  will  be  required 
to  be  dissipated  from  the  tube,  with 
resultant  danger  of  overheating  the 
tube  elements.  If  for  any  reason 
the  tube  stops  oscillating  under 
conditions  of  full  energy  supply, 
the  plate  voltage  should  be  im- 
mediately decreased  to  prevent  any 
damage  to  the  tube. 

Probable  Efficiencies  of  above 
Apparatus. — Poulsen  Arc. — Assum- 
ing sine  waves,  a  theoretical  effi- 
ciency of  50  per  cent  is  possible,  but 
probably  an  actual  arc  does  not  FiG<  40.— Spark  discharge  operation  of  the 
give  greater  than  40  per  cent.  For  circuit  of  Fig.  39. 

instance,   the   cooling   water    of   a 

certain  25  kw.  arc  carried  away  14  kw.  of  heat.  For  arc  oscillations 
of  the  third  class  (p.  5$7)  efficiencies  much  greater  than  50  per  cent  are 
conceivable,  but  as  this  type  of  oscillation  is  seldom  used,  we  assume  the 
efficiency  of  the  normal  arc  less  than  50  per  cent. 

Alexanderson  Alternator. — No  data  are  obtainable  regarding  the 
efficiency  of  the  large  Alexanderson  alternators,  but  it  seems  likely  that 
it  is  not  better  than  50  per  cent.  Examination  of  the  construction  of 
a  modern  machine  shows  the  likelihood  of  high  iron  losses  and  the  care 
taken  to  provide  adequate  cooling2  facilities  substantiates  this  idea. 

1  Since  writing  the  above  the  author  learns  that  tubes  with  an  output  of  about 
100  kw.  have  been  put  into  operation. 

2  See  Alexanderson,  "Transatlantic    Radio    Communication."     Proceedings  A.  I. 
E.  E.,  Oct.,  1919. 


620  CONTINUOUS-WAVE  TELEGRAPHY  [CHAP.  VII 

In  the  smaller  sets,  the  efficiency  may  be  extremely  low:  a  200,000-cycle 
machine,  for  example,  having  a  maximum  output  of  500  watts,  requires 
a  10  h.p.  driving  motor.  A  large  part  of  the  motor  output  is  apparently 
used  in  windage  losses  caused  by  the  high  rotative  speeds. 

Goldschmidt  Alternator. — Although  one  would  judge  that  the  effi- 
ciency of  this  type  of  machine  could  not  be  very  high,  the  great  care  taken 
in  the  construction  of  tioth  the  magnetic  and  electric  circuits  evidently 
keeps  the  losses  as  small  as  possible.  It  is  stated  by  Eccles  1  that  a 
12j-kw.  machine  of  this  type  (one  of  the  first  to  be  built)  had  an  effi- 
ciency of  80  per  cent. 

Static  Frequency  Changers. — It  is  estimated  by  the  inventor  of  one 
of  these  schemes  using  iron  cores  that  a  28-kw.  transformer  will  have 
an  efficiency  of  about  86  per  cent.2  It  seems  that  these  devices  use 
about  1  Ib.  of  iron  per  kw.  of  output  and  an  attempt  to  calculate  the 
probable  eddy  current  and  hysteresis  losses  gives  a  value  of  perhaps 
1  kw.  per  pound  of  core  used,  which  would  indicate  an  efficiency  in  the 
neighborhood  of  50  per  cent.  It  must  be  pointed  out,  however,  that 
attempts  to  calculate  the  core  loss  from  the  ordinary  formulae  are  probably 
inaccurate,  because  of  the  peculiar  magnetic  cycles  to  which  the  iron  is 
subjected. 

Marconi  Multi-gap  Generator. — This  method  is  essentially  a  combina- 
tion of  several  spark  transmitters,  and  so  should  have  about  the  same  effi- 
ciency as  a  spark  transmitter.  This  will  vary  with  the  condition  of  the 
gap,  its  quenching  action,  etc.,  but  probably  reaches  a  value  of  70  per  cent 
in  the  larger  installations.  For  a  small  transmitter,  an  efficiency  of  trans- 
formation from  low  to  high  frequency  of  40  per  cent  is  more  likely. 

Oscillating  Tube. — The  efficiency  of  an  oscillating  tube  varies  a  great 
deal  with  the  adjustments  of  the  circuit,  and  may  have  any  value  between 
25  per  cent  and  95  per  cent,  neglecting  the  amount  of  power  used  for 
heating  the  filament.  This  point  is  discussed  in  detail  in  Chapter  VI, 
p.  539  et  seq.  It  will  be  noted  in  comparing  tubes  with  an  arc  that  they 
consume  power  only  when  actually  used  for  transmission  whereas  the 
arc  is  using  full  power  whether  the  key  is  up  or  down. 

Methods  of  Signaling  with  Continuous- wave  Transmitters. — The 
generators  described  above  will  supply  a  continuous-power  input  to  the 
antenna  circuit  and  with  no  changes  in  the  antenna  or  supply  circuit, 
a  continuous  undamped  high-frequency  current  will  flow  through  the 
antenna.  The  power  radiation  from  the  transmitter  is  therefore  constant 
in  magnitude  and  frequency.  Three  methods  may  be  utilized  for  vary- 
ing this  radiated  energy  in  accordance  with  a  prearranged  code,  and  thus 
transmit  intelligence  to  the  distant  receiving  station.  The  three  methods 
of  sending  may  be  stated  as  follows: 

1  See  Eccles,  "  Wireless  Telegraphy  and  Telephony,"  p.  230.  2  Ibid.,  p.  235. 


CONTINUOUS-WAVE  SIGNALING   METHODS 


621 


1.  The  total  interruption  of  energy  radiation  during  a  "space."     This 
is  known  as  the  "  cut-in  "  method. 

2.  Continuous  radiation  of  energy  throughout  the  sending  of  a  message, 
the  space  and  signal  differing  only  in  the  wave-lengths  at  which  the  energy 
is  transmitted.     This  is  called  the  "  compensated  "  method. 

3.  The  total  interruption  of  energy  radiation  during  a  space  period, 
with  the  radiation  rapidly  interrupted  by  means  of  a  chopper  or  inter- 
rupter during  the  signal  period.     This  is  known  as  the  "  modulated  " 
method  of  sending,  and  possesses  advantages  under  certain  emergency 
conditions  as  described  later. 

The  high-frequency  current  flowing  in  the  transmitter  antenna  for 
each  of  three  methods  of  sending  is  indicated  in  Fig.  41. 


i 

Cut  In 
Method 


II 

Compensated 
Method 


FIG.  41. — Methods  of  transmitting  signals  from  continous  wave  stations. 

Signaling  Devices. — For  transmitting  by  means  of  the  above  methods 
one  of  the  following  devices  may  be  used,  depending  on  the  type  of  gener- 
ator used. 

I.  Chopper  or  buzzer  (choice  will  depend  on  the  amount  of  cur- 
rent to  be  interrupted.) 
II.  Wave-length  changing  switch. 

III.  Switching  to  dummy  antenna. 

IV.  Control  of  excitation  of  machine. 

The  application  of  these  devices  to  the  several  types  of  high-frequency 
generators,  previously  described,  will  now  be  considered. 

Methods  of  Sending  Applicable  to  the  Poulsen  Arc  Generator. — This 
generator  depends  for  its  operation  on  an  uninterrupted  supply  to  the 
arc  and  the  antenna  circuit  (which  is  the  sole  natural-frequency  circuit 
of  the  transmitter).  Therefore  the  means  indicated  under  II  and  III 


622 


CONTINUOUS-WAVE  TELEGRAPHY 


[CHAP.    VII 


Magnetically 

Operated 

viKey 


A  ft  fL-V        I I  *\  ">  A  ^  i 

am, ,mri 

•* <       ' — <, — I 


only  can  be  applied,  namely,  changing  the  wave-length  or  switching  to 
a  dummy  antenna.     A  change  in  wave-length  may  be  secured  by  simply 

connecting  the  transmitting  key  so 
as  to  short-circuit  one  or  more 
turns  of  the  antenna  inductance 
when  a  signal  is  being  transmitted, 
as  indicated  in  Fig.  42,  and  to  cut 
in  these  turns  during  the  space  in- 
terval. 

This  arrangement  is  practically 
universal  on  present  arc  installa- 
tions. On  the  higher  power  sets, 
the  key  does  not  directly  short 
circuit  the  inductance,  but  operates 
an  auxiliary  relay,  which  in  turn 

FIG.  42.-The  ordinary  method  of  signaling  actuates  the  solenoid-operated  con- 
with  a  Poulsen    arc;    by  short-circuiting    ,  ,,          .,       ~,  .      . 

a  small  part  of  the  loading  coil  the  wave  tact°r  at  the  COlL  Tms  ls  reclmred 
length  radiated  is  changed  slightly  and  due  to  the  heavy  current  which 
with  a  suitable  receiving  circuit  the  signal  must  be  broken,  and  rapid  signaling 
becomes  audible.  would  be  impossible  with  the  heavy 

and  massive  key  required  if  it  were 

attempted  to  operate  it  manually.  Sometimes,  instead  of  short-circuiting 
a  turn  of  the  antenna  load  coil,  an  independent  circuit  of  one  or  two 
turns,  connected  to  the  antenna  load 
coil  by  mutual  induction,  is  short-circuit- 
ed by  the  relay  key. 

The  connections  for  utilizing  a  dummy 
antenna  are  shown  in  Fig.  43.  In  this 
case  the  key  simply  acts  to  transfer  the 
arc  circuit  to  the  radiating  antenna  when 
it  is  desired  to  send  a  signal.  At  other 
times  the  arc  supplies  the  dummy  antenna 
and  no  energy  is  radiated.  The  energy 
radiation  would  thus  be  as  shown  in 
Method  I,  Fig.  41. 

This  method  is  relatively  little  used, 
but  illustrates  the  application  of  switch- 
ing to  a  dummy  antenna  to  secure 
"  cut-in  "  radiation.  The  constants  of 
the  dummy  circuit  should  be  identical 

with  the  constants  of  the  radiating  antenna  circuit,  so  that  the  condi- 
tions at  the  arc  are  constant. 

Referring  to  Fig.  42,  we  may  place  an  interrupter  or  chopper  at  A", 


FIG.  43. — Another  scheme  which  has 
been  tried  with  the  Poulsen  arc  is 
to  switch  the  arc  to  a  dummy  an- 
tenna. 


CONTINUOUS-WAVE  SIGNALING   METHODS 


623 


and  thus  secure  a  combination  of  methods  II  and  III.     The  antenna 
current  would  then  have  the  form  indicated  in  Fig.  44. 

Methods  of  Sending  Applicable  to  the  High-frequency  Alternator.— 
With  this  generator  the  frequency  is  fixed  by  the  speed  of  the  machine. 


a-  buzzer  contacts  closed 
5=      A  „       open 

FIG.  ii. — A  possible  type  of  radiation  from  a  Poulsen  arc  using  the  circuit  of  Fig.  42, 
with  an  interrupter  of  some  kind  at  X. 

Therefore,  transmission  by  Method  II  cannot  be  used  (a  variation  in 
antenna  inductance  simply  causing  a  decrease  in  the  amplitude  of  the 
antenna  current),  but  Methods  I,  and  III,  are  applicable,  the  former 
usually  being  used. 

Signaling  is  most  easily  accomplished,  however,  by  control  of  the  exci- 
tation, which  may  simply  involve  a  key  in  the  generator  field  circuit  as 
indicated  in  Fig.  45.  A  resistance,  may,  with 
advantage,  be  inserted  in  the  field  circuit,  to 

decrease  the  time  constant  (  ^)  of  the  circuit 

and  minimize  any  tendency  toward  sluggish- 
ness which  may  prevent  the  signals  from  being 
clean  cut  and  distinct,  and  thus  limiting  the 
sending  speed. 

A  method  has  also  been  developed  to  con- 
trol the  radiated  energy  by  means  of  a  shunt- 
ing circuit  across  the  alternator  terminals,  the 
impedance  of  this  circuit  being  controlled  by  the  FIQ  45  _Tne  simpiest  pos- 
sending  key.     The  connections  are  indicated  in      sibie  transmitting  scheme 
Fig.   46.      When   the   key   is   raised   (contacts      using    a    high-frequency 
closed)  the  current  flowing  through  L%  saturates      alternator, 
the  iron  cores  a  a,  and  the   reactance   of  Li 

decreases  accordingly.  This  effectively  spoils  the  tuning  of  the  alter- 
nator load  circuit  and  hence  brings  the  alternator  output  to  practically 
zero. 

When  the  core  is  saturated,  the  impedance  of  the  shunt  circuit  is  so 
low  as  to  amount  almost  to  a  short  circuit  on  the  alternator,  under  which 


624 


CONTINUOUS-WAVE  TELEGRAPHY 


[CHAP.  VII 


=-B 


condition  the  alternator  voltage  is  very  small  and  is  able  to  send  but  very 
little  current  through  the  antenna  circuit.  Therefore  the  radiated  energy 
will  decrease  to  a  very  small  value,  essentially  zero.  When  the  key  is 
depressed  (open  position),  the  iron  is  no  longer  saturated  and  the  impe- 
dance of  Li  increases  to  a  high 
value.  The  alternator  current  will 
then  flow  through  the  antenna 
circuit  in  preference  to  the  shunt 
circuit,  and  energy  will  be  radi- 
ated. 

At  the  New  Brunswick  station 
this    variable,    iron-cored    impe- 
dance is  connected    in    a    tuned 
circuit    (tuned   when    the    key  is 
open)    which    is    coupled   to   the 
FIG.  46.— A  method  of  sending  by  generator  antenna  and    alternator  as  shown 
which  employs  a  magnetically  controlled  in    Fig.    47.       When    the    key    is 
short-circuit  on  the  machine.       v  closed,  the  local  circuit  is  detuned 

and  the  energy   input  into    this 

circuit  becomes  very  small,  the  major  portion  of  the  energy  thus  being 
diverted  to  the  antenna  circuit.  The  transformer  indicated  in  the  figure 
is  an  integral  part  of  the  alternator  and  is  shown  supported  in  two  sec- 
tions above  and  on  either  side  of  the  alternator  in  Fig.  17,  p.  599. 

For  either  scheme  of 
control,  the  energy  ra- 
diation is  essentially  as 
shown  in  Fig.  41-1.  The 
use  of  a  chopper  or  buz- 
zer in  the  exciter  circuit 
may  not  be  entirely 
satisfactory,  due  to  the 
inability  of  the  machine 
voltage  to  follow  accu- 
rately the  rapid  varia- 
tions of  field  current  pro- 
duced. There  is  no 
doubt,  however,  that 


FIG.  47. — In  the  application  of  the  scheme  indicated  in 
Fig.  46  it  is  found  advisable  to  use  the  circuit  arrange- 
ment shown  above. 


Radiation   in   this  case 


satisfactory  results  could 

be  obtained  by  inserting 

the  interrupter  in  the   key  circuit   of   Fig.  47. 

would  be  nearly  as  indicated  in  Fig.  41-111. 

Methods  of  Sending  Applicable  to  the  Goldschmidt  Alternator. — As 
with  the  Alexanderson  alternator,  the  generated  frequency  for  this  machine 


CONTINUOUS-WAVE   SIGNALING   METHODS 


625 


Driving 
Motor 


Goldschmidt 
Alternator 


D.C.  Supply 


is  fixed  by  its  speed,  and  therefore  wave-changing  methods  are  not  appli- 
cable. Signaling  is  accomplished  by  means  of  the  "  cut-in  "  method 
using  field  excitation  control,  the  connections  are  indicated  in  Fig.  48. 
In  addition  to  opening  and  closing  the  exciter  circuit,  the  key  also  simulta- 
neously cuts  out  or  in  a  portion  of  the  driving  motor  field  resistance.  Thus, 
any  tendency  of  the  alternator  to  suffer  a  drop  in  speed,  when  the  exciter 
key  is  closed,  and  the 
load  applied,  is  com- 
pensated for  by  the 
cutting  in  of  a  certain 
amount  of  motor  field 
resistance,  which  will 
tend  to  raise  the 
speed.  In  addition, 
the  heavy  weight  and 
inertia  of  the  rotating 
element  effectually  aid  FIG.  48.— Scheme  of  sending  signals  with  the  Goldschmidt 
in  maintaining  con-  alternator  using  a  motor  speed  control  in  addition, 
stant  speed,  and  under 

operating  conditions  the  variation  in  wave-length  is  claimed  to  be  less  than 
one-tenth  of  1  per  cent. 

The  above  discussion  describes  the  only  method  which  has  yet  been 
used  for  controlling  the  output  of  this  alternator.  Switching  to  a  dummy 
antenna,  or  some  form  of  shunt  circuit,  as  described  for  the  Alexanderson 
machine,  would  also  be  applicable,  but  the  present  method  seems  to  be 
completely  satisfactory. 

Methods  of  Sending  which  May  be  Used  when  Frequency  Trans- 
formers are  Used. — Since  these  transformers  must  be  associated  with 
some  form  of  high-frequency  alternator,  whose  frequency  is  rigidly  fixed 
by  its  speed,  the  same  methods  as  described  above  for  the  Alexanderson 
and  Goldschmidt  machines  will  apply.  On  low-power  sets  the  key  may  be 
connected  to  open  the  supply  circuit  directly,  while  on  large-power  sets 
the  circuit  may  be  opened  indirectly  by  auxiliary  relays  actuated  by  the 
sending  key.  The  antenna  current  would  then  be  as  shown  in  Fig.  41-1. 
The  key  may  also  have  associated  with  it  some  form  of  interrupter  or 
chopper,  resulting  in  current  variation  as  shown  in  Fig.  41-111. 

For  the  larger  installations,  the  energy  would  be  controlled  by  means 
of  the  exciter  supply  due  to  the  smaller  power  involved.  Cut-in  send- 
ing would  be  the  most  feasible,  although  switching  to  a  dummy  antenna 
or  connecting  a  variable  impedance  across  the  alternator  terminals  as 
in  the  case  of  the  Alexanderson  machine  could  also  be  used. 

Energy  Radiation  Control  when  Marconi  Generator  is  Used. — For  a 
generator  of  this  type,  switching  to  a  dummy  antenna  would  be  a  satis- 


626 


CONTINUOUS-WAVE  TELEGRAPHY 


[CHAP.  VII 


factory  means  of  varying  the  radiated  energy,  the  "  cut-in  "  method  of 
sending  thus  being  used.  Some  form  of  absorbing  circuit  across  the 
generator  terminals  might  also  be  used  to  give  similar  results.  The  key 
might  be  placed  in  the  common  generator  lead  at  point  X,  Fig.  39,  p.  618, 
or  point  Y,  opening  the  supply  or  antenna  circuit  respectively.  An  inter- 
rupter element  may  be  associated  with  either  of  these  three  means,  giving 
the  "  modulated  "  method  of  sending  as  shown  in  Fig.  41-111.  It  would 
be  undesirable  to  employ  a  wave-changing  scheme,  as  this  would  require 
circuit  variations  in  each  of  the  four  primary  circuits  involved,  with 
resultant  complexity  of  connections,  etc.  On  larger  installations,  it  would 
be  preferable  to  place  the  key  in  the  exciter  circuit  of  the  d.c.  generators, 
in  preference  to  the  point  X.  This  would  probably  be  the  most  satis- 
factory means  of  control  for  the  same  reasons  as  stated  above  in  connec- 
tion with  high-frequency  alternator  installations. 

Control  of  Radiated  Energy  when  the  Oscillating-tube  Generator 
is  Used. — The  radiation  of  energy  from  an  antenna  supplied  from  an 
oscillating-tube  generator  may  be  in  accordance  with  any  one  of  the 
three  methods  indicated  in  Fig.  41.  The  method  employed  for  small 
sets  is  usually  a  direct  opening  of  the  antenna  circuit  by  means  of  the 
key,  which  may  or  may  not  be  associated  with  an  interrupter  (usually 
a  buzzer  for  small  field  sets)  to  obtain  the  modulated  method  of  sending. 

The  wave-length  change  may  be 
obtained  by  short  circuiting  a  por- 
tion of  the  antenna  circuit  induct- 
ance. Since  the  power  generated 
by  these  circuits  is  as  yet  com- 
paratively small,  there  is  no  neces- 
sity for  auxiliary  relay  equipment 
to  be  associated  with  the  key. 
The  most  feasible  control  scheme, 
however,  is  one  which  controls  the 
"grid  potential  "  of  the  oscillating 
tube;  by  making  this  sufficiently 
negative  the  tube  stops  generating 
power  as  described  in  Chapter  VI, 
and  illustrated  in  Fig.  117,  p.  500. 

Fig.  49  shows  the  diagram  of 
FIG.    49.— An    arrangement    whereby    the  &  .  ...     . 

output  of  this  small  tube  transmitter  can  connections  for  a  small  oscillating 
be  controlled  by  either  one  of  three  tube  set,  which  utilizes  three  of  the 
methods.  above-named  methods  of  sending. 

The     oscillating    circuit    involved 

were  described  in  Chapter  VI,  p.  513,  and  the  student  is  referred  there 
for  a  discussion  of  their  action. 


CONTINUOUS- WAVE  SIGNALING   METHODS  627 

Referring  to  the  diagram  and  assuming  the  switch  S  thrown  upward, 
i.e.,  open,  it  will  be  noted  that  the  antenna  circuit  will  be  completed  by 
the  closing  of  the  key  K.  Therefore,  if  the  key  is  open,  the  antenna 
circuit  is  open,  the  tube  does  not  oscillate,  and  no  energy  is  radiated. 
When  the  key  is  closed,  completing  the  antenna  circuit,  oscillations  will 
start  and  be  maintained,  if  the  proper  conditions  have  been  fulfilled. 
Thus  energy  will  be  radiated  as  long  as  the  key  is  held  closed  and  will 
cease  when  the  key  is  opened.  Therefore  with  the  switch  S  in  the  "  up  " 
position,  transmission  is  on  the  "  cut-in  "  method. 

If  the  switch  S  is  thrown  to  the  right  so  as  to  make  contact  with  ter- 
minal a,  then  transmission  will  be  by  the  "  compensated  "  method.  This 
may  be  seen  from  the  following:  with  the  key  open,  the  antenna  circuit 
is  completed  to  ground  through  Lx',  the  tube  will  therefore  oscillate 
and  the  antenna  radiate  energy  at  a  wave-length  determined  by  the  con- 
stants of  the  circuit,  including  L£]  the  wave-length  of  the  energy  radiated 
while  a  signal  is  being  sent  is  therefore  less  than  the  wave-length  of  the 
energy  radiated  during  a  space  interval.  Transmission  is  thus  in  accord- 
ance with  Fig.  41-11. 

Throwing  the  switch  S  to  the  left  so  as  to  make  contact  with  terminal 
b,  will  permit  sending  on  the  "  modulated  "  method.  With  the  key  open, 
the  antenna  circuit  includes  the  bUzzer  winding  and  so  the  set  will  not 
oscillate.  When  the  key  is  closed,  two  results  are  produced:  First,  the 
buzzer  circuit  is  completed  through  the  filament  battery  and  the  buzzer  will 
vibrate  as  long  as  the  key  is  down;  second,  the  vibrating  buzzer  armature 
alternately  makes  and  breaks  the  antenna  circuit;  therefore,  when  it  com- 
pletes the  circuit,  oscillations  occur  and  energy  is  radiated,  while  during  the 
break  no  oscillations  are  possible.  The  energy  radiated  is  thus  as  shown 
in  Fig.  41-111.  It  should  be  noted  that  when  the  buzzer  armature  is  in  the 
open  position,  the  antenna  circuit  is  not  actually  opened,  but  is  completed 
through  the  filament  battery  and  buzzer  winding  to  ground.  Due  to  the 
high  impedance  and  resistance  of  the  latter  to  the  flow  of  high-frequency 
currents,  oscillations  are  prevented  as  effectively  as  though  an  actual 
break  has  occurred  in  the  antenna  circuit. 

Use  of  Radiophone  Transmitting  Set  for  Undamped-wave  Teleg- 
raphy.— A  novel  and  effective  scheme  for  transmitting  undamped  wave 
signals  is  shown  in  Fig.  50. 

The  operation  and  action  of  the  radiophone  set  shown  is  discussed  in 
detail  in  a  later  chapter  (see  Chapter  VIII),  and  it  is  there  shown  that  when 
no  sound  waves  strike  the  transmitter  diaphragm,  a  high-frequency  cur- 
rent of  constant  amplitude  flows  in  the  antenna,  and  constant  power 
is  radiated.  When  the  transmitter  is  spoken  into,  the  amplitude  of  the 
antenna  current  (and  radiated  power)  varies  in  proportion  to  the  intensity 
and  frequency  of  the  sound  waves  set  up  by  the  speaker. 


628 


CONTINUOUS-WAVE  TELEGRAPHY 


[CHAP.  VII 


Antenna 


Similarly,  a  buzzer,  placed  in  front  of  the  transmitter,  would  set  up 
sound  waves  of  constant  frequency  and  intensity,  and  cause  the  radiated 
power  to  vary  in  accordance'  with  the  pitch  of  the  buzzer  note.  By  using 

* a    high    pitch    buzzer    of 

proper  construction,  a  very 
clear  transmission,  possess- 
ing a  high  degree  of  selecti- 
vity, may  be  easily  obtained. 
The   form    of   the    an- 
tenna   current    while    the 
buzzer     is     in     operation 
(key  closed)   would  be  as 
shown  in  Fig.  12,  p.  657, 
the  amplitude  varying  peri- 
odically at  buzzer  frequen- 
cy, above   and   below  the 
constant   amplitude   main- 
tained   when    the    key   is 
FIG.  50.— A  scheme  for  using  a  radiophone  set  to  send      open.       The     reception    of 
continuous-wave  telegraph  signals.    Of  course,         ,  u      •      ^i      •       •     -i 
the  buzzer  and  switch  may  be  inserted  directly      SUch   S1Snals    1S   Similar    in 
in  the  circuit,  in  place  of  the  microphone,  if  more      every  way    to    that    of    ra- 


diophone  messages  or  tele- 


complete  modulation  of  signals  is  desired. 

graphic  transmission  by  the  "  modulated  "  method,  no  "  beat  "  reception 
or  special  receiving  devices  being  required. 

Advantages  and  Disadvantages  of  the  Cut-in,  Compensated,  and 
Modulated  Methods  of  Signal  Transmission. — The  advantages  and  dis- 
advantages of  the  several  methods  of  sending  described  above  may  be 
summarized  as  follows: 

"  CUT-IN  "  METHOD.  Advantage. — Only  one  wave-length  is  radi- 
ated after  the  antenna  current  has  risen  to  its  normal  effective 
value,  and  energy  is  radiated  only  when  signal  is  being  sent. 
Signal  is  easily  received,  and  permits  of  a  high  degree  of 
selectivity. 

Disadvantage. — Not  suitable  for  such  generators  as  the  Poulsen 
arc,  which  do  not  operate  well  until  the  "  steady  state  "  has 
been  reached. 

"  COMPENSATED  "  METHOD.  Advantage. — The  oscillations  are 
continuous.  This  method  must  be  employed  for  the  Poulsen 
arc  (neglecting  the  dummy  antenna  as  an  alternative) .  Trans- 
mission is  reliable,  as  the  change  in  wave-length,  as  the  key 
is  operated,  is  positive  and  certain. 

Disadvantage. — The  power  efficiency  is  comparatively  low  because 
the  set  requires  full  power  all  the  time,  whether  radiating  a 


CONTINUOUS-WAVE  RECEPTION  629 

"  signal  "  or  not.  A  more  serious  disadvantage  arises  from 
the  fact  that  each  sending  set  "  uses  up  "  two  different  wave- 
lengths. This  latter  feature  is  especially  undesirable  when 
long  wave-lengths  are  employed;  the  difference  in  frequency 
of  the  signal  wave  and  compensation  wave  should  be  about 
1000  cycles  per  second,  and  thus  the  number  of  arcs  which 
can  be  used  in  one  district,  in  the  long  wave-length  range  may 
be  seriously  limited. 

"  MODULATED  "  METHOD.  Advantage. — The  primary  advantage 
of  the  modulated  method  is  that  the  signals  can  be  received 
by  means  of  an  ordinary  crystal  or  non-oscillating  vacuum- 
tube  receiving  set.  Thus,  if  the  special  continuous-wave 
receiver  is  out  of  service  for  any  reason,  the  ordinary  receiver 
may  be  used  for  reading  the  message.  Radiation  occurs  only 
while  key  is  closed,  thus  increasing  efficiency. 

Disadvantage. — Less  energy  is  radiated  since  the  energy  is  broken 
or  chopped  into  groups.  A  continuous  stream  of  energy,  with 
given  maximum  potential  on  the  antenna,  sends  off  more 
power  than  a  series  of  "  trains  "  and  when  utilized  in  a  proper 
receiving  set,  permits  communication  over  a  greater  distance 
than  the  modulated  signal.  With  the  modulated  signal  the 
selectivity  is  poorer  than  that  obtainable  by  means  of  the 
cut-in  method  under  similar  conditions;  thus  the  number  of 
neighboring  stations,  operating  in  a  given  wave-length  range, 
without  serious  interference,  is  less. 

Reception  of  Continuous-wave  Signal.  Necessity  for  Special  Receiv- 
ing Sets. — That  some  special  means  must  be  provided  for  the  reception 
of  continuous  wave  signals,  in  addition  to  the  simple  rectifying  device, 
i.e.,  a  crystal  or  vacuum  tube,  will  be  evident  from  the  following:  if  we 
consider  an  undamped  wave-generator  transmitting  on  the  "  cut-in  " 
method,  and  this  energy  being  received  by  a  simple  crystal  or  vacuum- 
tube  receiver,  the  potential  across  the  receiver  circuit  will  have  the  form 
indicated  in  Fig.  51,  curve  A. 

The  rectifying  action  of  the  crystal  or  tube  produces  an  asymmetrical 
change  in  current  through  the  phones,  the  mean  current  being  indicated 
by  the  dotted  line,  Fig.  51 B.  Since  the  diaphragm  is  only  actuated  to 
give  a  click  when  a  sudden  variation  of  the  mean  current  through  the 
phone  is  produced,  the  result  is  a  slight  click  at  the  beginning  and  end 
of  each  signal.  Evidently,  the  message  received  would  be  unintelligible. 

If  we  consider  signal  transmission  by  the  "  compensated  "  method, 
the  results  are  similar  and  may  be  even  worse,  depending  on  the  sharp- 
ness of  tuning  at  the  receiving  station.  Conditions  would  be  as  shown 
in  Fig.  52. 


630 


CONTINUOUS-WAVE  TELEGRAPHY 


[CHAP.  VII 


It  is  evident  that  if  the  signal  and  compensation  waves  are  practically 
equal  in  amplitude  (as  they  may  be  under  broad  tuning  conditions),  no 
clicks  at  all  will  be  heard  in  the  phones. 


Receiver 
Circuit 
Voltage 


Current 

through 

Phones 

(Crystal  Detector) 


(B) 


pln  51 — Action  of  crystal  detector  receiver  on  continuous-wave  signal  being  sent  by 

the  "cut-in"  scheme. 


Receiver 

Circuit 
Voltage 


Current 
through 
Phones 
(Crystal  Detector) 


pIG  52. — A  ft  ion  of  crystal  detector  for  compensated  continuous-wave  signal. 


Receiver 
Circuit 
Voltage 


Current 
through 
Phones 
(Crystal  Detector) 

FIG.  53.— Action  of  crystal  detector  on  a  modulated  continuous-wave  signal. 

If  the  set  is  sending  on  the  "  modulated  "  method,  the  signal  is  received 
exactly  as  in  the  case  of  a  spark  signal.  The  action  is  indicated  in  Fig. 
53.  This  shows  the  mean  current  through  the  phones  to  vary  at  audio 
frequency  (chopper  or  buzzer  frequency)  when  the  key  is  held  closed, 
and  the  signal  is  thus  made  audible  to  the  observer. 


CONTINUOUS-WAVE  RECEPTION 


631 


Tikker 


Action  of  Continuous-wave  Receivers. — The  above  curves  and  dis- 
cussion indicate  that  in  order  to  receive  continuous- wave  signals,  some 
device  must  be  used,  which,  when  interacting  with  the  incoming  signal, 
will  give  an  audio  frequency  component.  This  component,  in  turn,  after 
rectification,  causes  pulses  of  audio  frequency  to  occur  in  the  phones,  the 
corresponding  note  being  heard  - 
by  the  observer  as  long  as  the  — I 
incoming  signal  energy  continues. 
With  the  compensated  method  of 
sending  the  space  and  signal  note 
may  also  be  differentiated  by  their 
difference  in  pitch,  as  described 
later. 

Continuous   Wave   Receivers. 
Tikker. — The  connections  for  this 
device  are  indicated  in  Fig.  54.   Fifi   54<_Method  of  re(,civing  continuous- 
C2  is  an  ordinary  variable  tuning       wavc  signai  llsjng  a  tikkcr  as  detector, 
condenser   while   C   is   fixed   and 

comparatively  large  in  value  (about  1  ju/-).  The  tikker  T  consists  of 
a  revolving  brass  disk  upon  which  a  fine  steel  wire  is  placed  in  light 
contact.  Due  to  slight  irregularities  in  the  surface  of  the  disk  the 
contact  closes  and  opens  intermittently  at  an  audio  frequency  determined 
by  the  condition  and  characteristics  of  the  tikker.  While  the  contact  is  off, 
the  antenna  is  supplying  energy  to  the  closed  circuit,  L^—C^  and  a  com- 
paratively large  amplitude  of  current  builds  up  in  this  circuit.  The  action 
is  similar  to  the  action  of  the  resonance  transformer  of  a  spark  transmitter 
(see  p.  307).  When  the  tikker  makes  contact,  the  energy  accumulated 
in  condenser  €2  discharges  over  into  C,  which,  due  to  its  large  capacity, 
takes  a  long  time  to  charge,  and  the  contact  has  already  opened  before 
it  can  discharge  back  into  C2—  Lo.  Therefore  it  discharges  through  the 
phones,  producing  a  click.  A  click  will  be  produced  in  the  phones  for  each 
opening  of  the  tikker  and  the  note  heard  will  thus  depend  on  the  tikker 
constants,  and  is  therefore  controllable  by  the  speed  of  the  tikker  disk. 
It  should  be  noted  that  no  separate  rectifier  is  needed.  The  tone  obtained 
is  not  musical,  since  contact  may  occur  with  C  charged  to  varying  poten- 
tial differences  due  to  irregular  and  varying  contact. 

Chopper. — Instead  of  breaking  up  the  energy  at  the  transmitting  end 
as  in  the  "modulated"  method,  the  interrupter  element  may  be  connected 
at  the  receiver,  as  shown  in  Fig.  55. 

This  differs  from  the  tikker  in  that  a  detector  element  is  required 
while  the  large  condenser  across  the  phones  is  omitted.  Normally,  the 
chopper  consists  of  a  rotating  toothed  wheel  making  contact  with  a  brush 
element,  or  a  buzzer^  may  be  used.  The  action  is  simply  to  "chop  up" 


632 


CONTINUOUS-WAVE  TELEGRAPHY 


[CHAP.  VII 


the  stream  of  received  energy  into  audio  frequency  groups  of  oscillations 

which  are  then  rectified  to  produce 
an  audible  note  in  the  phone. 

The  Goldschmidt  Tone  Wheel  is 
essentially  an  interrupter  element, 
but  due  to  its  comparative  high 
speed  of  rotation  (near  synchronism) 
no  detector  element  is  required.  It 
consists  of  a  toothed  wheel,  making 
contact  with  a  brush,  and  designed 
to  run  at  synchronous  speed  at  a 
FIG.  55.-Scheme  using  chopper  and  reasonable  r.p.m.  If  we  assume  a 


rectifier    to 
signals. 


receive 


continuous-wave  wheel  with  800  teeth  and  slots  (of 
equal  width),  the  synchronous  speed, 
for  a  frequency  of  50,000,  would  be 

3750  r.p.m.,  which  is  within  safe  limits.  If  we  consider  a  signal  of  50,000 
cycles /sec.  frequency  (6000  meters)  being  received,  and  the  wheel  travel- 
ing at  synchronous  speed,  the  result  may  be  as  shown  in  Fig.  56,  B  or  C, 


(C) 


FIG.  56. — Use  of  tone  wheel  for  receiving  continuous-wave  signals;   at  synchronous 

speed  it  will  give  no  signal. 

depending  on  the  phase  of  the  interruptions  referred  to  the  high-frequency 
current. 

The  form  of  the  phone  current  will  be  different  for  different  points 
of  interruption,  but  in  any  case,  constant  amplitudes  will  be  obtained 
if  the  wheel  is  run  at  synchronous  speed  and  no  signal  will  be  obtained. 
If  the  wheel  is  run  above  or  below  synchronous  speed,  then  the  successive 


CONTINUOUS-WAVE  RECEPTION 


633 


cycles  are  not  interrupted  at  the  same  point,  but  the  point  of  interruption 
will  shift  as  shown  in  Fig.  57. 

The  telephone  will  thus  be  periodically  impulsed  by  the  audio  frequency 
component  of  the  resultant  current  flowing  through  the  phones  as  indi- 
cated by  the  dotted  curves  in  Fig.  57.  The  frequency  of  this  current 
is  the  difference  between  the  frequency  of  the  wheel  and  the  incoming 
signal.  Thus,  for  the  machine  considered  above,  and  an  incoming  f re- 


Telephone 
Current 


Speed 
below 

I  Synchronous 

i  Value 


Speed 
above 

Synchronous 
Value 


FIG.  57. — The  tone  wheel  run  either  higher  or  lower  than  synchronous  speed  will  act  to 
give  a  musical  note  signal,  the  pitch  being  fixed  by  the  difference  between  the 
actual  speed  of  the  tone  wheel  and  synchronous  speed. 

quency  of  50,000,  the  speed  would  be  as  shown  below  for  a  desired  audio 
frequency  of  1000  cycles  per  second. 

/=/i-/2  =  1000  =50,000 -49,000  running  below  synchronism 
/=/2-/i  =1000=51,000-50,000  running  above  synchronism 
where  /i  =  frequency  of  incoming  energy; 

/2  =  frequency  of  interruptions  caused  by  the  tone  wheel 


also 
thus 


.  of  teeth  =49,000,  or  51,000  =r.p.m.X 800 


synchronous  speed  =3750  r.p.m. 
and 

tone  wheel  speed  for/2  =49,000  =3680 r.p.m.  =  70 r.p.m.below synchronism 
tone  wheel  speed  for /2  =51,000  =3820  r.p.m.  =70  r.p.m. above  synchronism 


634 


CONTINUOUS-WAVE  TELEGRAPHY 


[CHAP.  VII 


The  note  may  thus  be  easily  adjusted  to  give  maximum  audibility  by  alter- 
ing the  speed  of  the  tone  wheel. 

This  device  operates  in  some  respects  similarly  to  the  heterodyne 
receivers  discussed  below,  although  no  local  frequency  is  generated.  The 
pitch  of  the  note  received  does,  however,  depend  on  the  speed  of  the  tone 
wheel,  which  permits  its  adjustment  to  give  a  musical  note  which  can 
easily  be  heard  through  static  and  minimizes  interference  to  some  extent. 
This  is  evident  when  it  is  considered  that  the  interfering  station  must 
radiate  practically  the  same  wave-length  as  the  station  whose  message 
it  is  desired  to  receive  if  much  interference  is  to  occur.  A  very  slight 
difference  in  the  wave-length  causes  a  relatively  large  difference  in  pitch 
of  the  resultant  note,  and  the  interference  is  thus  easily  identified  and 
may  be  eliminated  by  properly  altering  the  speed  of  the  tone  wheel. 

This  receiver  was  specially  developed  for  use  in  connection  with  the 
Goldschmidt  system  of  undamped  wave-transmission,  and  was  used  to 
some  extent  in  the  stations  utilizing  this  system,  notably  those  at  Hanover, 
Germany,  and  Tuckerton,  N.  J.,  U.  S.  A. 

Rotating  Plate  Condenser. — Another  scheme  for  the  reception  of 
undamped  wave  signals  is  shown  in  Fig.  58. 

The  movable  plates  of  condenser  €2  are  rapidly  rotated  by  a  small 

motor  or  similar  means  so   as 
to  cause   the  circuit  L^  —  C^  to 
be  in  tune  for  a  small  interval 
of  time  during  each  revolution. 
While  in  tune   the   current   in 
the  detector-phone  circuit  will 
be  much  greater  than  at  other 
times  and  a  series  of  impulses, 
one  for  each  revolution,  is  thus 
exerted    on  the   telephone  dia- 
FIG.  58.— By  rotating  the  plates  of  the  tuning  phragm.     The    action  is   some- 
condenser,  the  use  of  a  crystal  detector  makes  wna^    similar    to    that    of    the 
a  continuous-wave  signal  audible,  the  pitch  of     ,  ,.,-. 

,  chopper,  but  differs  in  that  no 
the  note  being  fixed  by  the  rotational  speed     .    v\ 

of  the  condenser.  Of  course  the  circuit  picks  up  circuits  are  interrupted, 
all  signals  in  wave  length  range  of  the  L2— C2          Heterodyne      Receiver      or 
circuit.  .  " Beat"  Receiver. — The  receiv- 

ers described  above  have  all  been  applied  to  the  reception  of  undamped 
wave  signals  in  the  past,  but  at  the  present  time  have  been  superseded 
by  receivers  involving  the  generation  of  local  high-frequency  currents 
by  means  of  oscillating  vacuum  tubes.  The  advantages  of  this  type  of 
receiver  over  the  earlier  schemes  are : 

1.  Ease  of  operation. 

2.  Simplicity. 


L2 


CONTINUOUS-WAVE   RECEPTION 


635 


3.  Greater  selectivity  and  sensitiveness. 

4.  Lower  cost. 

5.  Small  space  requirements  and  portability. 

Its  operation  is  based  on  the  idea  of  combining  two  currents  of-different 
frequencies  to  produce  a  resultant  current  the  amplitude  of  which  varies 
periodically  (first  used  by  R.  A.  Fessenden),  the  frequency  of  this  ampli- 
tude variation  being  the  difference  between  the  two  component  frequen- 
cies.1 This  method  is  known  as  the  heterodyne  or  "  beat  "  method,  of 
which  two  schemes  may  be  used,  known  as  the  separate  heterodyne  and 
self  heterodyne  (autodyne),  depending  on  whether  the  detecting  device 
is  distinct  from  the  local  high-frequency  generator,  or  whether  the  two 
functions  are  performed  by  the  same  piece  of  equipment,  i.e.,  a  vacuum 
tube.  The  former  is  sometimes  simply  called  the  "  heterodyne  "  method, 


Panel 


(A) 


FIG.  59. — The  oscillating  tube  as  receiver;  it  uses  the  beat  note  idea  and  is  used  to-day 

universally. 

while  the  latter  may  be  called  the  "  self-heterodyne  "  or  "  autodyne  " 
method  of  reception. 

Self-heterodyne  Receiver  or  Autodyne. — The  self-heterodyne  receiver, 
utilizing  an  oscillating  vacuum  tube  as  a  generator  and  detector,  is 
undoubtedly  the  most  important  of  recent  developments  in  the  field  of 
radio,  and  will  be  described  somewhat  in  detail.  A  possible  connection 
for  the  receiving  set  is  indicated  in  Fig.  59. 

If  the  various  oscillation  requirements  of  the  tube  have  been  satisfied, 
the  tube  will  oscillate  at  a  frequency  determined  by  the  constants  of  the 
local  circuit,  L/2,  LI,  C,  and  a  current  of  this  frequency  will  flow  in  the  local 
circuit.2  This  is  known  as  the  local  high-frequency  current,  and  is  indi- 


1  See  Chapter  VI,  p.  483,  for  mathematical  analysis. 

2  For  analysis  of  conditions  required  for  oscillation  see  Chapter  VI,  p.  510. 


636  CONTINUOUS-WAVE  TELEGRAPHY  [CHAP.  VII 

Gated  by  curve  a,  Fig.  60.  Assume  its  frequency  to  be  1,000,000  cycles /sec. 
Now  consider  that  the  transmitter  is  operated  on  the  "  cut-in  "  method 
and  is  radiating  at  a  frequency  of  999,000  cycles /sec.  A  portion  of  this 
energy  strikes  the  receiving  antenna,  which  is  tuned  to  it,  and  a  maxi- 
mum current  is  caused  to  flow  in  the  antenna.  This,  in  turn,  induces 
an  e.m.f.  in  the  coil  L%  and  causes  a  current  whose  frequency  is  999,000 
to  flow  in  the  local  oscillating  circuit.  This  current  is  called  the  incoming 
high-frequency  current  and  is  shown  in  curve  b.  (It  should  be  noted 
that  the  antenna  and  local  oscillating  circuits  are  slightly  detuned.) 

The  two  high-frequency  currents,  flowing  in  the  same  circuit,  com- 
bine to  give  the  resultant  current  indicated  in  curve  c,  which  shows  the 
periodic  variation  in  amplitude  produced.  These  periodic  variations  in 
amplitude  are  called  "  beats,"  and  the  beat  frequency  is  always  the  dif- 
ference between  the  component  frequencies.  (A  "  beat  cycle  "  consists 
of  one  complete  rise  and  fall  in  amplitude).  For  the  values  assumed  above 
the  beat  frequency  would  thus  be  1,000,000-999,000  =  1000  cycles /sec. 
It  is  to  be  particularly  noted  that  the  frequency  of  alternation  of  this 
resultant  current l  is  the  mean  of  the  two  component  frequencies,  namely, 
999,500  for  the  values  assumed.  The  resultant  current  is  therefore  a 
radio  frequency  current. 

The  drop  across  condenser  C  will  have  the  same  form  as  the  current 

curve  (  EC  =     fri)  and  is  identical  with  the  variation  in  grid  voltage  Ea. 

\  ATTjL  ' 

The  effect  of  this  variation  in  grid  voltage  upon  the  plate  current 
depends  on  the  point  of  the  characteristic  curve  at  which  the  tube  is  being 
operated.  If  it  is  assumed  that  operation  is  on  the  lower  bend,  the  plate 
current  will  vary  as  shown  on  curve  d.  This  variation  may  be  resolved 
into  two  components  as  shown  in  curves  e  and  /,  e  flowing  through  the 
bridging  condenser,  while  /  flows  through  the  phones.  The  latter  com- 
ponent varies  at  beat  frequency,  and  if  this  frequency  is  high  enough,  a 
musical  note  is  produced  in  the  phones,  which  is  maintained  as  long  as 
the  key  is  held  closed  at  the  transmitter.  Opening  the  key  leaves  only 
the  local  high-frequency  current  flowing  and  no  variation  of  plate  current 
at  beat  frequency  is  produced,  hence  no  note  is  heard  in  the  phones. 
If  the  tube  stops  oscillating  and  the  incoming  signal  is  maintained,  the 
same  result  is  obtained. 

If  it  is  assumed  that  the  tube  is  oscillating  symmetrically  with  respect  to 
the  upper  and  lower  bends  of  its  characteristic  curve,  the  mean  plate  cur- 
rent remains  unchanged  (giving  no  current  of  audible  frequency)  although 
a  beat  frequency  variation  in  amplitude  is  produced.  This  means  that 

1  On  the  basis  of  measuring  frequency  by  the  time  between  successive  zero  values. 
At  the  points  of  minimum  amplitude  the  phase  reverses  as  explained  in  Chapter  IV, 
p.  241. 


CONTINUOUS-WAVE  RECEPTION 


637 


the  tube  must  be  operated  on  a  rectifying  part  of  the  curve  if  a  signal  is  to 
be  heard.  Of  course  if  a  condenser  is  used  in  series  with  the  grid,  a  signal 
will  be  heard,  no  matter  what  part  of  the  curve  the  tube  is  operating  on, 
as  pointed  out  in  Chapter  VI,  p.  451. 


Local 

High  Frequency 
Current 


Incoming 

High  Frequency 

Current 


Resultant 

High  Frequency 

Current 

(Represents  also 
form  of  ECJ 

neglecting  phase 
displacement) 


Plate 
Current 


(Re 

I  form  of  E^ 

<  neglecting 

phase 
^displacement 


Alternating 
Component  of 
Plate  Current 

Mean 

Plate 

Current 


FIG.  60. — Action  of  the  tube  as  a  beat  receiver. 

The  above  discussion  indicates  that  the  receiving  tube  must  perform 
simultaneously  the  functions  of  oscillation  and  rectification.  Failure 
of  either  would  result  in  no  signals  being  received.  These  functions, 
which  are  performed  by  the  one  piece  of  apparatus  in  the  self-heterodyne 


638 


CONTINUOUS-WAVE  TELEGRAPHY 


[CilAP.    VII 


receiver  described  above,  may  evidently  be  performed  by  two  different 
tubes  or  a  tube  and  high-frequency  alternator.  Connections  for  a  "  sepa- 
rate heterodyne  "  receiver  utilizing  two  vacuum  tubes  is  indicated  in 
Fig.61.1 

Control  of  the  Beat  Frequency  or  Pitch  of  the  Signal  Note. — It  is 
evident  that  the  local  high  frequency  may  readily  be  controlled  by  the  vari- 
able condenser  C  of  Fig.  59.  If  the  incoming  high  frequency  is  1,000,000, 

and  condenser  C  is  of  too 
large  a  value,  the  local  fre- 
quency may  be  low,  for  in- 
stance 900,000  cycles /sec. 
The  beat  frequency  is  thus 
100,000  cycles/sec,  which 
is  above  the  audible  limit. 
As  the  value  of  C  is  de- 
creased, the  local  frequen- 
cy increases,  the  beat  fre- 
quency decreases,  and  as 
the  audible  values  are 
reached,  the  pitch  of  the 
note  heard  in  the  phones 
(i.e.,  the  beat  note)  will 
change  from  a  very  high 
pitch  to  lower  and  lower 
values,  until,  when  the 
two  frequencies  coincide, 
FIG.  61. — Instead  of  using  the  detector  tube  to  produce  the  beat  frequency  is  zero 


the  local  oscillations  for  beat  reception,  a  separate 
oscillating  tube  may  be  coupled  to  the  antenna. 


and  no  sound  is  heard  in 
the  phones.  (In  this  case 
we  have  the  addition  of  two 

currents  of  the  same  frequency,  producing  a  resultant  current  of  constant 
amplitude.  The  mean  plate  current  thus  has  no  periodic  variation  in 
amplitude;  i.e.,  the  beat  effect  is  absent.)  As  the  capacity  continues 
to  be  decreased,  the  local  frequency  increases,  and  the  difference  between 
the  local  and  incoming  frequencies  again  increases;  i.e.,  the  pitch  of  the 
beat  note  in  the  phones  again  rises  until  it  disappears  at  the  limit  of  audi- 
bility. The  above  phenomenon  is  illustrated  by  Fig.  62.  (Curve  A.) 

In  connection  with  the  foregoing  discussion  it  may  be  noted  that  in 
the  practical  installation  or  assembly  of  a  heterodyne  receiving  set,  the 
handle  of  the  variable  condenser  C  should  be  on  the  ground  side,  thus 
grounding  the  moving  plates.  If  the  apparatus  is  assembled  in  a  contain- 

1  For  more  detailed  study  of  the  action  of  this  type  of  receiving  circuit  see  Chapter 
VI,  p.  516, 


CONTiN UOUS-WAVE   RECEPTION 


039 


ing  case,  a  metal  plate  should  be  placed  in  front  of  the  condenser  and 
electrically  connected  to  the  moving  plates.  See  Fig.  59A.  This  pre- 
caution prevents  any  change  in  frequency  due  to  the  proximity  of  the 
observer's  hand  or  body  near  the  condenser  and  is  extremely  important 
on  short  wave-length  receivers.1 

Effect  of  Upper  Harmonics. — Since  the  vacuum  tube  does  not  generate 
a  pure  sine  current  of  fundamental  frequency,  but  also  produces  upper 
harmonics,  a  unique  phenomenon  is  observed  when  the  heterodyne  receiver 
is  close  to  an  oscillating  tube  transmitter,  as  may  be  the  case  in  the  labo- 
ratory. 

Harmonic 


90C 


100° 


FIG.  62. — A  diagram  for  analyzing  the  peculiar  noises  heard  when  ail  oscillating  tube 
receiver  is  close  to  a  continuous-wave  transmitter. 


Referring  to  Fig.  62  the  combination  of  the  fundamentals  will  pro- 
duce the  pitch  curve  designed  as  A,  this  note  being  assumed  as  becoming 
audible  2  when  the  condenser  is  set  to  the  100°  graduation  on  the  condenser 
scale.  As  the  condenser  value  is  decreased  from  100°,  a  value  is  reached 
(at  80°)  when  the  combination  of  the  second  harmonics  produce  a  just 
audible  beat  note,  this  note  as  well  as  the  fundamental  beat  note  being 
heard  simultaneously  as  the  condenser  value  is  further  decreased.  At 
certain  smaller  values  (73.3°  and  70°  on  the  scale)  of  condenser  capacity, 
the  interaction  of  still  higher  harmonics  (third  and  fourth)  produces  addi- 
tional beat  notes.  Thus,  in  the  figure,  four  beat  notes  will  be  heard  simul- 

1  Of  course  a  much  better  scheme  is  to  mount  all  the  parts  of  the  receiving  circuit 
inside  of  a  copper  box,  grounded;  heavy  copper  mesh  is  sometimes  used 

2  The  upper  limit  of  audibility  here  assumed,  is  much  higher  than  thai  of  the  ordinary 
person;    generally  an  adult  cannot  hear  a  note  higher  than  14,000-15,000  complete 
vibrations  per  second. 


640 


CONTINUOUS-WAVE  TELEGRAPHY 


[CHAP.  VII 


taneously  in  the  phones  at  condenser  adjustments  between  70°  and 
60°.  At  60°  the  fundamental  beat  note  and  the  upper  harmonic  beat 
notes  all  pass  through  zero  frequency  simultaneously,  and  as  the  condenser 
value  is  further  decreased,  the  beat  notes  increase  in  pitch  and  successively 
become  inaudible  again  as  shown.  These  effects  are  summarized  in  the 
following  tabulation : 


Harmonic  . 

Transmitter. 

Receiver  . 

Beat  Note. 

C  =  65°  • 

Fundamental 
2d  Harmonic 

1,000,000 
2,000,000 

997,500 
1,995,000 

2500 
5000 

C=60°           .1 

3d  Harmonic 
4th  Harmonic 

Fundamen  tal 
2d  Harmonic 

3,000,000 
4,000,000 

1,000,000 
2,000,000 

2,992,500 
3,990,000 

1,000,000 
2,000,000 

7500 
10000 

1 

C=55°  

3d  Harmonic 
4th  Harmonic 

Fundamental 
2d  Harmonic 

3,000,000 
4,000,000 

1,000,000 
2,000,000 

3,000,000 
4,000,000 

1,002,500 
2,005,000 

2500 
5000 

3d  Harmonic 
4th  Harmonic 

3,000,000 
4,000;000 

3,007,500 
4,010,000 

7500 
10000 

In  actual  reception  the  upper  harmonics  generated  by  the  receiver 
are  always  considerably  weaker  than  the  fundamental,  and  when  adjust- 
ments are  made  so  that  the  beat  frequency  heard  is  one  resulting  from 
the  combination  of  an  upper  harmonic  of  the  local  oscillation  and  the 
incoming  signal,  the  signal  strength  and  clearness  are  very  greatly  reduced. 
Thus,  in  adjusting  to  receive  a  1,000,000-cycle  wave,  the  operator  may 
adjust  his  receiving  circuit  to  a  fundamental  frequency  of  500,500,  tuning 
to  the  second  harmonic  (frequency  =  1,001,000)  for  a  1000-cycle  beat 
note,  or  he  may  adjust  his  set  to  a  fundamental  frequency  of  300,333, 
tuning  to  the  third  harmonic.  Similarly  he  may  tune  to  the  fourth  or 
higher  harmonics,  if  present,  reception  becoming  increasingly  inefficient 
and  difficult,  due  to  the  smaller  and  smaller  amplitudes  of  these  higher 
harmonic  components.  This  may  be  seen  from  inspection  of  the  curves 
of  Fig.  60;  if  the  local  high-frequency  amplitude  is  small,  little  change 
in  amplitude  occurs  in  the  resultant  current,  which  in  turn  determines 
the  strength  of  signal. 

Upper  harmonics  may  also  be  produced  by  the  transmitting  set  as 
already  noted.  In  this  case  the  receiving  set  may  have  its  fundamental 
frequency  adjusted  to  these  upper  harmonics,  and  again  weakness  of 
signal  and  inefficiency  result.  This  possibility,  however,  is  relatively 
small,  since: 


CONTINUOUS  WAVE  RECEPTION 


641 


1st.  The  upper  harmonics  radiated  by  the  transmitter  are  weak 
and  ineffective  unless  the  transmitter  is  close  to  the  receiver 
as  assumed  in  the  detailed  description  above. 

2d.  The  receiving  antenna  is  not  tuned  to  these  upper  harmonics, 
still  further  decreasing  their  effect  on  the  receiving  circuit. 


FIG.  63. — Front  view  of  a  small   continuous- wave  transmitter;    the  high-frequency 
power  is  generated  by  four  five-watt  tubes. 


For  illustration,  assume  the  fundamental  transmitter  frequency  as 
1,000,000,  with  a  second  and  third  harmonic  also  being  radiated.  The 
receiver  in  this  case  may  be  adjusted  to  a  fundamental  frequency  of 
2,000,000  or  3,000,000,  but  the  beat  note  in  either  case  will  be  very  much 
weaker  than  if  the  fundamental  incoming  frequency  had  been  utilized. 


642  CONTINUOUS-WAVE   TELEGRAPHY  [CHAP.  VII 

The  operator,  when  in  doubt,  should  vary  his  local  frequency  over  wide 
limits,  and  select  that  adjustment  giving  maximum  signal  strength. 

Possibility  of  Receiving  Undamped-wave  Signals  with   an  Ordinary 
Crystal.— An  ordinary  damped-wave   receiver,  using  a  crystal  or  simple 


FIG.  64. — Back  view  of  the  set  shown  in  Fig.  63;  toroidal  transmitting  coils  were  used 
to  eliminate  local  interference.  The  magnetically  operated  key  is  seen  in  the  opened 
box. 

vacuum-tube  circuit,  may,  under  certain  conditions,  receive  an  undamped- 
wave  signal.  The  possibility  arises  when  two  undamped-wave  trans- 
mitters are  operating  simultaneously  at  practically  the  same  wave-length. 
Thus,  if  station  A  sends  at  6000  meters  (50,000  cycles),  while  B  sends 
at  6060  meters  (49,500  cycles),  currents  of  these  frequencies  will  simul- 


CONTINUOUS-WAVE   TRANSMITTING   SETS 


643 


taricously  flow  in  the  receiving  antenna,  giving  a  resultant  current  having  a 
frequency  of  500  cycles,  which  will  cause  a  note  of  similar  frequency  to  beat 
be  heard  in  the  phones.  It  is  evident  that  for  the  signals  of  either  station 
to  be  correctly  received  the  second  transmitting  station  must  be  radiating 
continuously,  acting  simply  as  a  high-frequency  generator.  Thus,  if  B 
is  sending  while  A  is  tuning  his  set,  with  key  down,  operators  with  crystal 


FIG.  65. — Continuous-wave  transmitter  using  four  Type  P  pliotrons;    ammeters  are 
supplied  for  plates  and  grids,  and  voltmeter  for  filament  control. 

detector  sets  adjusted  for  receiving  a  frequency  close  to  that  used  by  A 
and  B  will  be  able  to  read  A's  signal. 

Use  of  Grid  Condenser. — It  will  be  recalled  that  the  tube  (in  the  self- 
heterodyne  circuit)  must  perform  the  functions  of  oscillation  and  detection. 
In  Chapter  VI  it  was  shown  that  the  best  point  for  oscillating  is  on  the 
straight  part  of  the  characteristic  curve,  while  the  best  point  for  detection 


644  CONTINUOUS-WAVE  TELEGRAPHY  [CHAP.  VII 

is  on  the  bend.  It  has  also  been  noted  that  the  use  of  a  grid  condenser 
improves  the  detecting  action  and  does  not  require  that  the  tube  be  oper- 
ated on  the  bend  of  the  curve.  In  fact,  the  detection  is  best  when  the 
tube  is  operated  on  the  straight  portion.  For  these  reasons  the  grid 
condenser  is  also  used  in  connection  with  the  heterodyne  receiver.1 


FIG.  66. — Back  view  of  the  set  shown  in  Fig.  65;  with  1500  volts  supplied  to  the  plate 
circuit  this  set  generates  1  kw.  of  high-frequency  power. 

The  one  disadvantage  of  using  a  grid  condenser  is  the  possibility  of 
the  tube  "  squealing  "  or  "  clicking  "  and  thus  obscuring  or  preventing 
entirely  the  reception  of  signals.  This  action  has  been  described  in  a 
previous  chapter 2  and  means  employed  for  its  prevention  were  con- 
sidered. These  means  are  not  uniformly  successful  in  getting  rid  of  the 


1  For  analysis  see  Chapter  VI,  p.  486. 

2  See  Chapter  VI,  p.  523. 


CONTINUOUS-WAVE  TRANSMITTING  SETS  645 

trouble,  however,  and  it  is  doubtful  if  the  use  of  a  grid  condenser  would 
always  be  desirable. 

Arrangement  of  Apparatus  in  Tube  Transmitting  Sets. — The  exact 
arrangement  of  apparatus  on  a  vacuum-tube  transmitting  set  depends  of 
course  in  general  upon  the  use  to  which  the  set  is  to  be  put.  In  so  far 
as  possible  all  the  apparatus  should  be  assembled  on  one  board,  with  suit- 
able instruments,  rheostats,  etc.  Figs.  63  and  64  show  front  and  rear 
views  of  a  set  having  an  output  of  about  15  watts;  it  is  intended  for 
laboratory  use,  so  that  extreme  compactness  was  not  necessary.  To 
eliminate  as  far  as  possible  disturbances  to  and  from  other  circuits  the 
coils  of  the  set  are  made  toroidal.  An  electrically  operated  key  is  shown 
in  the  rear  view,  this  serving  to  connect  the  receiving  amplifier  and  tele- 
phones whenever  the  sending  key  (which  operates  the  relay)  is  not 
depressed.  For  convenience  the  filaments  of  the  tubes  are  arranged  for 
power  from  the  110-volt  c.c.  laboratory  supply.  As  the  antenna  load 
coil  is  not  adjustable  (being  toroidal)  the  frequency  of  the  output  is 
regulated  by  an  adjustable  condenser,  in  parallel  with  the  antenna.  A 
Meissner  circuit  was  used  in  this  set,  the  plate  and  grid  coupling  being 
adjustable  so  that  maximum  output  might  be  obtained,  no  matter  what 
the  resistance  of  the  load  might  be. 

In  Figs.  65  and  66  are  shown  two  views  of  a  higher  power  set,  this 
using  four  Type  P  pliotrons  in  parallel,  and  having  an  output  of  one 
kilowatt  at  6000  meters. 


CHAPTER  VIII 
RADIO-TELEPHONY 

Field  of  Use. — The  radio-telephone  supplements  the  radio-telegraph 
in  the  same  manner  that  the  wire  telephone  supplements  the  wire  tele- 
graph. The  advantages  of  the  radio-telephone  over  the  radio-telegraph 
are  that,  while  the  latter  requires  an  experienced  operator  who  is  familiar 
with  the  code,  the  former  does  not,  and,  therefore,  the  conversation  may 
be  carried  on  directly  between  the  interested  parties.  In  other  words; 
the  same  factors  operate  in  favor  of  the  radio-telephone  over  the  radio- 
telegraph as  operate  in  favor  of  the  wire-telephone  over  the  wire-tele- 
graph. 

A  comparison  between  the  radio-telephone  and  the  wire-telephone 
is  exactly  similar  to  that  between  the  radio-telegraph  and  the  wire-tele- 
graph. The  radio-telephone's  accepted  field  of  use  is  from  ship  to  ship, 
ship  to  shore,  also  from  airship  to  airship  and  from  airship  to  ground, 
from  one  moving  train  to  another  and  from  train  to  station,  and,  again, 
in  places  over  land  and  over  water  where  it  would  be  either  impossible 
or  extremely  uneconomical  to  use  wires.  An  example  of  this  last  applica- 
tion would  be  the  speech  transmission  by  radio-phone  over  the  ocean, 
in  which  case  the  length  of  the  cable  and  the  impossibility  of  using  Pupin 
coils  and  repeating  amplifiers  make  wire  telephony  entirely  out  of  the 
question;  the  same  is  true  over  a  desert  or  other  undeveloped  region 
where  it  would  be  far  more  economical  to  use  the  radio-telephone  than 
the  wire  telephone.  The  above  does  not,  however,  mean  that  these  two 
systems  of  telephony  are  antagonistic;  on  the  contrary,  it  is  expected 
that  in  the  future  a  subscriber  to  a  wire-telephone  system  will  be  able 
to  communicate  with  passengers  on  board  ships  equipped  with  radio- 
phone, the  transmission  of  speech  being  accomplished  by  wire  overland 
to  a  central  radio  station  and  therefrom  by  radio  to  the  ship;  it  is  expected 
that  the  same  will  apply  to  airships.  Thus,  the  two  divisions  of  the 
telephone  art  will  work  hand  in  hand  rather  than  in  any  way  conflict 
with  each  other. 

Outline  of  Principle  of  Operation. — The  two  elements  necessary  for 
radio-telephony  are,  of  course,  the  transmitter  and  the  receiver.  We 
will  consider  the  transmitter  and  the  receiver  separately  and  in  their 
simplest  forms. 

646 


SIMPLE   RADIOPHONE   TRANSMITTER 


647 


The  Transmitter. — Consider  Fig.  1,  in  which  the  high-frequency  alter- 
nator, such  as  an  Alexanderson,  or  Fessenden,  alternator,  is  connected 
in  series  with  the  loading  inductance  L,  the  antenna,  and  the  microphone 
transmitter  T.  The  microphone  transmitter  may  be  one  of  the  ordinary 
carbon  granule  type,  the  construction  of  which  is  fully  explained  on 
p.  655;  without  going  into  details,  it  will  suffice  to  state  here  that  such 
a  microphone  consists  simply  of  an  elastic  diaphragm  bearing  against 
a  mass  of  carbon  granules  enclosed  in  a  suitable  chamber;  the  carbon 

granules  form  part  of  an  electrical  circuit  (in  the      | 

case  of  Fig.  1  the  circuit  of  the  alternator). 
When  the  microphone  is  not  being  spoken  into 
the  diaphragm  remains  stationary  and  exerts  a 
constant  pressure  upon  the  carbon  granules,  the 
resistance  of  which  remains,  therefore,  constant. 
On  the  other  hand,  when  the  diaphragm  is  set 
vibrating,  as  is  done  by  speaking  into  the  mi- 
crophone or  through  a  noise  or  sound  reaching 
it,  the  pressure  exerted  by  the  diaphragm  against 
the  carbon  granules  changes,  and  this  change  of 
pressure  causes  the  resistance  of  the  carbon 
granules  to  increase  or  decrease  in  accordance 
with  the  displacement  of  the  diaphragm  from 
its  position  of  rest. 

In  the  case  of  Fig.  1,  when  the  microphone 
is  not  being  spoken  into,  the  alternator  produces 
a  high-frequency  current  of  constant  amplitude,  "=* 

i.e.,  an  undamped  current;  the  amplitude  of  this  FIG.    1.  —  The     simplest 
current  is  adjusted  to  the  maximum  by  adjusting      scheme  for  radio-teleph- 
the  inductance    L   so   as   to   make   the   natural 
frequency  of  the  circuit  equal  to  the  frequency 
of  the  alternator.     The  current  flowing  through 
the  antenna  under  these  conditions  may  be  repre- 
sented by  Fig.  2,  which  simply  shows  an  alternating  current  of  constant 
amplitude,  I0. 

Now,  assume,  for  the  sake  of  simplicity,  that  a  vibrating  tuning  fork 
is  placed  in  front  of  the  microphone.  The  harmonic  vibrations  of  the 
tuning  fork  will  cause  harmonic  vibrations  of  the  microphone  diaphragm, 
and  these  will  produce  variations  in  the  resistance  of  the  microphone. 
Since  no  other  part  of  the  circuit  of  Fig.  1  is  undergoing  any  change,  it 
is  plain  that  a  variation  of  the  microphone  resistance  will  produce  a  cor- 
responding variation  in  the  amplitude  of  the  high-frequency  antenna 
current.  Thus,  when  the  diaphragm  is  displaced  inwardly  the  resistance 
of  the  microphone  and,  therefore,  of  the  entire  alternator  circuit,  decreases, 


ony  utilizes  a  source 
of  high  frequency  A,  and 
a  microphone,  T  in  series 
with  the  antenna. 


648 


RADIO-TELEPHONY 


[CHAP.  VIII 


and  the  amplitude  of  the  current  supplied  by  the  alternator  must  neces- 
sarily increase;  the  reverse  takes  place  when  the  diaphragm  is  displaced 
outwardly. 


FIG.  2. — When  no  sound  impinges  on  the  microphone  the  amplitude  of  the  high-frequency 
current  supplied  to  the  antenna  is  constant. 

i 

The  antenna  current  under  these  conditions  would  be  as  shown  in 
Fig.  3,  where  the  curve  of  the  displacement  of  the  microphone  diaphragm 
is  also  given. 

It  will  be  noted  that  the  frequency  of  the  antenna  current  (as  deter- 
mined by  time  between  successive  zero  values)  must  remain  the  same 


Operating 


Idle 


FIG.  3. — If  a  sound  wave  actuates  the  microphone,  its  inward  and  outward  displacement, 
varying  the  resistance  in  the  antenna  circuit,  results  in  a  highly-frequency  current 
in  the  antenna  of  variable  amplitude,  called  a  modulated  high-frequency  current. 

whether  the  microphone  diaphragm  is  operating  or  not,  since  it  is  solely 
determined  by  the  frequency  of  the  alternator;  but  the  amplitude  of  this 
high-frequency  current  is  made  to  vary  in  accordance  with  the  tuning- 
fork  vibrations,  in  so  far  as  this  amplitude  changes  from  the  maximum 
of  AiFi,  corresponding  to  the  maximum  inward  diaphragm  displacement 
of  B\H i,  to  the  minimum  of  CiGi,  corresponding  to  the  maximum  out- 


RADIO-TELEPHONE   RECEIVER 


649 


ward  diaphragm  displacement  of  D\L\.  The  time  between  the  maxi- 
mum current  amplitudes  at  A\  and  A2  or  between  the  minimum  ampli- 
tudes at  Ci  and  €2  is  the  same  as  that  between  the  maximum  positive 
diaphragm  displacements  at  B\  and  82  or  between  the  maximum  negative 
diaphragm  displacements  at  DI  and  I>2.  Or,  in  other  words,  the  frequency, 
with  which  the  antenna  current  amplitude  changes  from  maximum  to 
minimum  and  back  to  maximum,  is  the  same  as  the  frequency  of  the  micro- 
phone diaphragm  and  of  the  tuning-fork  vibrations.  When  the  displace- 
ment of  the  microphone  diaphragm  is  zero,  as  after  the  point  K,  the 
antenna  current  becomes  the  same  as  in  Fig.  2,  i.e.,  of  unvarying  amplitude. 

The  antenna  current  represented  by  Fig.  3  is  said  to  be  "  modulated" 
The  high  frequency  is  known  in  this  case  as  the  "  carrier  frequency"  and 
the  frequency  of  the 
microphone  diaphragm, 
which  is  impressed  upon 
the  antenna  current,  is 
known  as  the  "modulating 
frequency  " 

It  now  remains  to 
show  how  the  modulated 
antenna  current  repre- 
sented by  Fig.  3,  when 
received  by  the  receiving 
antenna,  may  be  made  to 
so  affect  the  diaphragm  of 
a  telephone  receiver  as  to 
reproduce  the  note  emit- 
ted by  the  tuning  fork. 

The  Receiver.  —  The 
receiver  is  exactly  the 
same  as  used  for  spark 
telegraphy,  and  is  repro- 
duced  below  (Fig.  4)  for 

the  sake  of  convenience.  A  crystal  detector  has  been  shown  as  the 
rectifying  element,  but  a  vacuum  tube,  or  any  other  rectifying  device, 
may  be  used  instead. 

The  manipulations  necessary  for  the  operation  of  this  receiver  are  the 
same  as  for  any  spark  receiver;  the  antenna  circuit  and  the  closed  circuit 
must  be  tuned  to  the  incoming  high  frequency,  and  the  coupling  between 
the  antenna  circuit  and  the  closed  circuit  should  ordinarily  be  made  loose. 

It  is  plain  that  the  e.m.f.  impressed  upon  the  receiving  antenna,  due 
to  the  electromagnetic  waves  emanating  from  the  transmitter,  will  be 
an  exact  reproduction  of  the  current  in  the  transmitting  antenna;  let  it 


IG*  ^  —  ^or  receiying  a  radio-telephone  signal  an  ordi- 
nary  receiving  set  using  crystal  detector  is  sufficient- 


650 


RADIO-TELEPHONY 


[CHAP.  VIII 


be  represented  by  the  curve  below,  Fig.  5,  wherein  the  part  between 
S  and  K  corresponds  to  a  period  of  action  of  the  distant  microphone 
diaphragm  and  the  rest  of  the  curve  corresponds  to  a  position  of  rest  of 

the  microphone  diaphragm.  Assume, 
for  the  sake  of  simplicity,  that  the 
rectifier  used  in  the  receiving  circuit 
has  the  characteristic  represented  by 
Fig.  6;  i.e.,  a  characteristic  such  that 
a  negative  e.m.f.  impressed  upon  the 
circuit  of  the  rectifier  produces  no 
current  whatsoever  and  a  positive 
e.m.f.  produces  a  current  which  varies 
directly  with  the  e.m.f.1 

It  is  then  plain  that  the  e.m.f. 
impressed  upon  the  receiving  antenna 
and  transferred  to  the  rectifier  circuit 
by  suitable  coupling  coils'  will  pro- 
duce a  current  in  the  rectifier  circuit 
of  the  form  shown  in  Fig.  7.  The 
current  of  Fig.  7,  though  unidirection- 
al, is  yet  one  which  changes  at  high 
frequency,  and  as  such  it  cannot  flow 
through  the  high-impedance  winding 
of  the  telephone  receiver;  therefore, 
the  current  in  the  receiver  will  be 
the  average  current  shown  by  the 
dotted  curve  entered  in  Fig.  7. 

It  will.be  noted  that  the  current 
in  the  telephone  receiver  between  F 
and  H,  Fig.  7,  which  corresponds 
to  a  period  of  activity  of  the  micro- 
phone at  the  distant  transmitting 
station,  is  one  which  changes  period- 
ically, between  a  maximum  and 
a  minimum,  at  the  "  modulating 
frequency";  on  the  other  hand  the 
current  between  H  and  M  correspond- 

1  Rectifiers  used  in  radio  work  (such  as  crystal  detectors  and  tubes  with  or  without 
grid  condenser)  have  a  characteristic  such  that  the  current  varies  with  the  square  of  the 
e.m.f.;  the  action  of  these  rectifiers  in  connection  with  spark  telegraph  reception  is  fully 
discussed  on  pp.  343-349.  The  assumption  of  a  rectifier  with  linear  characteristic,  as 
in  Fig.  6,  does  not  involve  any  change  in  the  fundamental  principle  of  radio-p"hone 
reception,  and  is  here  made  purely  for  the  sake  of  presenting  this  matter  in  the  simplest 
possible  manner. 


RADIO-TELEPHONE  RECEIVER 


651 


Voltage 


ing  to  a  period  during  which  the  microphone  transmitter  is  idle,  is  con- 
stant. The  result  is  that  during  this  latter  period  the  receiver  diaphragm 
will  suffer  a  constant  displacement  represented  by  D0  in  Fig.  8;  while 
during  the  period  of  activity  of  the  transmitting  microphone  the  dis- 
placement of  the  receiver  diaphragm  will  change  somewhat  as  shown 
by  Bi — Di — B2 — D2  on  Fig.  8,  or,  in  other  words,  the  receiver  diaphragm 
will  be  caused  to  vibrate  at  the  modulating  frequency,  i.e.,  the  frequency 
of  the  tuning  fork  at  the  transmitting  station.  Thus,  the  vibrations  of 
the  tuning  fork  and  the  sound 
produced  thereby  will  be  dupli- 
cated by  the  vibrations  of  the 
receiver  diaphragm  at  the  re- 
ceiving station.  It  will,  of 
course,  be  understood  that  the 
amplitude  of  the  vibrations  of. 
the  receiver  diaphragm,  and 
hence  the  volume  of  sound 
emitted  thereby,  will  depend 

upon  the  strength  of  the  elec,    — 

tromagnetic  field  on  reaching 
the  receiving  antenna  and  upon 
the  receiver  and  detector  sensi- 
tiveness, etc. 

It  now  remains  to  show  that 
such  a  jadio-phone  system  as 
was  discussed  above  will  trans-  FlG.  6.— To  make  the  discussion  of  the  received 
mit  speech.  That  is,  it  is  neces-  signal  simple  a  rectifier  with  this  simple  recti- 
sary  to  show  that,  if  we  speak  fication  characteristic  is  assumed.  « 

into    the    transmitting    micro- 
phone and  thereby  cause  its  diaphragm  to  vibrate  in  accordance  with  the 
complex  air  vibrations  produced  by  speaking,  the  diaphragm  of  the  tele- 
phone   receiver  at   the  distant  receiving  station  will  vibrate  in  such  a 
manner  as  to  reproduce  speech. 

To  begin  with,  the  very  complex  vibrations  of  the  microphone  dia- 
phragm, due  to  speech,  may  be  resolved  into  an  infinite  number  of  har- 
monic components  of  different  frequencies,  different  amplitudes,  and 
bearing  certain  phase  relations  to  one  another.  Experimental  investi- 
gation has  shown,  however,  that,  while  the  number  of  these  components 
is  theoretically  infinite,  yet,  practically,  only  the  components  having 
frequencies  between  about  300  and  2000  cycles  per  second  need  be  con- 
sidered, since  the  amplitude  of  the  others  is  so  small  as  to  be  negligible. 

It  has  been  proved  l  that,  as  long  as  the  amplitudes  of  the  harmonic 
1  See  Bureau  of  Standards  Scientific  Paper  No.  127,  by  Lloyd  and  Agnew. 


652 


RADIO-TELEPHONY 


[CHAP.  VIII 


components  of  the  microphone  diaphragm  vibrations  are  reproduced  in 
the  vibrations  of  the  receiver  diaphragm  in  the  same  ratios  as  they  have 
for  the  transmitter  diaphragm,  without  any  reference  whatever  to  phase 
relations,  then  the  speech  which  caused  the  vibrations  of  the  microphone 


diaphragm  will  be  faithfully  reproduced,  without  any  distortion,  by  the 
receiver  diaphragm.  In  other  words,  without  paying  any  attention  to 
phase  relations,  it  is  sufficient  for  transmitting  speech  that  if,  as  is  gener- 
ally the  case,  the  simple  components  of  the  vibrations  of  the  microphone 
diaphragm  are  reproduced  by  the  receiver  diaphragm  with  changed  ampli- 


RADIO-TELEPHONE  RECEIVER  653 

tudes,  the  percentage  change  be  alike  for  the  amplitudes  of  all  the  component 
frequencies.  This  principle  is  of  very  great  practical  importance  not  only 
in  radio-telephony,  but  in  wire-telephony  as  well. 

We  have  already  shown  how  harmonic  vibrations  of  the  microphone 
diaphragm  having  a  single  frequency,  such  as  those  caused  by  ii  tuning 
fork,  may  be  reproduced  in  the  receiver  diaphragm.  It  is  plain  that  the 
amplitude  of  the  displacement  of  the  receiver  diaphragm  depends  upon  the 
intensity  of  the  electromagnetic  field  on  reaching  the  receiving  antenna 
and  upon  the  constants  of  the  receiving  circuit,  including  the  sensitiveness 
of  the  rectifier  and  of  the  telephone  receiver,  as  well  as  the  amount  of 
coupling  between  the  open  and  closed  circuits,  the  damping  thereof,  and 
also  whether  the  rectified  current  is  amplified  by  a  suitable  amplifier  or 
not.  Of  course  the  intensity  of  the  electromagnetic  field  at  the  receiving 
antenna  is  a  function  of  the  distance  between  the  transmitting  and  receiving 
antennas,  the  wave-length  ^corresponding  to  the  carrier  frequency,  the 
height  of  the  two  antennas  and  the  absorption  of  energy  due  to  the  inter- 
vening medium,  which  is  in  turn  a  function  of  the  wave-length;  hence, 
no  matter  what  the  value  of  the  modulating  frequency  or  the  frequency 
of  the  transmitter  diaphragm,  the  per  cent  change  in  amplitude  as  related 
to  the  displacement  of  the  receiver  diaphragm  must  be  the  same  for  all 
values  of  modulating  frequency,  because  the  percentage  of  radiated  energy 
which  reaches  the  receiving  antenna  is  dependent  upon  the  carrier  fre- 
quency and  not  upon  the  modulating  frequency.  Again,  as  regards  the 
effect  of  the  constants  of  the  receiving  circuit  upon  the  amplitude  of  the 
receiver  diaphragm  displacement  the  receiving  circuit  may  be  so  chosen 
and  adjusted  that  it  will  affect  all  modulating  frequencies  within  the  speech 
range  to  approximately  the  same  extent. 

It  follows  from  the  above  that,  if  the  transmitting  diaphragm  be 
spoken  into,  the  displacement  of  the  diaphragm  corresponding  to  each 
of  the  possible  harmonic  components  of  its  vibrations  will  be  reproduced 
in  the  receiver  diaphragm  with  practically  the  same  percentage  change  in 
amplitude,  and  hence  speech  will  be  correctly  reproduced. 

The  carrier  frequency  should  be  much  higher  than  the  highest  important 
speech  frequency,  which  is  in  the  neighborhood  of  5000  cycles  per  second ; 
therefore,  the  carrier  frequency  should  be  at  least  above,  say,  15,000 
cycles  per  sec.  and,  as  a  matter  of  fact,  in  actual  practice  it  is  seldom  lower 
than  100,000  cycles  per  sec.,  and  a  frequency  as  high  as  6,000,000  cycles 
per  sec.  has  been  used. 

It  might  be  thought  that  this  carrier  frequency  may  be  dispensed 
with  and  the  vibrations  of  the  telephone  diaphragm  may  be  caused  to 
produce  antenna  currents  of  audio  frequency,  by  means  of  a  circuit  arrange- 
ment somewhat  as  shown  in  Fig.  9,  where  the  microphone  M  would,  on 
being  spoken  into,  produce  audio  frequency  currents  in  the  antenna, 


654 


RADIO-TELEPHONY 


[CHAP.  VIII 


through  the  means  of  the  transformer  T.  This  system  would  fail,  because 
it  would  require  a  prohibitively  large  antenna  in  order  that  the  audio 

- frequency  currents   might  cause 

sufficient  energy  to  be  radiated 
for  successful  transmission  over  a 
reasonable  distance;  hence  the  use 
of  the  "  high-frequency  carrier."  1 
It  is  hardly  necessary  to  em- 
phasize the  fact  that  the  genera- 
tor of  the  high-frequency  carrier 
must  be  such  as  to  cause  by 
itself  no  change  in  the  amplitude 
of  the  high-frequency  carrier; 
otherwise  this  would  be  heard 
in  the  receiver,  together  with  the 
speech,  and  would  interfere  with 
the  latter.  In  other  words,  the 

high-frequency   generator    must 

FIG.  9. — Such  a  scheme  as  this,  dispensing  with        ,  -    ,      ,.  -xl    ^  ,   ,    ,. 

the  carrier  frequency,  cannot  be  used  because  ROt  mterfere  wlth  the  modulation 
practically  no  power  can  be  radiated  from  of  the  high-frequency  current  as 
an  antenna  with  currents  of  voice  frequency,  brought  about  by  the  microphone 

transmitter. 

Sources  of  Power. — The  sources  of  power  which  may  be  used  are 
those  which  will  produce  undamped  high-frequency  currents.     (See  p.  580, 
Chapter  VII.)     Of  these  various  sources  the  following  have  been  most 
generally  used  for  radio-telephony: 
The  Poulsen  Arc. 

The  Alexanderson  or  Fessenden  Alternator. 
The  Oscillating  Vacuum  Tube. 

All  of  the  above  have  been  fully  described  in  Chapters  VI  and  VII,  and  we 
shall,  in  this  chapter,  study  the  manner  only  in  which  each  of  them  may 
be  connected  for  successful  radio  transmission  of  speech. 

Before  going  any  further  we  will  first  briefly  describe  various  types 
of  telephone  transmitters  and  will  later  discuss  the  manner  of  using  them 
in  radio-telephone  circuits. 

Transmitters. — The  transmitters  used  for  radio-telephone  are  broadly 
divided  into  two  general  classes  on  the  basis  of  their  current  carrying 
capacity,  i.e.: 

(a)  Low-current  or  low-capacity  transmitters. 
(6)  High-current  or  high-capacity  transmitters. 
The  low-current  transmitter  for  radio-telephony  does  not  differ  from 

1  It  is  shown  in  Chapter  IX,  that  the  power  radiated  from  a  simple  antenna  increases 
with  the  square  of  the  frequency . 


THE   MICROPHONE   TRANSMITTE 


655 


the  transmitter  used  in  wire  telephony,  and  its  most  common  type  will 
here  be  described.  This  type  is  known  as  the  solid-back  carbon  trans- 
mitter. The  simple  schematic  diagram  of  Fig.  10  illustrates  its  construction 
when  stripped  of  details.  It  consists  of  an  elastic  diaphragm  A  mounted 
upon  the  rubber  ring  FF,  which  is  in  turn  held  against  E,  the  diaphragm 
being  mechanically  connected  to  the  carbon  block  B'.  B'  is  placed  opposite, 
another  carbon  block  B  in  a  chamber  filled  with  small  carbon  granules  C; 
this  chamber  is  closed  by  means  of  the  mica 
washer  G  and  the  insulating  nut  H.  The 
two  carbon  blocks  B  and  B'  form  the  two 
electrical  terminals  of  the  transmitter;  the 
wall  of  the  chamber  containing  the  granules 
is  covered  with  a  strip  of  paper  designated 
by  D;  if  a  source  of  e.m.f.  be  connected 
to  B  and  B'  it  will  send  a  current  from  B 
through  the  carbon  granules  and  to  B',  or 
vice  versa.  On  speaking  into  the  trans- 
mitter the  diaphragm  is  caused  to  vibrate, 
and  these  vibrations  are  mechanically  trans- 
ferred to  the  block  B'  so  that  the  latter's 
pressure  upon  the  carbon  granules  is  made 
to  vary;  this  varies  the  resistance  between 
B  and  B',  and  hence  it  varies  also  the  cur- 
rent in  the  circuit  wherein  the  transmitter 
is  connected. 

Such  an  arrangement  is  very  sensitive  to  FIG.  10. — Internal  construction  of 

changes  in  pressure  on  the  diaphragm  and  is  theu  ordinary  microphone;  the 
,  ,  -,,  mi  carbon  granules  between  plates 

known  as  a  microphone  transmitter.     The      g  and  * ,  are  the  seat  J  ^ 

current  carried  by  such  a  transmitter  is  very      variable  resistance, 
small  because  of  the  fact  that  a  limit  is  soon 

reached  beyond  which  "  arcs "  are  developed  between  granules,  the 
contact  points  of  which  become  red  hot,  and  the  transmitter  becomes 
useless.  The  current-carrying  capacity  of  an  ordinary  transmitter  is 
about  0.1  ampere,  and  its  average  resistance  when  not  spoken  into  is  50 
to  100  ohms,  so  that  the  power  capacity  is  a  maximum  of  0.12X100  or 
1  watt.  Some  special  microphone  transmitters  "  low  resistance,"  may  be 
obtained  which  have  a  resistance  of  10  to  20  ohms  and  a  current-carrying 
capacity  of  0.5  ampere,  or  a  maximum  power  capacity  equal  to  0.52X20 
or  5  watts. 

The  high-current  or  high-capacity  transmitter  has  received  a  good 
deal  of  attention  at  the  hands  of  radio  engineers  and  inventors,  and  many 
types  have  been  developed,  the  most  important  of  which  will  be  very 
briefly  described.  The  reader  is  referred  for  more  information  upon 


656  RADIO-TELEPHONY  [CHAP.  VIII 

this  subject  to  a  more  detailed  treatise  on  radio  telephony.1    These  trans- 
mitters might  be  grouped  into  two  general  classes: 

(1)  Those  using  carbon  granules. 

(2)  Those  using  liquid  jets. 

In  the  first  class  belong  several  types  of  transmitters  wherein  the 
carbon  granules  of  the  microphone  transmitter  previously  described  are 
kept  from  overheating  by  an  air  fan,  or  by  the  circulation  of  water  or  by 
using  a  slowly  flowing  stream  of  carbon  granules.  Again,  in  one  type, 
a  number  of  microphones  are  connected  in  series — multiple,  thus  producing 
a  transmitter  of  much  larger  current  and  power  capacity  than  the  individual 
microphones;  such  transmitters  may  be  constructed  to  carry  from  3  or  5 
amperes  without  overheating. 

Typical  of  the  second  class  is  Chambers'  liquid  microphone,  illustrated 
in  Fig.  11.  This  consists  briefly  of  a  metallic  diaphragm  A,  against  which 

there  is  made  to  flow  a  stream  of  electro- 
lyte  B  coming    from    the   pipe    C.      The 
terminals  of  the  transmitter  are  attached 
to  A  and  C.     The  vibrations   of  the   dia- 
FIG.  ll.-A  simple  type  of  liquid  PhraSm  ™y  the  area  of  contact  between 
jet  microphone,  designed  to  give  itself  and  the  jet  and  thus  vary  the  resist- 
low  resistance  and  high  power-  ance  between  C  and  A.     The  capacity  of 
absorbing  capacity.  Buch  a  transmitter  is  quite  high,  in  so  far 

as  the  only  limitation  is  the  eventual  boil- 
ing of  the  liquid;   it  has  been  constructed  to  take  care  of  400  watts. 

Thus,  low-capacity  transmitters  may  be  constructed  of  1  to  5  watt 
capacity  and  100  to  10  ohms  resistance  respectively,  while  high-capacity 
transmitters  have  been  constructed  of  50-  to  500-watt  capacity  and  of 
about  8  to  4  ohms  resistance,  respectively. 

Conditions  for  Best  Modulation. — We  will  again  note  that  the  speech 
transmission  is  brought  about  simply  by  changing  the  amplitude  of  the 
transmitting  antenna  current  (modulation  of  antenna  current) ;  in  other 
words,  if  the  amplitude  of  the  antenna  current  should  be  changed  but 
little  by  the  operation  of  the  telephone  transmitter,  speech  would  be 
transmitted  but  poorly  and  to  a  short  distance,  while  the  opposite  is  true. 
In  other  words,  the  range  and  quality  of  transmission  does  not  quite 
depend  upon  the  amount  of  current  in  the  transmitting  antenna,  but 
upon  the  change  in  this  current  or  the  extent  of  the  modulation.  Hence, 
a  radio-phone  system  should  be  so  designed  as  to  enable  the  telephone 
transmitter,  when  spoken  into,  to  produce  the  maximum  possible  change 
in  the  antenna  current.  This  corresponds  to  a  condition  where  the  antenna 
current  amplitude  is  caused  to  reach  a  miminum  of  zero,  and  a  maximum 
which  is  dependent  upon  the  characteristic  of  the  rectifier  in  the  receiving 
1  See  "  Radio-Telephony,"  by  A.  N.  Goldsmith;  The  Wireless  Press. 


ANALYSIS  OF   MODULATION 


657 


circuit.  It  is  therefore  necessary  to  investigate  at  this  point  the  effect 
of  the  rectifier  characteristic  upon  the  best  conditions  for  modulation. 

Analysis  of  Modulation. — Assume,  as  before,  the  simple  transmitting 
circuit  represented  by  Fig.  1  and  thej  simple  receiving  circuit  represented 
by  Fig.  4;  and  let  us  again  suppose  that  a  harmonically  varying  sound 
pressure  is  impressed  upon  the  microphone  diaphragm  by  means  of,  say, 
a  tuning  fork  placed  in  front  of  it.  We  then  desire  that  the  telephone 
receiver  in  the  receiving  circuit  shall  give  off  a  pure  sine  wave  tone  of  the 
frequency  of  the  tuning  fork. 

We  will  first  investigate  the  case  where  the  amplitude  of  the  trans- 
mitting antenna  current  is  made  to  change  by  the  action  of  the  micro- 
phone from  a  maximum  of  twice  that  corresponding  to  the  microphone  idle 
to  a  minimum  of  zero,  this  being  what  is  known  as  a  "  completely  modu- 
lated current."  Fig.  12  shows  the  curve  of  the  e.m.f.  produced  in  the 


FIG.  12. — A  completely  modulated  antenna  current,  having  a  sine-wave  envelope. 

receiving  antenna  circuit  by  the  flow  of  the  completely  modulated  current 
in  the  transmitting  antenna;  the  e.m.f.  across  the  rectifier  in  the  receiving 
circuit  of  Fig.  4  will  be  of  the  same  form  as  Fig.  12,  though,  of  course, 
reduced  in  amplitude. 

If  we  assume,  as  we  did  before,  a  rectifier  giving  a  rectified  current 
proportional  to  the  first  power  of  the  impressed  voltage  than  the  har- 
monically modulated  e.m.f.  of  Fig.  12  would  produce  a  rectified  current 
the  amplitude  of  which  would  vary  harmonically,  as  shown  by  the  points 
marked  A  in  Fig.  13,  and  the  result  would  be  that  the  average  current 
in  the  telephone  receiver  would  also  vary  harmonically  and  cause  this 
to  give  off  a  pure  harmonic  note  of  the  same  pitch  as  that  of  the  tuning 
fork. 

But,  as  already  pointed  out  in  the  footnote  on  p.  650,  practically  all 
rectifiers  give  a  rectified  current  proportional  to  the  square  of  the  impressed 
voltage;  hence  the  harmonically  modulated  e.m.f.  of  Fig.  12  would  pro- 
duce the  rectified  current  represented  by  curve  B  in  Fig.  13,  and  the  curve 


658 


RADIO-TELEPHONY 


[CHAP.  VIII 


of  the  average  current  in  the  telephone  receiver  would  be  as  represented 
by  the  dotted  curve  C  of  Fig.  13,  and  would,  evidently,  not  vary  harmon- 
ically. So  that,  in  this  case,  the  receiving  circuit  telephone  would  give 


Average  Current  through 
Telephone  Receiver 


FIG.  13. — The  current  of  Fig.  12,  in  combination  with  such  a  rectifier  as  that  assumed  in 
Fig.  6,  would  give  a  rectified  current  as  shown  by  the  points  A ;  its  average  value 
would  be  a  sine-wave  current.  If  an  ordinary  rectifier  is  used  the  rectified  current 
is  as  shown  by  the  solid  line  curves,  the  average  value  of  which  is  shown  by  the 
dotted  curve  which  is  not  a  simple  harmonic  current  but  is  more  complex  in  form. 

off  a  note,  which,  though  of  the  same  pitch  as  that  impinging  upon  the 
transmitting  microphone,  would  be  of  a  more  complex  quality. 

To  remedy  the  objectionable  condition  brought  about  by  the  combina- 
tion of  a  harmonically  modulated  transmitting  antenna  current  and  a 
rectifier  giving  a  current  proportional  to  the  square  of  the  impressed 


FIG.  14. — A  type  of  modulated  current  in  which  the  square  of  the  amplitude  varies  as  a 

sine  wave. 

voltage  it  is  necessary  that  the  transmitting  antenna  current  be  differently 
modulated.  Thus,  assume  that  the  transmitting  antenna  current  is 
modulated  in  such  a  manner  that  the  difference  between  the  square  of 
its  amplitude  when  modulated  and  that  when  not  modulated  varies 
with  the  sine  of  a  uniformly  varying  angle,  so  that,  if  /o  =  amplitude 


ANALYSIS   OF   MODULATION 


659 


of  antenna  current  with  microphone  idle,  the  maximum  amplitude 
will  be  \/2  /o  and  the  minimum  zero.  Then,  the  curve  of  the  e.m.f. 
acting  upon  the  receiving  antenna  will  be  as  represented  by  Fig. 
14,  the  rectified  current  will  be  as  represented  by  curve  A,  Fig.  15,  and 
will  have  amplitudes  which  will  vary  harmonically,  and,  therefore,  the 
average  current  through  the  telephone  receiver,  represented  by  curve  B, 
Fig.  15,  will  vary  harmonically.  The  result  will  be  the  reproduction  in 
the  telephone  receiver  of  the  tuning  fork  note  without  any  change  in  the 
quality  of  the  sound. 

From  this  analysis  it  follows  that,  if  the  sound  at  the  receiver  is  to 


FIG.  15.— Such  a  current  (as  that  shown  in  Fig.  14)  in  the  transmitting  antenna,  with  an 
ordinary  type  of  detector  will  give  in  the  receiving  circuit  a  rectified  current  as  shown 
by  curves  A,  the  average  value  of  which  is  curve  B,  a  sine- wave  current. 

be  similar  in  quality  to  that  acting  at  the  transmitter,  either  of  the  two 
following  conditions  must  be  satisfied: 

(a)  If  the  receiver  circuit  rectifies  proportionally  to  the  first  power  of 
the  voltage  impressed  upon  it,  then  the  difference  between  the  amplitude 
of  the  antenna  current  with  the  microphone  in  operation  and  that  with 
the  microphone  idle  should  vary  in  direct  proportion  to  the  pressure  of 
the  sound  waves  on  the  microphone,  or,  in  symbols 

I-Io=kp (1) 

where  7=  amplitude   of  the   antenna   current   with   the   trans- 

mitter in  operation; 

/o  =  amplitude   of   the   antenna   current   with   the   trans- 
mitter idle ; 

k  =a  constant  of  proportionality; 
p  =the  pressure  of  the  sound  waves  upon  the  microphone. 

(6)  If  the  receiver  circuit  rectifies  proportionally  to  the  square  of  the 
voltage  impressed  upon  it  then  the  difference  between  the  square  of  the  ampli- 


660  RADIO-TELEPHONY  [CHAP.  VIII 

tude  of  the  antenna  current  with  the  microphone  in  operation  and  that 
with  the  microphone  idle  should  vary  in  direct  proportion  to  the  pressure 
of  the  sound  waves  on  the  microphone,  or,  in  symbols  : 

P-I02  =  kp,      .........     (2) 


where  7,  IQ,  p  have  the  same  significance  as  in  Eq.  (1)  and  k  =  the  con- 
stant of  proportionality. 

Of  course,  in  practice,  neither  of  the  two  conditions  set  forth  above 
is  fully  and  entirely  satisfied  throughout  the  entire  range  of  pressures 
impressed  upon  the  microphone  diaphragm,  and  the  speech  transmission 
is,  therefore,  never  ideal. 

Percentage  of  Modulation.  —  The  percentage  of  modulation  is  expressed 
by  means  of  the  following  equation  : 


(3) 


where  /o  =  amplitude  of  antenna  current  with  microphone  idle; 

Di  =  difference  between  IQ  and  minimum  antenna  current 

amplitude  ; 
M  =  percentage  of  modulation. 

In  the  ideal  case  of  a  "  completely  modulated  "  antenna  current  D\  =/o 
and  M  =  100  per  cent. 

Of  course,  in  designing  a  radio-phone  transmitter,  the  aim  is  to  make 
the  percentage  of  modulation  as  large  as  possible  without,  at  the  same 
time,  interfering  with  the  quality  of  the  transmission. 

In  view  of  this  the  idle  resistance  of  the  telephone  transmitter  and 
the  change  in  the  resistance  must  be  carefully  chosen  with  respect 
to  the  resistance  of  the  rest  of  the  system.  Thus,  considering  the  simple 
circuit  represented  by  Fig.  1,  p.  647,  it  is  plain  that  if  the  idle  resistance 
of  the  telephone  transmitter  were  much  lower  than  that  of  the  balance 
of  the  circuit,  then  any  change  in  the  former  could  not  appreciably  affect 
the  total  resistance  and,  hence,  could  not  effectively  modulate;  on  the 
other  hand,  if  the  reverse  were  the  case  the  antenna  power  radiation 
would  be  very  small,  since  the  largest  percentage  of  the  alternator  power 
output  would  be  absorbed  by  the  transmitter.  Thus,  there  must  be  a 
best  telephone  transmitter  resistance  and  this  was  shown  by  Seibt  to 
be  equal  to  that  of  the  rest  of  the  antenna  circuit. 

In  many  of  the  systems  of  radio-telephony  the  telephone  transmitter 
is  not  placed  directly  in  the  antenna  circuit,  but,  in  practically  every 
case,  it.  is  so  connected  that,  by  speaking  into  it,  an  effect  is  produced 
which  is  equivalent  to  changing  the  resistance  of  the  antenna  circuit; 
the  telephone  transmitter  resistance  may,  in  these  cases,  be  transferred 


ANALYSIS  OF   MODULATION  661 

in  the  form  of  an  equivalent  resistance,  to  the  antenna  circuit.  Hence 
in  practically  every  case,  whether  the  telephone  transmitter  is  directly 
in  the  antenna  circuit  or  not,  it  should  be  observed  that  the  optimum 
idle  resistance  of  the  telephone  transmitter  is  such  that,  when  trans- 
ferred to  the  antenna  circuit,  it  should  be  equal  to  the  rest  of  the  antenna- 
circuit  resistance. 

As  regards  the  variation  in  the  telephone  transmitter  resistance  it 
will  be  noted  that,  considering  the  simple  system  of  Fig.  1,  and  assuming 
the  idle  resistance  equal  to  the  balance  of  the  antenna  circuit,  then  in 
order  to  obtain  100  per  cent  modulation  with  a  harmonic  sound  wave 
and  with  a  receiver  rectifying  proportionally  to  the  square  of  the  impressed 
voltage  the  resistance  of  the  telephone  transmitter  should  change  from 
41  per  cent  of  its  idle  resistance  to  infinity.  For,  when  it  is  41  per  cent 
of  the  idle  resistance  the  antenna  current  amplitude  would  be  \/2  /o, 
and  when  it  is  infinity  the  amplitude  of  the  antenna  current  would  be  zero. 
Of  course,  it  will  be  easily  realized  that  such  extreme  variation  of  resistance 
is  almost  impossible  of  practical  accomplishment  by  means  of  a  micro- 
phone; hence  100  per  cent  modulation  by  this  scheme  is  impossible. 

In  practice  50  to  60  per  cent  modulation  is  striven  for;  higher  values 
may  be  obtained,  but  are  not  desirable  with  the  circuit  arranged  as  in 
Fig.  1,  because  with  such  wide  variations  of  microphone  resistance  the 
current  variations  do  not  truly  represent  the  voice,  and  the  received 
signal  under  these  conditions  is  indistinct  and  blurred. 

Various  Schemes  for  Modulation. — These  depend  very  much  upon 
the  source  used  for  producing  undamped  high-frequency  currents,  although 
they  vary  even  for  the  same  type  of  source.  The  most  important  ones 
will  be  considered  in  connection  with  the  high-frequency  alternator  and 
the  Poulsen  arc,  and  a  special  section  will  be  devoted  to  the  case  of  tube 
oscillators. 

Referring  to  Fig.  16,  in  which  various  schemes  are  shown  (a)  is  the 
same  as  Fig.  1  of  p.  647,  and  has  already  been  discussed.  (6)  shows 
the  telephone  transmitter  connected  in  series  with  the  exciting  field  of  the 
alternator;  as  the  resistance  of  the  telephone  transmitter  is  changed  the 
alternator  e.m.f.  is  changed  and  so  is  the  amplitude  of  the  antenna  cur- 
rent, (c)  is  similar  to  (a)  except  that  the  high-frequency  current  is  sup- 
plied to  the  antenna  by  a  Poulsen  arc  and  not  by  an  alternator,  (d)  has 
the  telephone  transmitter  in  the  oscillating  circuit  of  the  Poulsen  arc, 
thus  changing  the  amplitude  of  the  current  in  this  circuit  and  hence  in 
the  antenna  circuit.  Many  other  ways  of  connecting  the  telephone  trans- 
mitter, especially  for  the  Poulsen  arc,  have  been  tried  and  found  more 
or  less  successful. 

As  regards  the  four  types  illustrated  above  it  is  plain  that  in  every 
one  except  (6)  the  transmitter  should  be  of  large  current  capacity — low 


662 


RADIO-TELEPHONY 


[CHAP.  VIII 


resistance,  since  it  carries  either  the  antenna  current  or  the  current  in  the 
oscillating  circuit  of  the  Poulsen  arc.  In  case  (6)  the  transmitter  need 
only  be  of  low  capacity — high  resistance,  since  it  only  carries  the  field 
current  of  the  alternator.  However,  in  this  case  a  certain  change  in  the 
resistance  of  the  transmitter  may  not  produce  a  proportional  change  in  the 
amplitude  of  the  antenna  current  (a  requirement  for  good  modulation) 
unless  the  magnetic  field  of  the  alternator  is  far  from  saturated  and  the 
self-induction  of  the  field  circuit  is  sufficiently  low. 


"==•      Field  ofx  Alternate 


To  D.C. 

Supply 


(c) 


FIG.  16. — Various  simple  schemes  for  connecting  the  microphone  to  the  source  of  power 
to  produce  modulation;  none  of  these  is  used  in  the  better  types  of  radio-telephone 
transmitters,  however. 

The  Vacuum  Tube  in  Radio-Telephony. — Fig.  17  shows  an  elementary 
type  of  circuit  which  has  been  very  seldom  used  but  which  illustrates 
the  principle  very  well.  It  consists  of  the  oscillating  circuit  illustrated 
by  Fig.  126,  p.  513,  with  the  telephone  transmitter  connected  directly 
in  series  with  the  antenna.  Its  principle  of  operation  is  exactly  the  same 
as  that  of  the  simple  system  illustrated  by  Fig.  1  except  that  the  tube 
oscillator  has  replaced  the  alternator.  This  particular  tube  oscillator 
circuit  is  known  as  the  Meissner  circuit. 


SCHEMES  OF   MODULATION 


663 


Fig.  18  illustrates  a  method  of  connecting  the  telephone  transmitter 
in  the  grid  circuit  of  the  oscillator.  In  this  case  if  the  telephone  trans- 
mitter is  idle  the  amplitude 
of  the  antenna  current  will 
be  constant,  but  if  the 
transmitter  is  excited  by 
sound  waves  a  changing 
current  will  be  produced 
in  the  circuit  of  (1),  which 
will  produce  an  e.m.f .  across 
the  terminals  of  the  coil  S, 
this  e.m.f.  being  a  function 
of  the  vibrations  of  the 
telephone  diaphragm.  Thus 
the  grid  of  the  oscillator 


FIG.  17. — Simple  circuit  for  telephone  transmitters 
using  a  vacuum  tube  for  power:  this  has  been 
sometimes  used  in  low  power  sets. 


will  have  impressed  upon 
it  not  only  the  high-fre- 
quency e.m.f.  due  to  the 

interactions  of  the  coils  A-B,  but  also  the  low-frequency  e.m.f.  due  to  the 
speech;  the  effect  of  this  low-frequency  e.m.f.  is  to  increase  or  decrease 
the  grid  potential  above  or  below  what  it  would  otherwise  be  if  the  trans- 
mitter were  idle; 
and  since  the  grid 
potential  reacts 
upon  the  antenna 
current  by  means 
of  the  tube  and 
the  coils  C-A,  it 
is  plain  that  the 
amplitude  of  the 
antenna  current 
will,  instead  of 
being  constant,  be 
changed  in  accord- 
ance with  the 

FIG.  18. — In  this  scheme  of  modulation  (frequently  used  in  low-  e  m  f  of  *S  or  of 
power  transmitters)  the  current  from  the  transmitter  circuit  ,J  -i  t*Ons  of 
operates  to  change  the  average  potential  of  the  grid  of  the  oscil-  . . 

lating  tube,  thus  effectively  modulating  the  antenna  current.  tne  telephone  dia- 
The  condenser  shunting  S  must  have  a  low  reactance  for  the  phragm.  In  this 
radio  frequency  and  should  have  at  least  106  ohms  for  the  type  of  connection 
highest  voice  frequency .  it  ig  plajn  tnat  the 

telephone  transmitter  may  be  of  very  low  power  capacity;  this  is  such  an 
evident  advantage  that,  as  a  matter  of  fact,  practically  all  of  the  modern 


664 


RADIO-TELEPHONY 


[CHAP.  VIII 


radiophone  tube  systems  have  their  telephone  transmitters  connected  in 
some  such  way  to  the  grid  of  a  tube. 

The  above  two  methods  of  telephone  transmitter  and  tube  oscillator 
are  typical,  in  so  far  as,  while  they  have  been  shown  for  a  certain  type 
of  oscillator  circuit,  they  may  be  applied  in  an  exactly  similar  manner 
to  any  type  of  tube  oscillator. 

We  will  now  discuss  another  type  of  radiophone  tube  connection 
due  to  Heising,  wherein  two  tubes,  or  two  sets  of  tubes,  must  be  used; 
it  is  illustrated  in  Fig.  19.  In  this  system  the  part  to  the  left  of  the  dotted 
line  represents  the  oscillator  circuit,  which  has  been  discussed  on  p.  561, 
Chapter  VI.  When  the  telephone  transmitter  is  not  operative  the  poten- 
tial difference  across  the  points  Q  and  0  is  constant,  and  hence  the  ampli- 
tude of  the  high-frequency  antenna  current,  as  well  as  the  plate  current  for 


Modulator 


FIG.  19. — A  scheme  of  modulation  due  to  Heising  in  which  a  separate  tube  is  used  to 
accomplish  modulation;  the  scheme  has  been  extensively  used  in  small  transmitters 

the  modulator  tube,  is  constant.  However,  if  the  telephone  transmitter 
is  spoken  into  e.m.f.'s  are  induced  in  the  coil  S,  which  change  the  potential 
of  the  modulator  grid  in  accordance  with  the  vibrations  of  the  transmitter; 
this  changes  the  plate  current  of  the  modulator  or  the  current  between  the 
points  Q  and  Pm,  this  change  taking  place  at  speech  frequency,  or  audio 
frequency.  In  virtue  of  this  the  battery  B  will  be  called  upon  to  supply 
a  current  varying  at  audio  frequency,  which  current  must  flow  through 
the  iron-core  inductance  D ;  since  the  impedance  of  this  is  very  high 
at  audio  frequency,  it  follows  that  it  will  cause  a  large  audio-frequency 
-drop  of  potential  over  itself,  and  thus  the  potential  difference  between 


HE1S1NG  SCHEME  FOR  MODULATION  065 

the  points  Q  and  0  will  be  varied  at  audio  frequency  and  in  accordance 
with  the  vibrations  of  the  telephone  transmitter.  Again,  since  the  poten- 
tial difference  impressed  upon  the  plate  of  the  oscillator  (i.e.,  that  across 
Q  and  0)  is  being  varied,  it  finally  follows  that  the  amplitude  of  the  antenna 
current  will  thereby  be  varied,  since  the  amplitude  of  the  antenna  current 
increases  with  increase  of  the  plate  voltage.  Thus,  the  vibrations  of  the 
telephone  transmitter  are  finally  reproduced  in  the  antenna  as  variations 
in  the  amplitude  of  the  antenna  current  or,  in  other  words,  the  antenna 
current  is  thereby  modulated. 

The  function  of  the  coil  D  may  be  more  clearly  seen  if  the  coil  were 
assumed  to  be  short-circuited.  Under  these  conditions,  no  matter  how 
much  the  modulator  plate  current  were  caused  to  vary  by  the  action  of 
the  transmitter,  the  potential  difference  across  the  points  Q  and  0  would 
remain  constant,  and  no  change  would  be  effected  in  the  amplitude  of 
antenna  current. 

The  function  of  the  choke  coil  A,  which  should  be  an  air  core  coil, 
is  to  prevent  the  plate  circuit  of  the  modulator  tube  from  taking  from  the 
antenna  circuit  any  of  the  high-frequency  power  which  the  oscillator  tube 
is  supplying  to  it;  the  proper  amount  of  inductance  for  coil  A  depends 
upon  the  types  of  tubes  used,  but,  in  general,  its  reactance  should  be  con- 
siderably greater  than  the  plate-circuit  resistance  of  the  modulator  tube. 

Analysis  of  Heising  Scheme  of  Modulation.1 — This  scheme  of  modu- 
lation is  probably  better  than  any  other  so  far  suggested,  and  we  are 
therefore  giving  a  more  complete  analysis  of  its  operation. 

Let  us  first  suppose  that  the  coil  D,  Fig.  19,  has  so  much  reactance 
that  no  appreciable  change  of  current  through  it  occurs  due  to  the  action 
of  the  microphone.  We  will  assume,  as  has  been  done  before,  that  the 
microphone  is  actuated  by  a  sine  wave  of  sound,  and  furthermore,  that  the 
sine  wave  of  sound  gives  a  sine  wave  of  e.m.f.  across  the  secondary  termi- 
nals of  the  transformer  S.  (In  order  that  the  possible  variation  in  the 
impedance  of  the  grid-filament  circuit  of  the  modulating  tube  may  not  pro- 
duce distortion  of  the  terminal  voltage  of  the  transformer  secondary,  a 
high  resistance  R  of  constant  value  is  permanently  connected  across  the 
secondary  to  give  the  load  circuit  of  the  transformer  an  essentially  constant 
impedance.)  The  potential  variations  of  the  modulator  grid  will  cause 
its  plate  current  to  pass  through  sinusoidal  variations,  and  will  thus 
make  the  plate  circuit  of  the  modulator  behave  like  a  variable  resistance 
connected  across  the  points  Q  and  0  in  multiple  with  the  plate  circuit 
of  the  oscillator  tube.  This  is  schematically  indicated  in  Fig.  20,  where 
-Rmod  represents  the  variable  resistance  of  the  oscillator  plate  circuit  and 
ROM  represents  the  resistance  of  the  oscillator  plate  circuit. 

Let  7mod  =  current  in  plate  circuit  of  modulator;  1^  =  current  in  plate 
circuit  of  oscillator;   Ib  =  current  supplied  by  the  plate  battery. 
1  See  Radio  Review,  Feb.  1922,  p.  110. 


666 


K  AU10-TELEPHON  Y 


[CllAP.  VIII 


If  we  now  suppose  that  /mod  is  due  to  the  vibrations  of  the  microphone 
diaphragm,  caused  to  change  from  zero  to  twice  its  average  value,  then, 

since  we  have  assumed  that  the  coil  L 
has  such  reactance  as  to  keep  h  essen- 
tially constant,  it  follows  that  the  cur- 
rent /osc  must  increase  and  decrease 
about  its  average  value  to  the  same 
extent  as  does  /mod.  Of  course,  as  the 
value  of  /osc  is  changed  in  response  to  the 
vibrations  of  the  microphone  diaphragm, 

FIG.  20.-Simple  representation  of  the    the  POW6r    ^iven  tO  the  antenna    in  the 


mod 


Heising  scheme  of  modulation. 


form  of  high-frequency  current  must  be 
changed  and  so  must  the  amplitude  of 
the  antenna  current;  in  other  words,  modulation  of  the  antenna  current 
is  made  to  take  place. 

The  variations  of  some  of  the  quantities  involved  in  this  scheme  of 
modulation  are  represented  in  Fig.  21,  where  the  various  curves  are  self- 
explanatory;  the  current  /osc  for  any  instant  is  obtained  by  subtracting 
from  the  essentially  constant  /&  the  value  of  /m0d  at  that  instant. 

Now,  if  we  investigate  the  variation  in  the  power  supplied  to  the  oscil- 
lator, it  will  be  noted,  by  referring  to  Fig.  20,  that,  since  .Rose  is  a  constant 
resistance  the  current  through  which  is  changing  from  zero  to  twice  its 
average  value,  then  the  power  expended  in  Row  must  vary  from  zero  to 
four  times  its  average  value.  But  since  the  power  expended  in  ROM  is 
equal  to  the  current  multiplied  by  the  voltage  across  it,  it  follows  that 
not  only  must  the  current,  /osc,  vary  from  zero  to  twice  its  average  value, 
but  the  voltage  across  it  must  also  do  the  same  ;  that  is,  the  voltage  across 
the  points  Q-0,  Fig.  19,  must  vary  from  zero  to  twice  its  average  value. 

This  result  would  seem  to  be  contradictory  to  our  assumption  pre- 
viously made  that  the  current  ID  is  constant;  for  if  Ib  is  constant  there 
can  be  no  change  whatever  in  the  voltage  across  Q  and  0.  But,  as  a  matter 
of  fact,  Ib  does  vary,  though  the  amount  of  this  variation  may  be  small 
if  the  inductance  of  the  coil  D  (Fig.  19)  is  large;  thus  it  might  easily  be 
that  a  variation  in  /&  of  only  20  per  cent  at  the  modulating  frequency 
would  cause  the  voltage  across  Q  and  0  to  change  from  zero  to  double 
its  average  value.  In  some  actual  radiophone  sets  employing  this  circuit 
we  have  the  following  : 

Average  value  of  h  =0.08  ampere 
Inductance  of  coil  D  =  2  henries. 
Voltage  of  plate  battery  =300 

If,  then,  a  maximum  variation  in  /&  of  20  per  cent  should  take  place  at 
a  modulating  frequency  of  1000  cycles  per  sec.  we  would  have: 

Maximum  voltage  drop  over  D  =  2ir  X  1000  X  2  X  0.2  X  0.08  =  200 


HEISING   SCHEME  FOR   MODULATION 


667 


Hence  the  voltage  across  Q  and  O  would 
vary  from  300-200  to  300+200  or  from 
100  to  500. 

The  circuit  shown  in  Fig.  20  is  not 
exactly  equivalent  to  the  actual  tube  cir- 
cuit, because  in  this  the  value  of  R^  does 
not  remain  constant,  but  decreases  as  the 
voltage  impressed  on  the  tube  is  increased. 
(See  p.  425,  Chapter  VI.)  The  result  of 
this  is  that  the  variation  of  the  power  given 
to  the  oscillator  is  less  than  from  zero  to 
four  times  the  average;  but  in  all  cases, 
however,  the  power  variation  is  greater 
than  from  zero  to  twice  the  average. 

If  the  power  input  to  the  antenna  in  the 
form  of  high-frequency  current  is  a  constant 
fraction  of  the  power  given  to  the  oscillator 
plate,  i.e.,  if  the  efficiency  of  the  tube  as  a 
d.c.-a.c.  converter  is  assumed  constant,  the 
power  supplied  to  the  antenna  would  vary 
about  as  shown  in  curve  (h)  of  Fig.  21  and 
the  amplitude  of  antenna  current  would 
vary  as  the  square  root  of  the  amplitude  of 
this  power  curve. 

The  radiophone  circuits  using  tubes,  and 
discussed  above,  are  only  a  few  of  the  very 
large  number  of  tube  systems  used  in 
radiotelephony,  but  they  are  typical  of  such 
systems,  and  if  the  reader  fully  understands 
these  three  he  will  have  no  difficulty  in 
grasping  any  other  system.  It  must  be 
remembered  that  every  such  system  must, 
to  begin  with,  have  an  oscillator  to  pro- 
duce high-frequency  currents  in  the  an- 
tenna, and,  in  addition,  it  must  have  some 
means  of  changing  the  amplitude  of  the 
antenna  current  in  accordance  with  sound 
waves  of  the  voice;  this  may  be  done,  as 
has  already  been  shown,  by  placing  the 
telephone  transmitter  directly  in  series 
with  the  antenna  or  in  the  grid  circuit 
of  the  oscillator  tube,  or,  again,  in  the 
grid  circuit  of  an  additional  tube,  known 


splace 
Microp 
Diaphr 

o 


1.1 


Out 


(*) 


vy 


In 


.«• 

ll 


f°o 

•So 


(d) 


v 


fs. 

nr 


is- 


FIG.  21. — Analysis   of  the  action 
of  the  Heising  scheme  of  modu- 
.  lation. 


668  RADIO-TELEPHONY  [CHAP.  VIII 

as  modulator,  and  which  amplifies  the  effects  of  the  telephone  trans- 
mitter. 

Requirements  for  Good  Modulation. — The  fundamental  requirement 
for  good  modulation  has  been  shown  on  p.  660  to  be  that  I2  —  /o2  should 
be  proportional  to  the  pressure  of  the  sound  waves  acting  upon  the  micro- 
phone diaphragm,  assuming  the  receiving  circuit  uses  an  ordinary  detector. 
It  has  been  stated  that  it  is  difficult  and  even  undesirable  to  obtain  large 
percentages  of  modulation  when  the  transmitter  is  placed  directly  in  the 
antenna,  because  of  the  extreme  variation  required  in  the  resistance  of 
the  telephone  transmitter.  However,  in  the  case  of  tube  systems,  where 
the  transmitter  is  placed  in  the  grid  of  either  the  oscillator  or  modulator, 
che  change  in  the  resistance  of  the  microphone  does  not  need  to  be  so 
extreme;  but,  unfortunately,  the  introduction  of  so  much  other  apparatus 
makes  it  more  difficult  to  fulfill  the  fundamental  requirement  for  good 
modulation.  Thus,  in  the  case  of  Fig.  19,  which  represents  one  of  the 
more  complex  systems,  the  following  conditions  would  need  to  be  satis- 
fied: 

(1)  When  the  transmitter  is  spoken  into,  the  amplitude  of  the 
displacement  of  the  diaphragm  must  be  proportional  to  the 
amplitude  of  the  sound  waves.     This  is  obtained  by  suitable 
construction  of  transmitter. 

(2)  The  variation  of  the  direct  current  in  the  circuit  of  (1)  (see 
Fig.  19)  must  be  directly  proportional  to  the  displacement  of 
the  diaphragm.     Fulfilled  within  certain  limits  by  suitably 
choosing  the  resistance  of  transmitter  and  impedance  of  pri- 
mary of  transformer. 

(3)  The  variation  in  the  plate  current  of  the  modulator  tube  must 
be  directly  proportional  to  the  variation  in  the  grid  potential 
of  this  tube;   this  is  brought  about  by  using  the  tube  on  the 
straight  portion  of  its  characteristic,  hence  the  necessity  for 
the  use  of  the  grid  battery  K  (see  Fig.  19),  another  use  of  which 
is  to  keep  the  plate  current  low,  thus  preventing  the  possibility 
of  ionization  (shown  by  blue  glow),  and  to  prevent  the  grid 
from  taking  appreciable  current  from  the  secondary  of  the 
transformer;    this  condition  being  fulfilled  by  having   K  of 
sufficient  voltage  that  even  with  the  loudest  sounds  impressed 
on  the  microphone,  the  grid  potential  does  not  become  positive. 

(4)  The  action  of  the  c.c.  power  supply  circuit  (battery  B  and  coil 
D)  should  be  such  that  the  power  supply  to  the  plate  circuit 
of  the  oscillator  tube  should  be  directly  proportional  to  the 
variation  in  plate  current  of  the  modulator  tube. 

(5)  The  action  of  the  oscillator  tube  itself  should  be  such  that  the 


ALEXANDERSON  SCHEME   FOR   MODULATION  069 

power  it  supplies  to  the  antenna  is  a  constant  fraction  of  the 
c.c.  power  input  to  its  plate  circuit. 

(6)  Even  though  the  modulator  and  power  generator  are  acting 
perfectly  the  speech  at  the  receiving  station  will  be  poor  unless 
the  decrements  of  the  three  tuned  circuits,  transmitting  an- 
tenna, receiving  antenna,  and  closed  tuned  circuit  at  receiving 
station  are  all  rather  high,  as  explained  on  p.  678. 

In  view  of  the  many  .conditions  to  be  fulfilled  for  correct  modulation 
it  is  plain  that  very  great  care  must  be  exercised  in  the  use  of  such  a  cir- 
cuit or  similar  circuits,  since  the  non-fulfillment  of  one  or  more  of  the 
above  conditions  would  seriously  affect  transmission,  making  the  received 
speech  drummy  and  indistinct. 

High-power  Telephone  Sets  Using  Tube  Generators. — In  case  a  tube 
outfit  is  used  for  a  radiophone  transmitter  of  more  than  perhaps  200  watts 
it  is  necessary  to  use  a  battery  of  oscillators,  instead  of  one  only  as  shown 
in  Fig.  19.  For  such  an  installation  two  tubes  are  arranged  as  modulator 
and  oscillator  (as  shown  in  Fig.  19)  but  the  oscillator  feeds  a  closed  circuit 
instead  of  the  antenna.  The  battery  of  high-power  tubes  are  all  connected 
in  parallel,  their  plate  circuits  feeding  into  the  antenna  and  their  grids, 
all  in  parallel,  are  excited  from  the  closed  circuit  of  the  "  pilot  "  oscillator 
which  is  of  course  modulated.  These  high-power,  separately  excited, 
tubes  are  generally  called  amplifiers,  it  being  their  function  to  amplify 
the  modulated,  high-frequency  oscillations  of  the  pilot  oscillator. 

In  recent  attempts  to  keep  the  U.  S.  S.  George  Washington  in  radio 
telephonic  communication  with  the  United  States  during  the  passage 
across  the  Atlantic,  a  combination  of  two  tubes,  modulator  and  oscillator, 
served  to  excite  a  battery  of  twelve  large  power  tubes,  the  high-frequency 
output  being  in  the  neighborhood  of  3  kw. 

It  is  generally  not  feasible  suitably  to  modulate  the  plate  current  of 
a  high-power  tube  directly  from  the  secondary  of  the  transmitter-operated 
transformer.  If  the  modulator  is  a  250-watt  tube  it  is  likely  that  the 
transmitter  transformer  will  connect  to  the  grid  circuit  of  a  small  tube, 
say  5-watt  capacity,  and  the  plate  circuit  of  the  5-watt  tube  will  furnish 
the  excitation  for  the  grid  of  the  high-power  modulator. 

Alexander  son's  Scheme  of  Modulation. — Alexander  son  has  devised 
a  scheme  whereby  the  output  of  very  large  alternators  may  be  modulated 
by  the  use  of  low-capacity  telephone  transmitter.  The  method  used 
is  mainly  based  upon  the  following  idea.  Consider  the  coils  A  and 
B,  wound  upon  an  iron  core  as  shown  in  Fig.  22;  if  a  direct  current 
be  sent  through  coil  B  then  the  impedance  of  A  will  vary  according 
to  each  value  of  direct  current.  This  is  due  to  the  fact  that,  as  the  direct 
current  in  B  changes,  the  permeability  of  the  iron  changes  and  hence 


670 


RADIO-TELEPHONY 


[CHAP.  VIII 


the  impedance  of  the  coil  A.  This  principle  is  applied  in  Alexanderson's 
scheme  in  the  manner  illustrated  by  the  diagram  Fig.  23. 

LS  in  this  diagram  corresponds  to  coil  B  of  Fig.  22,  wherein  a  direct 
current  is  caused  to  flow  by  the  battery  F.     LI  and  L2  correspond  to  coil 
A  of  Fig.  22  and  their  impedance  is  caused  to  vary 
by  the  change  in  the  direct  current  of  coil  LS.     The 
magnetic  circuit  and  the  coils  are  arranged  and 
connected  as  shown,  because  in  so  doing  an  alter- 
nating current  flowing   through   LI   and    L2   can 
induce  but   small  e.m.f.'s  in  coil   LS,  as  may  be 
FIG.  22.  —  If  continuous  easily  seen.     The  coils  LI  and  L2  are  connected 
current  is  sent  through  across  the  high-frequency  alternator  A,  which  is,  in 
coil  A  the  alternating  turn,  connected  to  the  antenna  in  the  usual  way. 
It  will  be  noted  that  the  circuit  of  the  antenna  and 
that  of  the  coils  Li-L2  are  in  multiple  with  respect 
to  the  alternator;  since  the  alternator  armature 
has  impedance  it  is  plain  that  by  changing  the 

current  in  the  circuit  of  Li-L2  the  voltage  across  the  alternator  terminals 
is  thereby  changed,  and  hence  the  current  in  the  antenna  is  changed. 
Thus,  if  the  impedance  of  Li-L2  is  made  very  low  a  large  current  will 
flow  therein  and  the  alternator  voltage  will  fall,  and  so  will  the  antenna 
current;  the  opposite  takes  place  when  the  impedance  of  Li-L2  is  made 
high.  Hence,  if  the  transmitter  is  spoken  into,  and  the  direct  current  in 


current  impedance  of 
coil  B  will  vary  with  the 
amount  of  current  in 
coil  4. 


FIG.  23. — Current  through  coil  L3  changes  the  permeability  of  both  the  inside  cores, 
thus  changing  the  effective  inductance  of  L\  and  La,  both  of  which  are  connected 
in  parallel  with  the  generator. 

coil  La  is  thereby  changed,  the    impedance  of  the  coils  Li-L2  will  be 
changed,  and  the  antenna  current  will  thus  be  modulated. 

The  adjustment  of  the  value  of  the  direct  current  in  LS,  with  the  trans- 
mitter inoperative,  has  an  extremely  important  bearing  upon  the  oper- 
ation. To  begin  with,  it  must  be  noted  that  this  current  may  be  adjusted 
so  that: 


ALEXANDERSON   SCHEME   FOR   MODULATION 


671 


1st.  On  increasing  the  current  in   L3   the  inductance  of  Li-La 

increases,  and  vice  versa. 
2d.  On  increasing  the   current  in   L3   the   inductance   of   Li-L2 

decreases,  and  vice  versa. 

3d.  The  inductance  of  Li-L2  decreases  both  when  the  current 
in  L3  is  increased  and  when  decreased. 

The  above  statements  are  illustrated  by  means  of  curve  Fig.  24.  The 
first  condition  would  be  realized  by  adjusting  the  direct  current  to  /i, 
the  second  condition  by  adjusting  to  72,  and  the  third  condition  by  adjust- 
ing to  73. 

Of  course,  the  third  condition  is  one  which  cannot  be  used  at  all,  and 
it  has  been  found  in  practice  that  the  second  is  the  best.  In  this  case, 
if  the  telephone  diaphragm  is 
inwardly  displaced,  and  the  direct 
current  is  thereby  increased,  the 
inductance  of  Li-L2  will  decrease 
and  the  current  in  the  antenna 
will  decrease;  so  that  an  inward 
displacement  of  the  transmitter 
diaphragm  produces  a  decrease  of 
antenna  current. 

Again  it  must  be  noted  that  the 
coils  L3  and  Li-L2  must  be  so  de- 
signed, and  the  direct  current  in 
LS  must  be  so  adjusted  that  a 
change  in  the  high-frequency  cur-  Direct  Current  in  i_3 

rent    flowing   through    Li-L2    will   FIG.  24.— Variation  in  effective  self-induction 
not  produce   a   change   in   its   in-      of  Lt  and  L2  as  the  current  in  L3  is  changed, 
ductance;    in    other    words    the 

change  in  the  inductance  of  Li-L2  must  take  place  only  because  of  the 
change  of  the  direct  current  in  L3,  and  not  because  of  the  change  in  the 
high-frequency  current  in  Li-L2. 

The  system  as  actually  used  in  practice  introduces  a  number  of  con- 
densers in  the  circuit  of  Li-L2  as  shown  in  the  diagram,  Fig.  25.  The 
condensers  C\  and  C2  are  used  in  order  to  prevent  the  variations  of  current 
in  L3  from  producing  currents  in  the  closed  circuit  of  Li-L2;  for,  it  will 
be  found  that,  when  the  current  in  L3  is  changed,  e.m.f.'s  are  induced 
in  Li  and  L2  in  such  a  direction  as  to  be  additive  in  the  circuit  of  LI  and 
L2;  these  e.m.f.'s  would  produce  currents,  which,  by  Lenz's  law,  would 
tend  to  hinder  the  change  of  flux  being  produced  by  L3.  The  condensers 
Ci  and  C2  are  chosen  so  that  they  will  offer  a  very  large  impedance  to  the 
flow  of  audio-frequency  currents  anil  very  small  impedance  to  radio- 
frequency  currents;  hence  very  little  current  will  flow  in  Lj-L2,  due  to 


672 


RADIO-TELEPHONY 


[CHAP.  VIII 


the  audio-frequency  changes  in  the  current  of  LS,  while  little  or  no  oppo- 
sition will  be  offered  by  these  condensers  to  the  flow  of  radio  frequency 
currents  from  the  alternator.  The  condensers  C  and  €3  are  used  in  order 
to  make  the  relation  between  the  changes  in  the  direct  current  of  LS  and 


C, 


411 


FIG.  25. — The  circuit  of  Fig.  23  is  found  to  function  better  if  proper  condensers  are 
utilized  as  indicated  in  this  diagram. 

the   antenna   current   a   linear  one   through   a  large   range   of  direct- 
current  values. 

It  will  be  noted  that  if  the  condensers  C  and  €3  are  left  out,  and,  con- 
sidering Ci  and  €2  as  having  an  extremely  low  impedance  to  radio  fre- 
quency currents,  the  circuit  of  the  alternator,  antenna  and  Li-L2,  may 
be  fundamentally  represented  as  in  Fig.  26,  where 

La  represents  inductance  of  alternator  armature ; 
Ca  represents  capacity  of  antenna; 
Li-Z/2  represents  inductance  of  coils  L\-L<z, 

while  if  condenser  C  is  inserted  in  series  with  Li-Z/2    the  schematic  dia- 
gram would  be  as  in  Fig.  27.     It  is  found  on  varying  Li-L2  of  Fig.  26 

that  the  current  in  Ca  (antenna  current)  varies 
but  little  and,  for  certain  values  of  Z/i-Z/2,  docs 
not  vary  at  all;  while  the  reverse  is  true  of 
Fig.  27.  This  is  graphically  represented  in 
the  conventional  curves  of  Fig.  28,  where 
curve  (A)  has  a  very  much  smaller  slope  than 
curve  (B). 

In  the  case  of  curve  (B) ,  the  working  part 
would  be  between  the  points  K  and  D.  The 
condenser  €3  is  shown  diagrammatically  in 

Fig.  29.     This  condenser  seems  to  further  increase  the  sensitiveness  of 
the  arrangement,  since  it  forms  with  Li-L2  a  multiple-resonant  circuit 


FIG. 


26. — Detail   circuit   of 
Fig.  23. 


ALEXANDERSON  SCHEME  FOR   MODULATION 


673 


whose  impedance  is  more  susceptible  to  variations  of  Li-Z/2  than  if  this 
alone  were  used. 

It  has  already  been  stated  that  in  this  system,  as  used  in  practice,  the 
antenna  current  is  made  to  decrease  as  the  direct  current  increases;  there- 
fore an  inward  movement  of  the  transmitter 
diaphragm  may  produce  an  outward  movement 
of  the  receiver  diaphragm,  or,  in  other  words, 
the  displacements  of  the  two  diaphragms  may 
be  180°  apart. 

The    ability    of    Alexanderson's    apparatus 
to  modulate  may  be  best  gathered  from  the 

statement  that  a  change  in  the  current  of  the   . 

FIG.   27.— Detail   circuit   of 
transmitter  of  0.2  ampere  has  been  made  to  pro-       Fi    23     {+h      condenser 


introduced  in  the  common 
lead  of  Li-L2. 


(A)  No  Condenser  in  Series  with  Lj- 

(B)  Condenser  in  Series  with   l-L 


duce  a  change  of  37  kilowatts  in  the  antenna 

power   output;    a   battery  of  large  three-elec- 

trode tubes  was  in  this  case  suitably  used  to  change  the  current  in  Z/3, 

the  transmitter  "  talking  "  to  the  grid  of  the  exciter  of  these  big  tubes. 
Receiving    System.  —  The    receiving    system    for    radio-telephony    is 

exactly  the  same  as  that  used  in  receiving  damped-wave  telegraphic  signals. 

It  must  be  understood  that,  as  pointed  out  on  p.  649,  the  incoming  modu- 

lated waves  must  be  rectified  and, 
for  this  purpose,  either  a  crystal 
detector  or  a  vacuum-tube  detector, 
suitably  adjusted  to  act  as  a  recti- 
fier, may  be  used.  The  connections 
are  the  same  as  those  used  for  re- 
ceiving damped  waves,  and,  in  fact, 
a  station  fitted  to  receive  damped 
waves  will  also  receive  radiotele- 
phonic  messages.  One  difference 
between  the  reception  of  damped 
waves  and  radiotelephonic  messages 
lies  in  the  fact  that  in  the  case  of  the 

waves 


Inductance  of  Ll-L2  latter>       the       incoming      waves      are 

FIG.  28.  —  Effect  of  the  condenser  in  series  undamped  (in  the  ordinary  meaning 
with  Li-La  on  the  amplitude  of  antenna  of  the  word),  though  modulated;   but 

it  must   be  borne  in  mind  that   in 
such   a    receiving    system    no    local 

oscillations  are  needed,  as  in  receiving  undamped  waves  for  telegraphic 
purposes,  for,  while  in  the  latter  case  the  amplitude  of  the  incoming 
waves  is  constant,  in  radio-telephony  the  amplitude  of  the  incoming 
waves  is  continually  changing  and  it  is  this  change  in  amplitude  which 
must  be,  and  is,  detected  by  suitable  rectifying  devices. 


674  RADIO-TELEPHONY  [CHAP.  VIII 

Analysis  of  Modulated  Wave.  —  It  is  important  at  this  point  to  note 
that,  though  the  alternator,  or  any  other  source 
that  might  be  used  at  the  transmitting  station, 
produces,  when  no  modulation   is   taking   place, 
an  undamped  current  of  constant  amplitude  and 
^    HT~C;?  single  frequency,  except  for  any  harmonics  that 
might  be  present,  yet,  when    modulation    takes 
Lri_2  place,      the      current       flowing      through      the 

FIG.  29.-The  condenser  C3  tran^itting  antenna  may  be  shown  to  be 
makes  with  L,-L2  a  paral-  equivalent  to  a  number  of  component  har- 
lel  resonant  circuit  the  monic  currents  of  different  amplitudes  and 
impedance  of  which  varies  frequencies.  Thus,  consider  the  simple  case 
much  more  rapidly  with  illustrated  by  Fig.  3  of  p.  648,  which  repre- 
change  m  Li~L2  than  does  ,  .  ,  .  „  , 

the  impedance  of  L-L    sen^s  a  harmonic  current,  harmonically   modu- 
itself.  lated. 

Let  /o  =  amplitude  of  unmodulated  antenna  current  ; 

co  =  angular  velocity  of  unmodulated  antenna  current  in  radians 
per  second  ; 

a  ^instantaneous  value  of  unmodulated  antenna  current. 
Let  the  equation  of  this  current  be 

a  =  /o  sin  at,    .........     (3) 

when  modulation  takes  place  the  amplitude  of  the  current  is  varying 
between  the  maximum  of  (/o  +/'o)  and  the  minimum  of  (/o—  /'o),  and 
this  variation  takes  place  harmonically. 

Let  coi  =  angular  velocity  in  radians  per  second  of  modulating  dis- 

turbance, or  angular  velocity  corresponding  to  the  cycle 
represented  by  A\  —  A<z  in  Fig.  3; 
i  =  instantaneous  value  of  modulated  antenna  current. 

Then,  the  equation  of  i  will  be: 

i  =  (/o-f/'o  cos  wiQ  sin  wt  .......     (4) 

Eq.  (2)  is  similar  to  Eq.  (1)  except  that  the  amplitude  of  the  current  is 
now  (/o+/'o  cos  ojiO,  instead  of  just  70. 
Eq.  (2)  may  be  changed  as  follows  : 


i  =  /o  sin  ioJ-j-/'o  sin  coJ  cos 


Jt  77 

=  /o  sin  iwf+TT  sin  ut  cos  ^\t-\-~  sin  co<  cos 


ANALYSIS  OF  MODULATED   WAVE  675 

Jf 

And,  adding  and  subtracting  -^-  cos  ut  sin  toi£,  we  have: 

Jf  Jf 

i  =  Io  sin  co£  -\—^  sin  ut  cos  onH — ^  cos  ut  sin  coi/+ 
J  Z 

jf  jf 

+-—  sin  o>£  cos  coi£  —  -^  cos  ut  sin  coi£, 

or: 

T/  T/ 

fc=/o  sin  ^+-^  sin  (co+coi)£+- ^  sin  (cu  — coi)<     .     .     .     (5) 

Or,  letting 

/  =  frequency  corresponding  to  co; 

/i  =  frequency  corresponding  to  wi, 
^=/0sin27r^+^sin27r(/-f/i)«+Y  sin  2ir(/-/i)<,      .     .     (6) 

which  last  equation  shows  that  the  harmonically  modulated  current  of 
Fig.  3  is  made  up  of  three  component  harmonic  currents  of  the  following 
amplitudes  and  frequencies: 

Amplitude.     Frequency. 
Component  No.  1 /o  / 

Component  No.  2 .  .      .  .  ~        (f+ /O 

z 

jt 

Component  No.  3 —        (/-/i) 

4 

Thus,  if  /  =  300,000 

and  /i  =1,000, 

then  the  three  frequencies  will  be: 

300,000,  301,000,  299,000, 

which  means  a  difference  between  the  smallest  and  largest  frequencies 
of  2000  cycles  or  about  two-thirds  of  1  per  cent  of  the  frequency  of  the 
unmodulated  wave  (carrier  wave).  On  the  other  hand  if: 

/  =  20,000  (X  =  15,000  meters) 
and  /i  =  1,000 

then  the  three  frequencies  would  be: 

20,000,  21,000  19,000 

which  means  a  difference  between  the  smallest  and  largest  frequencies 
of  about  10  per  cent  of  the  frequency  of  unmodulated  wave. 


676  RADIO-TELEPHONY  [CHAP.  VIII 

Of  course,  a  speech-modulated  current  is  made  up  of  currents  of  a  very 
large  number  of  frequencies,  one  of  which  is  the  frequency  of  the  carrier 
wave,  /,  and  the  others  are 


where          /i,/2,/3,  ......  /»=  frequencies  included  in  the  human  voice. 

The  larger  the  frequencies  /i  or  /2  or  /3  ....  or  /„  and  the  smaller 
the  frequency  /,  the  larger  becomes  the  difference  between  the  smallest 
and  largest  frequency  expressed  as  a  percentage  of  the  carrier  frequency. 

This  analysis  leads  us  to  the  following  conclusions  : 

Since  the  current  in  the  receiving  antenna  is  to  be  a  reproduction  of 
that  in  the  transmitting  antenna,  it  follows  that  the  receiving  antenna 
current  must  have  the  same  frequencies  as  the  transmitting  antenna 
current.  Thus,  we  at  once  conclude  that  the  receiving  antenna  circuit 
must  not  be  sharply  tuned  to  any  one  frequency,  to  the  partial  or  entire 
exclusion  of  all  the  others,  but  must  be  so  designed  as  to  be  able  to  pick 
up  all  these  various  frequencies  equally  well.  This  means  that,  if  the 
difference  between  the  maximum  and  minimum  frequencies,  expressed 
as  a  percentage  of  the  carrier  frequency,  is  very  large,  the  tuning  of  the 
receiving  circuit  must  be  broad,  in  order  for  it  to  respond  equally  well  to 
a  wide  range  of  frequencies. 

Again,  in  order  for  it  to  be  possible  to  use  a  sharply  tuned  receiving 
circuit,  such  as  may  be  obtained  by  the  circuit  discussed  on  p.  518,  Chapter 
VI,  the  frequency  of  the  carrier  wave  must  be  very  high,  that  is,  of  the 
order  of  500,000  or  more,  corresponding  to  a  wave-length  of  600  meters 
or  less. 

Furthermore,  it  would  seem  as  if,  for  a  receiving  circuit  having  a  certain 
degree  of  sharpness  of  tuning,  a  high-pitched  voice  would  be  less  distinct 
than  a  low-pitched  one;  this  effect  is  very  noticeable  if  the  proper  adjust- 
ment of  the  receiver  circuit  is  made. 

The  effect  noted  above  is  well  illustrated  when  listening  to  radio- 
telephone transmission  on  long  wave-  lengths,  say  20,000  meters;  using 
an  amplifying  circuit  such  as  shown  in  Fig.  127,  p.  514,the  tuning  character- 
istics of  which  are  given  in  Fig.  130,  p.  518,  the  speech  is  very  drummy,  only 
the  low  vowel  sounds  coming  through.  It  is  quite  possible  to  adjust  the 
receiving  circuit  to  such  sharp  resonance  that  the  speech  is  unintelligible, 
although  very  loud;  decreasing  the  coupling  of  the  tickler  coil  will  decrease 
the  sharpness  of  resonance  of  the  receiving  circuit,  making  the  resistance 
of  the  circuit  higher.  This  will,  of  course,  decrease  the  strength  of  the 
received  signal,  but  at  the  same  time  will  improve  the  quality. 

In  a  radio-telephone  outfit,  both  the  receiving  and  transmitting  sets 
of  which  have  been  properly  adjusted,  the  speech  transmission  is  much 
better  than  that  over  the  average  wire  line;  due  to  the  fact  that  all  fre- 
quencies are  attenuated  alike  (whereas  in  wire  speech  the  high-frequency 


OSCILLATING  TUBE  AS  DETECTOR  677 

currents  attenuate  much  more  than  the  lower)  the  enunciation  of  the 
received  signal  is  so  distinct  that  the  voice  of  the  operator  talking  at  the 
transmitting  station  may  be  easily  recognized. 

The  Use  of  an  Oscillating  Receiving  Set  for  Radio-telephony.1 — It 
is  possible  to  receive  speech  by  radio-telephony  even  if  the  receiving  set  is 
adjusted  to  oscillate,  by  suitable  setting  of  the  tickler  coil  (Fig.  127,  p.  514). 
Such  an  oscillating  receiving  set  requires  more  skill  in  handling  and  a 
much  better  transmitting  set  than  for  reception  by  crystal  or  non-oscillat- 
ing tube,  but  to  offset  these  difficulties  it  has  the  advantage  of  being  by 
far  the  most  sensitive  arrangemejnt  possible.  The  local  oscillations  are 
adjusted  to  give  "  zero-beat  frequency  "  with  the  carrier  frequency  of 
the  transmitting  set;  it  will  be  realized  at  once  that  the  maintenance 
of  this  condition  is  not  easy,  especially  if  the  carrier  frequency  is  high. 

The  slightest  variation  of  frequency  in  either  the  transmitter  or 
receiver  would  produce  a  musical  beat-note  which  would  make  the  speech 
tones  unintelligible.  Even  with  a  carefully  designed  receiver  set  main- 
taining a  constant  local  frequency,  it  will  be  found  that  the  average  radio- 
telephone transmitter  has  sufficient  variation  in  the  carrier  frequency  to 
make  this  scheme  unfeasible.  With  the  lower-frequency,  high-powered 
transmitters,  having  accurate  frequency  control,  it  will  be  found  that  the 
zero-beat  reception  scheme  exceeds  any  other  for  sensitiveness.  The 
tickler  coil  should  be  set  with  a  coupling  somewhat  greater  than  the  critical, 
otherwise  the  tuning  of  the  receiving  circuit  is  too  sharp,  and  the  higher 
voice  frequencies  encounter  considerably  more  impedance  than  the  lower 
ones,  and  hence  the  speech  is  distorted.  The  lower  voice  frequencies, 
which,  combined  with  a  carrier  frequency,  give  frequencies  quite  close 
to  the  carrier  frequency,  come  in  much  louder  than  the  higher  ones,  mak- 
ing the  speech  a  series  of  low-pitched  vowel  sounds. 

With  an  oscillating  tube  for  detector  the  rectified  current  is  directly 
proportional  to  the  impressed  voltage  instead  of  to  the  voltage  squared, 
which  is  the  case  for  the  non-oscillating  rectifier.  (See  p.  483.)  For 
this  type  of  receiver,  therefore,  the  modulation  at  the  transmitter  should 
be  such  that  the  difference  between  the  amplitude  of  the  antenna  current 
with  the  microphone  in  operation  and  that  with  the  microphone  idle 
should  vary  in  direct  proportion  to  the  pressure  of  the  sound  waves  on 
the  microphone  in  accordance  with  Eq.  (1),  p.  659. 

The  oscillating  receiver  serves  as  a  convenient  check  upon  the  degree 
of  modulation  at  the  transmitter.  If  the  local  oscillations  are  made  to 
differ  from  the  carrier  frequency  by  several  hundred  cycles  per  second, 
the  received  beat  signal  should  be  of  about  the  same  intensity  as  the  speech 
tones  when  the  receiver  is  set  for  zero  beat  frequency;  if  the  beat  signal 

1  When  using  an  oscilllating  tube  set  for  zero  beat,  a  disagreeable  singing  note  is 
heard  continually  if  another  telephone  station,  within  range,  is  sending  on  nearly  tk/ 
same  wave. 


678 


RADIO-TELEPHONY 


[CHAP.  VIII 


is    much    louder    than    the     speech     it    shows    that     the    modulation 
is    poor,     namely,    the    antenna    current    is    not    being    varied    much 

by  the  action  of  the  mi- 
crophone. 

Effect  of  Decrements 
upon  the  Quality  of 
Received  Speech.  —  As 
mentioned  on  p.  669,  the 
radio-telephone  speech  is 
indistinct  and  drummy 
if  the  decrement  of  the 
transmitting  antenna  or 
that  of  either  of  the  two 
FIG.  30.— Form  of  voltage  acting  on  a  receiving  antenna  tuned  circuits  at  the  re- 
for  perhaps  one  thousandth  of  a  second.  ceiving  station  is  made 

low.      This    condition,    it 

will  be  noted,  is  exactly  opposite  to  that  required  for  good  telegraphic 
communication  by  radio,  and  is  therefore  worth  being  analyzed. 

It  is  presumed  that  the  modulator  and  generator  are  functioning  prop- 
erly at  the  transmitting  station,  which  means  that  the  oscillator  is  impress- 
ing upon  the  antenna  a  high-fre- 
quency e.m.f.,  the  amplitude  of 
which  faithfully  follows  the  sound- 
wave fluctuations  of  the  voice. 
This  is  indicated  by  Fig.  30,  show- 
ing the  e.m.f.  impressed  upon  the 
antenna  for  a  small  part  of  the 
voice  sound.  Now  the  question 
arises,  if  such  an  e.m.f.  is  impressed 
upon  the  receiving  antenna  what 
kind  of  a  current  will  flow?  The 
elements  of  this  problem  were  taken 
up  in  Chapter  IV,  p.  268,  wherein 
it  was  shown  that  the  current 
produced  by  a  damped  wave  of 
e.m.f.  impressed  upon  a  resonant 
circuit  depends  upon  two  factors, 
viz.,  the  ratio  of  the  frequency  of 
the  impressed  e.m.f.  to  the  natural 
frequency  of  the  circuit,  and  the 
relative  value  of  the  decrement  of  the  impressed  e.m.f.  to  that  of  the 
circuit  itself. 

If  the  decrement  of  the  circuit  is  lower  than  that  of  the  impressed 


Impressed  E.M.F.  of 
high  decrement 


Current  set  up  in 

circuit  of  low 

decrement 


FIG.  31. — A  highly  damped  wave  of  e.m.f. 
impressed  upon  a  receiving  circuit  of  low 
decrement  will  produce  a  current  lasting 
much  longer  than  the  e.m.f.  and  of  en- 
tirely different  form. 


EFFECT  OF   DECREMENTS  ON   SPEECH  QUALITY  679 

e.rn.f.  the  current  will  be  more  sustained  than  the  impressed  e.m.f.  itself. 
If,  for  example,  a  highly  damped  pulse  of  e.m.f.  is  impressed  upon  a  cir- 
cuit of  low  decrement  and  the  same  natural  frequency  as  the  e.m.f.,  the 
current  will  be  about  as  shown  in  Fig.  31;  the  current  builds  up  slowly 
and  dies  down  slowly.  We  can  conclude  that  any  changes  in  th^  ampli- 
tude of  the  e.m.f.  impressed  on  such  a  circuit  will  be  followed  but  slowly 
by  corresponding  changes  in  current.  It  follows  that  if  a  modulated 
high  frequency  e.m.f.  similar  to  that  shown  in  Fig.  30  is  impressed  on  a 
low-decrement  circuit,  of  the  same  natural  frequency  as  that  of  the 
impressed  e.m.f.,  though  a  large  amplitude  current  will  flow  in  the  circuit, 
the  changes  in  the  amplitude  of  this  current  caused  by  the  changes  in  the 
impressed  e.m.f.  amplitude  will  be  comparatively  small.  If,  on  the  other 
hand,  the  decrement  of  the  circuit  is  very  materially  increased,  by  adding 
resistance,  the  current  produced  by  the  action  of  the  modulated  e.m.f  will  be 
much  smaller  in  amplitude  than  before,  but  the  fluctuations  in  amplitude  of 
the  current  will  follow  very  closely  those  of  the  modulated  e.m.f. 

An  extreme  case  of  this  effect  is  illustrated  in  Fig.  32,  wherein  the 
impressed  e.m.f.  (curve  a)  is  assumed  to  be  made  up  of  two  distinct  damped- 
wave  trains.  In  curve  (6)  is  shown  the  current  set  up  by  this  e.m.f.  in 
a  low-decrement  circuit,  and  in  curve  (c)  is  shown  the  current  set  up  in 
a  high-decrement  circuit.  Quite  evidently,  the  current  in  the  latter  case 
very  closely  resembles  the  e.m.f.  acting  on  the  circuit,  whereas  the  much 
larger  current  in  the  case  of  the  low-decrement  circuit  is  very  far  from  being 
similar  in  form  to  the  e.m.f. 

The  modulated  e.m.f.  involved  in  radio-telephony  circuits  would  act 
on  high-  and  low-decrement  circuits  in  a  manner  similar  to  that  indicated 
for  the  damped  e.m.f.  of  Fig.  32;  the  low-decrement  circuit  would  have 
large  currents  set  up  in  it,  but  the  variations  in  amplitude  of  these  currents 
would  not  follow  the  variations  in  the  impressed  e.m.f.  amplitude,  whereas 
the  high-decrement  circuit  would  have  much  smaller  currents  (same  L 
and  C  supposed  as  for  low-decrement  circuit)  but  the  variations  in  ampli- 
tude would  more  accurately  follow  those  of  the  impressed  modulated 
e.m.f.  Since  the  voice  sounds  are  conveyed  by  the  variations  in  the  ampli- 
tude of  the  current  and  not  by  the  magnitude  of  the  current  itself  it  is 
evident  that  the  high-resistance  circuit  would  be  the  one  to  use  for  suc- 
cessful radio-telephony. 

Applying  this  general  idea  to  an  actual  case  of  speech  transmission, 
we  come  to  the  conclusion  that  the  decrements  of  the  transmitting  antenna, 
the  receiving  antenna,  and  closed-tuned  circuit  at  the  receiver  must  all 
be  higher  than  the  highest  decrement  occurring  in  the  modulated  e.m.f. 
Thus  in  Fig.  30  the  e.m.f.  (which  is  supposed  accurately  to  represent  the 
voice  sounds)  has  its  more  rapid  change  in  amplitude  from  A  to  B;  in 
ten  cycles  its  amplitude  decreases  in  the  ratio  of  1  :  10,  which  corresponds 


680 


RADIO-TELEPHONY 


[CHAP.  VIII 


to  a  decrement  of  0.11.  The  decrement  of  none  of  the  three  circuits 
taking  part  in  the  transmission  and  reception  should  be  as  low  as  this  value, 
if  clear  well-enunciated  speech  is  expected  at  the  receiving  end. 

For  short  wave  work  this  idea  is  not  of  so  much  importance,  because 
the  permissible  value  of  the  decrement,  from  this  standpoint,  is  lower 
than  that  generally  attained  in  the  construction  of  sets.  Thus,  if  the 
time  between  A  and  B,  Fig.  30,  is  taken  as  0.0001  second  and  the  wave- 


FIG.  32. — A  series  of  damped  waves  of  e.m.f.  acting  on  a  low  resistance  receiving  circuit 
produce  a  current  as  indicated  in  (b),  evidently  not  of  the  same  form  as  the  e.m.f. 
a  high-resistance  circuit  will  have  currents  as  shown  in  (c)  which  current  closely 
resembles  the  e.m.f.  causing  it. 

length  used  is  300  meters,  the  number  of  cycles  from  A  to  B  would  be  100; 
a  decrease  in  amplitude  to  one-tenth  of  its  initial  value  in  100  cycles  cor- 
responds to  a  decrement  of  0.023,  which  would  be  practically  never  obtained 
in  either  of  the  antenna  circuits  and  could  only  be  obtained  in  the  closed- 
tuned  circuit  of  the  receiving  set  by  having  a  tickler  coupling  to  the  plate 
circuit. 

Multiplex  Radio-telephony. — It  is  possible  to  carry  on,  by  means  of 
a  scheme  of  "  double  modulation,"   several  radio-phone  conversations 


MULTIPLEX   RADIO-TELEPHONY 


681 


QQOQOC 


in  the  same  area  and  using  exactly  the  same  high-frequency  carrier  wave 
for  all  stations;  the  extra  complications  of  the  scheme  are  worth  while 
only  in  regions  of  congested  communication. 

The  general  idea  of  the  scheme  is  conventionally  indicated  in  Fig.  33, 
wherein  A  is  a  modulator  and  B  is  a  long  wave-oscillator;  C  is  a  modu- 
lator and  D  is  a  short  wave-oscillator;  the 

connections  of  a  tube-transmitting  set  utiliz-  ^    ( t  ^ 

ing  this  idea  are  shown  in  Fig.  34.  From 
these  two  diagrams  it  is  evident  that  the 
antenna  sends  out  a  "  doubly  modulated  " 
high-frequency  wave,  that  is,  the  amplitude 
of  the  high-frequency  wave  follows  a  curve 
which  is  a  voice-modulated  long-wave  radio- 
frequency.  Thus  generator  B,  Fig.  33,  might 
generate  oscillations  of  25,000,  and  the  ampli- 
tude of  this  25,000-cycle  current  is  voice- 
modulated  by  the  action  of  A.  This  vari- 
able amplitude,  25,000-cycle  wave,  controls, 
through  the  action  of  modulator  C,  the  am- 
plitude of  the  high-frequency  current  generated 
by  D  and  sent  out  from  the  antenna. 

Fig.  34  shows  how  the  Heising  modulation 
scheme  may  be  made  to  function  for  multi- 
plex transmission,  and  Fig.  35  shows  the  general 
reception  scheme  for  multiplex  telephony.  The 
antenna  circuit  and  the  closed  circuit,  Li-Ci, 
are  tuned  to  the  high  frequency  generated  by 
the  oscillator  exciting  the  transmitting  anten- 
na. The  action  of  the  grid  condenser  and 
leak  is  to  produce  in  the  plate  circuit  a  pul- 
sating current,  the.  form  of  which  is  the  same 
as  the  envelope  of  the  high-frequency  wave 
received  by  L\-C\.  This  envelope  is  itself  of 
inaudible  frequency,  it  being  perhaps  a  voice- 
frequency  modulated,  25,000-cycle  current. 
This  25,000-cycle  current  acts  on  the  tuned  cir- 
cuit Z/2-C2  coupled  to  the  plate  circuit  of  the  first 
tube.  The  grid  condenser  and  leak  of  this  second  detecting  tube  act  to 
produce  in  the  plate  circuit  of  this  tube  (in  which  the  telephones  are  con- 
nected) a  pulsating  current  of  the  form  of  the  envelope  of  the  25,000- 
cycle  current.  This  envelope  is,  however,  of  voice  frequency,  and  there- 
fore makes  audible  the  speech  carried  by  the  doubly  modulated  high- 
frequency  wave. 


682 


RADIO-TELEPHONY 


[CHAP.  VIII 


Several  stations  in  the  same  area  might  transmit  on  a  carrier  frequency 
of  3,000,000  cycles;   one  of  the  stations  would  send  out  this  wave,  modu- 


lated  by  a  voice-modulated  25,000-cycle  wave,  another  would  use  a  voice- 
modulated  35,000-cycle  wave,   another  a  voice-modulated  45,000-cycle 


MULTIPLEX   RADIO-TELEPHONY 


683 


wave,  etc.  The  selecting  of  the  proper  message  at  the  receiving  station 
is  done  by  the  tuning  of  the  L2-C2  circuit  (Fig.  35) ;  as  this  is  tuned  to 
the  various  long-wave  frequencies  being  used,  the  conversations  from  the 
several  transmitting  stations  become  audible.  All  receiving  stations  tune 
their  respective  antennas  and 
Li-Ci  circuits  to  the  same  high 
frequency  carrier  current. 

By  using  several  high-fre- 
quency carrier  waves,  far  enough 
apart  in  frequency  so  that  no 
interference  is  encountered,  and 
using  several  long  wave-modula- 
tions of  each  of  these,  it  might 
be  possible  to  carry  on,  in  the 
same  area,  without  serious  inter- 
ference, perhaps  fifty  different 
conversations. 

Another  scheme  for  carrying 
on  multiplex  telephony  uses  an 
antenna  tuned  to  several  differ- 
ent frequencies  and  coupled  to 
this  antenna  the  same  number 
of  ordinary  singly-modulated 
transmitting  sets;  it  seems  that 
this  scheme  may  be  made  to 
work  satisfactorily.1 

Amounts  of  Power  Required 
to  Cover  Distances. — As  regards 
the  distance  range  of  radio- 
telephonic  transmission  it  must 
be  remembered  that  the  re- 
sponse at  the  receiving  end  is 
due  not  to  the  total  power  in  the 
transmitting  antenna,  but  to 
the  variation  of  this  power; 
therefore,  it  might,  as  a  general 
statement,  be  said  that  those 
formulae  would  apply  to  radio- 
telephonic  transmission  which  apply  to  undamped-wave  telegraph 
transmission  as  given  on  p.  738,  with  the  proviso  that,  in  these  formu- 

1  See  Proc.  I.R.E.,  Vol.  VIII,  No.  6,  for  report  on  the  feasibility  of  such  a  scheme, 
article  by  Ryan,  Tolmie,  and  Bach,  entitled  "  Multiplex  Radio  Telegraphy  and  Teleph- 
ony." 


684  RADIO-TELEPHONY  [CHAP.  VIII 

lae,  the  change  in  antenna  current  must  be  substituted  for  the  antenna 
current  itself.  Furthermore,  while  in  the  case  of  telegraphic  transmission 
the  signals  may  be  very  faint  and  yet  be  understood  by  an  experienced 
operator,  in  the  case  of  radio-telephone  transmission,  the  signals  must 
be  several  times  more  audible,  in  order  that  speech  may  be  fully  under- 
stood, especially  by  an  inexperienced  operator. 

Practically,  the  following  have  been  found  to  be  the  dependable  trans- 
mission ranges  for  a  fair  modulation,  i.e.,  not  less  than  50  per  cent: 

Antenna  power.  Range  of  reliable 

communication  in  miles. 

5  watts ; 10 

0.1  kw 50 

1.0  kw 200 

10.0  kw 500 

As  pointed  out  in  previous  discussions  on  the  amount  of  power  required 
to  cover  a  certain  distance,  only  very  approximate  values  can  be  given. 
The  amount  of  atmospheric  disturbance  present,  the  conditions  of  refrac- 
tion, reflection  and  absorption,  and  above  all  the  manipulative  skill  of 
the  receiving  operator  in  adjusting  his  receiver  may  change  the  above 
figures  as  much  as  10  to  1.  Thus  it  was  possible  for  an  antenna  power  of 
perhaps  20  kw.  to  transmit  a  radio-telephone  message  from  Arlington, 
U.  S.  A.,  to  Hawaii,  a  distance  of  5000  miles,  and  more  recently  a  small 
100-watt  set  has  been  heard  3000  miles. 

The  Radio-phone  Set. — We  have  so  far  considered  the  radio-phone 
transmitter  and  the  radio-phone  receiver  as  two  separate,  distinct  parts. 
It  remains  to  show  how  the  transmitter  and  receiver  are  combined  into 
a  single  unit  constituting  what  may  be  called  the  "  radio-phone  set." 
The  manner  in  which  this  is  done  depends  on  whether  one  or  two  antennas 
are  used  at  each  station. 

If  one  antenna  is  used  at  each  station  the  circuits  are  generally  arranged 
so  that  the  operator  cannot  send  and  receive  simultaneously.  A  double- 
throw  switch  is  then  placed  within  easy  reach  of  the  operator  so  that  he 
may,  while  carrying  on  the  conversation,  throw  the  antenna  either  over 
to  the  transmitting  circuit,  when  he  wishes  to  speak,  or  over  to  the  receiving 
circuit,  when  he  wishes  to  receive. 

A  conventional  diagram  for  such  an  arrangement,  as  applied  to  a 
Heising  transmitter  and  a  vacuum-tube  receiver,  is  shown  in  Fig.  36. 
The  switch  S  connects  the  antenna  either  to  the  receiving  circuit  by 
means  of  contact  a  or  to  the  transmitting  circuit  by  means  of  contact  6; 
the  switch  may  normally  be  held  in  the  receiving  position  by  means  of  the 
spring  c,  and  the  operator  would  change  over  to  the  transmitting  position 
by  pressing  down  on  the  insulated  handle  of  the  switch. 


ARRANGEMENT  OF  APPARATUS 


685 


68G 


RADIO-TELEPHON  Y 


[CHAP.  VIII 


It  is  apparent  that  in  a  set  of  this  kind  it  may  often  happen  that  an 
operator  changes  from  receiving  to  sending  before  the  distant  operator  is 
through  talking;  thus  it  may  well  be  that  both  operators  may  be  listening 
or  talking  at  the  same  time.  In  spite  of  this  fault  the  single  antenna 
arrangement  is  still  in  use  because  of  the  simplicity  and  low  first  cost  and 
also  because  a  system  of  simultaneous  sending  and  receiving  cannot  be 
said  to  have  been  as  yet  commercially  developed. 

Simultaneous  Radiophone  Transmission  and  Reception. — In  order  to 
overcome  the  difficulty  encountered  in  the  single  antenna  radiophone  set 
two  antennas  are  used  at  each  station,  one  for  transmitting  only  and  the 


Transmitting 
Antenna 


Receiving 
Antenna 


FIG.  37. — Scheme  for  simultaneous  transmission  and   reception   using    two  antennae, 
spaced  a  considerable  distance  from  one  another  and  tuned  to  different  wave-lengths. 

other  for  receiving;  each  operator  can  then  talk  and  listen  at  the  same 
time,  as  is  done  in  ordinary  wire  telephony.  Attempts  have  been  made 
to  use  a  single  antenna  for  simultaneous  transmission  and  reception,  but 
the  results  are  not  reported  to  have  been  very  satisfactory.  One  possible 
scheme  uses  in  the  transmitting  circuit  two  antennae  of  identical  char- 
acteristics, one  a  real  antenna  and  one  a  dummy;  adjustments  are  so 
carried  out  that  half  the  power  from  the  transmitter  goes  through  each 
antenna.  The  receiving  coil  of  the  receiving  circuit  is  coupled  to  both 
antenna  equally,  so  that  when  transmitting  practically  no  voltage  is 
induced  in  the  receiving  circuit.  When  the  distant  station  is  transmitting 
only  the  real  antenna  is  excited  so  that  the  signal  is  received  all  right.  A 
brief  description  of  such  a  set  is  given  in  the  Radio  Review,  Vol.  I,  No.  15, 
by  M.  B.  Sleeper, 


SIMULTANEOUS   RECEPTION   AND  TRANSMISSION 


687 


An  arrangement  wherein  two  antennae  are  used  is  conventionally 
shown  in  Fig.  37.  The  two  antennae  are  put  up  at  some  distance  from 
each  other  and  the  wave-lengths  of  the  two  transmitters  are  made  very 
different  from  each  other.  The  reader  will  at  once  note  that  in  such  a 
scheme  the  receiving  antenna  has  impressed  upon  it  not  only  the_  feeble 
e.m.f.'s  due  to  the  distant  transmitting  antenna,  but  also  the  far  greater 
e.m.f.'s  due  to  the  local  transmitting  antenna;  the  latter  e.m.f.'s  are  not 
wanted,  in  so  far  as  they  "  swamp  "  the  smaller  e.m.f.'s  due  to  the 
distant  transmitting  antenna  and  make  reception  therefrom  impossible  or, 
at  least,  very  difficult. 


TransmfSrmjr 
Antenna 


Receiving 
Antenna 


Modulated 

High  Frequency 

Currents 


Receiving 
Circuit 


FIG.  38. — The  scheme  for  balancing  out  of  the  receiving  antenna  the  strong  signals 
induced  by  the  local  transmitting  antenna. 


Hence,  in  a  system  of  this  kind  some  scheme  must  be  applied  whereby 
the  e.m.f.'s  induced  in  the  receiving  antenna  by  the  local  transmitting 
antenna  shall  be  prevented  from  interfering  with  the  signal  e.m.f.'s  from 
the  distant  transmitter.  Such  a  scheme  is  known  as  a  "  balancing  out  " 
or  "  neutralization  "  device.  A  great  many  neutralization  devices  have 
been  invented  and  used  with  more  or  less  success.  These  devices  may  be 
divided  into  three  classes: 

(a)  Those  in  which  the  receiving  and  transmitting  circuits  are  inter- 
connected (either  magnetically  or  statically  or  both)  in  such  a  manner 
that  the  e.m.f.'s  induced  into  the  receiving  antenna  by  the  local  trans- 


688 


RADIO-TELEPHONY 


[CHAP.  VIII 


mitting  antenna  are  opposed  and  balanced  out  by  means  of  e.m.f  .'s  induced 
directly  by  the  transmitting  into  the  receiving  circuit. 

(6)  Those  wherein  filters  are  used  to  minimize  the  effect  of  the  e.m.f.'s 
produced  by  the  local  transmitter. 

(c)  The  "  Barrage  Receiver  "  invented  by  E.  F.  W.  Alexanderson. 

To  class  (a)  belongs  the  simple  magnetic  balancing-out  scheme  l 
illustrated  by  Fig.  38,  where  the  e.m.f.'s  induced  from  antenna  A\  into 
the  antenna  Az  are  opposed  by  the  e.m.f.'s  induced  in  coil  D  by  the  Currents 
in  B.  Of  course  the  phases  of  these  two  sets  of  e.m.f.'s  may  not  be  exactly 


Transmitting 
antenna 


To  receiving 
circuit 


Modulated 

high  frequency 

currents 

FIG.  39.  —  A  scheme  whereby  the  action  of  condensers  Ci  and  C2  is  utilized  to  eliminate 
from  the  receiving  antenna  the  strong  signals  from  the  local  transmitting  antenna. 

the  same,  in  which  case  it  is  more  difficult   completely   to   nullify  the 
action  of  A\  on  A^ 

A  second  scheme  which  may  be  included  under  class  (a)  is  Alexander- 
son's  static  balance  illustrated  in  Fig.  39.  In  this  case,  it  is  endeavored 
to  so  adjust  the  condenser  Ci  as  to  make  the  potential  of  the  point  B  and 
that  of  top  of  the  receiving  antenna  (A%)  due  to  the  action  of  the  local 
transmitting  antenna  A\  equal  to  each  other;  if  this  is  accomplished 
no  currents  can  flow  in  A^C^B  due  to  the  local  transmitter.  This  scheme 


1  See  "Simultaneous  Sending  and  Receiving,"  by  E.  F,  W.  Alexanderson,  Proceedings 
I.R.E.,  Aug.,  1919,  and  discussion. 


SIMULTANEOUS  RECEPTION  AND  TRANSMISSION 


689 


is  better  understood  by  referring  to  the  diagrammatic  sketch  of  Fig.  40, 
wherein  the  two  antennae  and  the  mutual  capacity  between  them  have 
been  replaced  by  the  condensers  Ct,  Cr,  Cm. 

cm 

F  H 


Modulated 

high  frequency 

currents 


.Cr. 

G 


:c2 


•=-G 


FIG.  40. — Conventional  diagram  of  the  circuit  of  Fig.  39. 
,  Transmitting  Antenna  Receiving  Antenna 


Modulated 

.High  Frequency 

Currents 


FIG.  41. — Another  scheme  for  balancing  at  the  local  signal,  by  suitable  coupling  of  the 

detector  circuit. 

In  this  diagram 

Ct  represents  the  equivalent  capacity  to  the  ground  of  the  trans- 
mitting antenna; 

Cr  represents  the  equivalent  capacity  to  the  ground  of  the  receiving 
antenna ; 

Cm  represents  the  mutual  capacity  between  the  two  antennas. 

It  will  now  be  noted  that  starting  at  the  point  D  we  have  the  following 
two  multiple  circuits  to  ground:    DC \BCzG  and  DFCmHCrG.     It,  there- 


690 


RADIO-TELEPHONY 


[CHAP.  VIII 


Receiving 
antenna 


fore,  follows  that  if  the  capacity  C\  is  made  equal  to  Cm  and  €2  equal  to 
Cr  the  difference  of  potential  between  H  and  B  will  be  zero  and  no  current 
will  flow  through  the  receiving  circuit. 

A  third  scheme  belonging  to  class  (a)  is  the  so-called  detector  balance 
circuit  shown  in  Fig.  41,  wherein  the  e.m.f.'s  induced  into  A%  by  A\  are 
caused  to  produce  a  current  in  the  circuit  of  A%  which  in  turn  is  made  to 
induce  e  m.f.'s  in  the  receiving  circuit  (1)  through  the  action  of  F  on  H; 

at  the  same  time  e. m.f.'s  are  induced  directly 
by  the  transmitter  into  the  receiving  circuit 
by  means  of  the  coils  B-D;  these  two  sets 
of  e.m.f.'s  should  of  course  be  made  equal 
and  opposite. 

In  all  of  the  above  schemes  the  neutrali- 
zation is  generally  incomplete  in  view  of  the 
different  phases  of  the  opposing  electromotive 
forces. 

To  class  (6)  belong  the  Infinite  Impedance 
and  the  Zero  Impedance  circuits  illustrated 
by  Figs.  42  and  43.  In  the  case  of  Fig.  42 
the  multiple  circuit  of  L2— C2  and  R  may  be 
so  adjusted  that  the  impedance  between  F 
and  Y  at  the  frequency  of  the  local  trans- 
mitter is  very  large  and  hence  the  local  trans- 
mitter e.m.f.'s  will  produce  but  little  current 
in  the  receiving  circuit.1 

FIG.  42.— In  this  circuit  the  reso-  On  the  other  hand  in  the  case  of  Fig.  43 
nant  circuit  consisting  of  L2  tne  circuit  of  C2#2L2,  which  is  tuned  to  the 
andC2  in  parallel  is  adjusted  j  ^  transmitter  freqllency,  presents  a  very 
to  give  very  high  impedance  .  J  '  , ' 

for  the  frequency  of  the  local  low  impedance  to  currents  of  that  frequency, 
signal,  thus  much  decreasing  and,  therefore,  the  e.m.f.'s  due  to  the  local 
its  effect.  transmitter  produce  currents  in  the  circuit 

C2#2L2   rather  than   in    CsLs,  which  latter 
circuit  is  tuned  to  the  frequency  of  the  distant  transmitter. 

The  "  barrage  receiver  "  invented  by  E.  F.  W.  Alexanderson  represents 
a  departure  from  other  neutralization  schemes,  which  is  claimed  to  be 
very  effective.  In  this  scheme  the  receiving  antenna  consists  of  two 
horizontal  antennas  stretching  out  in  opposite  directions  and  connected 
to  the  receiving  circuit  in  the  manner  illustrated  in  Fig.  44.  Each  hori- 
zontal antenna  consists  of  a  single  long  wire  (Alexanderson  has  used  a 
wire  8  miles  long  laid  on  the  ground  and  insulated  therefrom).  The  cir- 
cuits between  PI  and  0\  and  P2  and  02  constitute  two  phase  changers; 
these  phase  changers  are  built  in  the  same  manner  as  a  split-phase  induc- 
1  For  analysis  of  this  point  see  Chapter  I,  p.  68.  and  Chapter  IV,  p.  266. 


To  receiving 
circuit 


SIMULTANEOUS   RECEPTION   AND   TRANSMISSION 


691 


Receiving 
antenna 


tion  motor  and  consist  in  each  case  of  two  coils  such  as  B  and  D,  the  cur- 
rents through  which  are  not  in  time 
phase  due  fco  the  different  power 
factors  of  the  circuit  of  B  and  that  of 
D;  furthermore  the  coils  B  and  D  are 
fixed  in  space  quadrature  with  respect 
to  each  other.  Thus,  if  an  alternat- 
ing potential  difference  be  impressed 
across  the  points  0\P\  or  OzP?  a  re- 
volving magnetic  field  will  be  produced 
by  the  coils  BD  or  FK.  By  turning 
the  coils  Lg  or  LQ  within  the  field  of 
the  respective  phase  changer  the  phase 
of  the  e.m.f.  induced  in  L$  or  LQ  is 
changed,  though  the  magnitude  of  this 
e.m.f.  remains  nearly  the  same.  If, 
then,  it  is  desired  that  the  e.m.f.'s  in- 
duced in  the  two  receiving  antennas 

by  the  action  of   the  local   transmitting  FlQ    43 _In   thig   cir~it 
antenna   be   neutralized,   so    as    to    pre-      offers  a  low  impedance  to  ground 
vent  them   from   affecting   the   receiving       for  the  local  signal,  thus  minimiz- 
circuit  we  manipulate  the  phase  changers      ing  this  signal  in  circuit  L3-C3 
and  the    degree  of  coupling  between  L\ 
and  La  and  L%  and  L±  in  such   a   manner   that   the   e.m.f.   induced  in 


Horizontal  Receiving  Antenna 

H 


Horizontal  Receiving  Antenna 


To  Receiving  Circuit 

FIG.  44. — Alexanderson's  so-called  "Barrage  receiver,"  it  is  an  attempt  to  use  rotating 
fields  as  phase  changers  to  neutralize  the  local  signals. 


692 


RADIO-TELEPHONY 


[CHAP.  VIII 


1/5  is  exactly  equal  and  opposite  to  that  induced  in  Z/G.  It  is  ap- 
parent that  this  may  be  done  no  matter  what  the  phases  or  yalues 
of  the  e.m.f.'s  induced  in  each  antenna  by  the  local  transmitter  may  be; 
again,  if  the  e.m.f.'s  due  to  the  local  transmitter  are  neutralized  those  due 
to  the  distant  transmitter  are  not  neutralized  because  of  the  different 
phases  and  values  for  each  antenna  and  also  because  of  the  different  fre- 


FIG.  45. — View  of  the  construction  of  the  set  shown  in  Fig.  46;  the  set  uses  the  Heising 
scheme  of  modulation,  and  has  besides  the  receiving  detector  tube,  two  low 
frequency  amplifying  tubes,  coupled  by  iron  core  inductances. 

quency.  In  the  words  of  the  inventor  such  an  arrangement  is  very  effect- 
ive, not  only  for  the  purpose  of  making  simultaneous  radiophone  trans- 
mission and  reception  possible,  but  also  for  the  purpose  of  eliminating 
interference  from  other  stations. 

Construction  of  Radio-telephone   Sets. — At  present   radio-telephone 
sets  are  made  in  comparatively  small  powers  only;   about  100  watts  out- 


TYPICAL  RADIOPHONE   SET 


693 


put  represents  che  largest  present  commercial  set.  An  idea  of  the  arrange- 
ment of  apparatus  in  a  small  set  (output  about  4  watts),  may  be  had  from 
Figs.  45  and  46,  which  show  an  outfit  designed  for  communication  over 


FIG.  46. — Panel  view  of  a  small  radiophone  set. 

about  10  miles  distance.  A  300-volt  dynamotor  run  from  a  12-volt  storage 
battery  furnishes  power  for  the  plate  circuit;  the  various  parts  are  suf- 
ficiently well  indicated  to  make  the  cuts  self-explanatory. 


CHAPTER  IX 
ANTENNAE  AND  RADIATION 

Simple  Antennae — Mechanism  of  Radiation. — As  already  understood 
an  antenna  consists  of  one  or  more  wires,  suitably  arranged,  by  means 
of  which  electromagnetic  waves  are  radiated  when  high-frequency  cur- 
rents are  sent  into  the  wires. 

The  simplest  type  of  antenna  is  the  one  shown  in  Fig.  1,  consisting  of 
two  wires,  BC  and  DF  with  an  alternator,  A,  or  some 
other  source  of  high-frequency  power,  connected  in  the 
middle.  In  this  arrangement  one  of  the  two  wires  may 
be  considered  as  the  "  aerial/'  while  the  other  performs 
the  function  of  a  "  counterpoise."  Both  wires,  in  this  case, 
however  radiate  electromagnetic  waves,  whereas  in  most 
arrangements  the  counterpoise  is  so  arranged  that  it 
radiates  but  poorly  compared  to  the  aerial  proper. 

The  fundamental  action  of  the  alternator,  as  its 
electromotive  force  varies  from  positive  to  negative  and 
vice  versa,  is  to  charge  the  wire  BC  positively,  while,  at 
the  same  time,  wire  DF  is  charged  negatively,  and,  later, 
to  reverse  the  charges  on  the  two  wires.  It  is  plain  that 
if,  say,  BC  is  to  be  charged  positively,  electrons  must  be 
taken  from  it  by  the  alternator  and  transferred  to  some 
other  conductor,  which,  in  this  case,  is  DF.  Again,  when 
BC  is  charged  negatively,  electrons  must  be  taken  away 
from  DF  and  transferred  to  BC.  Hence  the  obvious 
necessity  of  having  electric  conductors  capable  of  storing 
FIG  1  -Theoret-  electricity,  or  conductors  with  a  reasonable  amount  of 
ically  the  sim-  "capacitance,"  connected  on  both  sides  of  the  alternator, 
plesttypeofan-  Thus,  it  would  not  be  advisable  to  use  the  arrangement 
tenna,  the  two  shown  in  Fig.  2,  for,  in  this  case,  the  storage  capacity  of 
wires  CB  and  BC  WQuld  be  reiatively  smau  As  pointed  out  in  Chapter 
DF  form  the  TT  J  . 

two  plates  of  an  **»  ^ne   caPacity  of   such    a    combination    (BC    and    Dr) 

o/?ew condenser,  depends  upon  the  surface  of  each  conductor;  if  either  of 

them  is  made  very  small  the  capacity  of  the  combination 

(which  determines  how  many  electrons  may  be  transferred  by  the  action 

of  alternator  A)  approaches  zero  and  the  amount  of  radiation  possible 

694 


ACTION  OF  SIMPLE  ANTENNA  695 

also  approaches  zero.     On  the  other  hand,  it  is  common  practice  to  con- 

nect as  shown  in   Fig.  3,  where   the   ground  G  forms   a 

very  good  second  plate  of  the  condenser,  since  its  surface 

is  very  large,  giving   a   reasonable  capacity  to  the  con- 

denser made  up  of  BC  for  one  plate  and  the  earth  for  the 

other. 

In  order  to  more  fully  understand  how  energy  may 
be  radiated  in  the  form  of  electromagnetic  waves  by 
means  of  an  antenna,  we  will  first  go  over  some  funda- 
mental principles  in  connection  with  magnetic  and  elec-  xz£ 

trie  fields.  y 

An  electric  field  is  the  region  wherein  electric  forces 

are  manifested,  and  the  intensity  of  such  a  field  at  any  FlG-  2-    Wlthout 

...  i  i       -  1       r  .  •  •  ,     i  the  lower  wire 

point  is  measured  by  the  force  acting  upon  a  unit  charge      th    ca      -t      f 

of  electricity  placed  at  the  point  in  question.  the  condenser  is 

Similarly,    a    magnetic    field   is   the    region   wherein  so  small  that  the 

magnetic    forces    are   manifested,   and    the  intensity  of  alternator  could 

such  a  field  at  any  point  is  measured  by  the  force  acting  not  foTce  an  ap~ 

upon  a  unit  magnetic  pole  placed  at  the  point  in  ques- 

to  now^  in 


tion.     The  lines  of  action  of  the  electric  or  magnetic      tne  Upper  wire. 
forces  are  called  electric  or  magnetic  lines   of  force  and 
represent,  at  any  point,  the  direction   of   the   force.     It  is  also  conveni- 
ent to  represent  graphically  the  intensity   of  the  electric  or  magnetic 

field  by  drawing  more  or  less  lines  per  unit 
area  corresponding  to  a  stronger  or  weaker 
field  respectively;  but  it  must  be  kept 
in  mind  that  the  force  exists  everywhere 
throughout  the  space  in  which  the  lines 
are  drawn  and  not  only  at  the  "  lines  " 
themselves;  thus  the  number  of  lines  of 
force  per  unit  area  (electric  or  magnetic) 
which  might  be  drawn  at  any  point  is,  no 
matter  what  the  intensity  of  the  field, 
infinite.  In  other  words,  while  it  is  well 
to  visualize  a  field  by  means  of  lines,  the 
FIG.  3.-By  connecting  the  lower  significance  of  these  lines  should  always  be 
end  of  the  alternator  to  earth  kept  in  mind,  and  it  should  never  be  for- 
the  semi-conducting  surface  of  gotten  that  an  electric  field  or  a  mag- 
the  earth  takes  the  place  of  wire  netic  field  is  characterized  by  the  existence 
DF  of  Fig.  1  and  enables  the  Qf  forceg  ^  an  electric  charge 

generator    to   send   appreciable  ..  ,.      ,  ,        .  , 

current  up  the  wire  BC.  or  a  ma£netlc  Pole  respectively,  and  exists 

between  the  "  lines  of  force  "   as  much  as 
it  does  at  the  point  through  which  one  of  the  lines  passes. 


696  ANTENNAE  AND   RADIATION  [CHAP.  IX 

Without  attempting  to  go  into  the  nature  of  a  magnetic  or  an  electric 
field  we  may  say,  however,  that  either  field  is  accompanied  by  a  strain 
in  the  material  (ether  or  otherwise)  present  in  the  field,  and  that  the  forces 
manifested  in  the  field  may  be  considered  as  due  to  the  elasticity  of  the 
material  under  stress,  in  much  the  same  way  that  a  stretched  spring  will 
exert  a  force  because  of  the  elasticity  of  the  material  tending  to  return 
the  spring  to  its  unstressed  condition.  Whatever  the  nature  of  the 
stresses  and  strains  in  an  electric  or  a  magnetic  field,  we  may  lay  down 
certain  well-known  facts  regarding  them. 

1st.  An  electric  field  or  a  magnetic  field  represents  a  definite  amount 
of  energy  per  unit  volume  of  the  field.  It  may  be  shown  that  this  energy 
is,  for  the  case  of  air,  given  by  :  1 

H2 
Wm=-£-  ergs  per  cu.  cm  .......     (1) 


per  cu.  cm. 

O7T 


26  X  10* 


where          Wm=  energy  in  ergs  per  cubic  centimeter  of  a  magnetic  field; 
We  =  energy  in  ergs  per  cubic  centimeter  of  an  electric  field  ; 
H  =  intensity  of  the  magnetic  field  in  gilberts  per  centimeter, 

or  in  gausses; 

£'  =  intensity  of  the  electric  field,  in  e.s.u.  per  centimeter; 
£  =  intensity  of  the  electric  field  in  volts  per  centimeter. 

2d.  A  magnetic  field  in  motion  produces  an  electric  field.  This  is 
nothing  but  the  phenomenon  of  electromagnetic  induction,  for,  the  motion 
of  the  magnetic  field  induces  an  electromotive  force,  which  must  neces- 
sarily produce  an  electric  stress  or  field.  From  Faraday's  law,  if: 

H  =  intensity  of  magnetic  field  in  gausses  ; 
£  =  in  tensity  of  electric  field  in  volts  per  centimeter; 
V  —  velocity  of  magnetic  field  in  centimeters  per  second; 

e.=F#X!0-8  .........     (3) 

3d.  An  electric  field  in  motion  produces  a  magnetic  field. 

H=aVt,      ..........     (4) 

where  a=a  constant  of  proportionality. 

xSee  J.  J.  Thomson,  "Elements  of  Electricity  and  Magnetism,"  1904,  p.  72  and 
p.  268. 


ACTIONS   OF  ELECTRIC   AND   MAGNETIC   FIELDS 


697 


This  action  of  the  moving  electric  field  is  not  as  easily  realized  as  is 
that  action  by  which  a  moving  magnetic  field  generates  an  electric  field. 
Every  revolving  field  alterna- 
tor furnishes  evidence  of  the 
latter  effect.  A  revolving  field 
(depicted  in  Fig.  4)  generates 
an  e.m.f.  in  one  of  the  arma- 
ture conductors,  shown  at  M ; 
one  end  of  the  conductor,  a, 
becomes  -f  and  the  other  be- 
comes — ,  this  polarity  revers- 
ing when  a  south  pole  takes 
the  place  of  the  north  pole 
active  in  Fig.  4. 

The  point  to  be  empha- 
sized here  is  this— between 
the  two  points  a  and  b  (in 


FIG.  4. — The  poles  of  the  revolving  field  induce 
an  e.m.f.  in  the  armature  conductor  M;  it  is 
important  to  note  that  the  moving  magnetic 
field  will  produce  a  difference  of  potential 
(hence  an  electric  field)  between  points  a  and 


the    diagram    located    at    the          b  whether  the  conductor  M  is  there  or  not. 

terminals    of    conductor    M) 

the  moving  magnetic  field  produces  a  difference  of  electric  potential  or 

e.m.f.  whether  the  conductor  M  is  there  or  not. 

The  reciprocal  relation, — a  moving  electric  field  producing  a  magnetic 

field — is  not  so  well 
brought  out  in  the  action 
of  ordinary  electric  ma- 
chinery even  though  it 
is  really  the  basis  of 
every  electromagnetic 
field.  To  illustrate  the 
action  let  us  imagine  a 
gun  shooting  electrons 
at  high  speed,  one  fol- 
lowing another  rapidly 
in  the  same  path,  indi- 
cated in  Fig.  5.  Each 

equivalent  to  an  electric  current  and  hence  will  pro-  °f  theSG  e|ectrons  wl11 
duce  a  magnetic  field  at  any  point  A;  this  magnetic  carry  with  it  its  electric 
field  is  really  caused  by  the  moving  electric  fields  of  the  field  and  SO  at  any  point 
electrons.  Arrowheads  pointing  away  from  the  elec-  in  space  near  the  stream 
trons  indicate  direction  of  motion.  of  movmg  electrons  (A— 

Fig.   5)   there  will  exist 

a  moving   electrostatic    field.     But  we  know  that  there  will  be  at  A  a 
magnetic  field  (at  right  angles  to  the  stream  of  electrons  and  also  to  the 


Gun  shooting 
negative  charges 

FIG.  5. — A    stream   of   electrons    shot    from 


098 


ANTENNAE  AND  RADIATION 


[CHAP.  IX 


> 


Compass 
needle 


Arrows  indicate  tendency 
for  needle  to  turn  as  field 
moves  by 


direction  of  the  electric  field)  because  this  stream  of  electrons  is  really  an 
electric  current,  the  magnitude  of  current  depending  upon  the  number 
of  electrons  passing  a  given  point  per  second.  Thus  if  there  were  6.28  X 1018 

electrons  passing  a 
given  point  in  one 
second,  the  stream 
of  electrons  would 
be  equivalent  to 
one  ampere  of  cur- 
rent. 

Upon  exact  anal- 

Motion ^""  ys*s  ^  w^  ^e  found 

that  the    magnetic 

FIG.  G. — A  compass  needle,  pivoted  so  that  it  is  free  to  swing   figi^  a+  ^    whether 
in  the  horizontal  plane,  will  tend  to  set  itself  at  right  angles  '  , 

to  the  motion  of  the  electric  field  as  long  as  the  electric  field  calculate 
is  moving  past  it,  thus  demonstrating  the  fact  that  a  moving  well-known    law   of 
electric  field  generates  a  magnetic  field,  at  right  angles  to  magnetic  field  sur- 
itself  and  to  its  motion.  rounding  a  conduc- 

tor   carrying    cur 
rent,  or  from  the  relation  given  in  Eq.  (4),  has  the  same  value. 

To  illustrate  this  point  by  another  simple  experiment  (easier  to  con- 
ceive than  to  carry  out,  however),  we  suppose  two  metal  plates,  A  and 
B,  Fig.  6,  charged  so  that  there 
is  an  electrostatic  field  between 
them  as  indicated.  Suppose  a 
compass  needle,  oriented  in  the 
same  direction  as  the  motion  of 
the  plates,  is  so  placed  that  it 
is  situated  in  the  electric  field 
as  the  plates  move  by.  A 
magnetic  force  will  act  on  the 
compass  needle  tending  to  make 
it  place  itself  at  right  angles  to 
the  position  shown  in  the  dia- 
gram, so  long  as  the  electric 
field  is  moving  past,  thus  de-  FIG.  7. — A  toroidal  coil  is  a  good  illustration  of 
monstrating  the  presence  of  a  a  dosed  masnetic  fielcL 

magnetic  field  as  long  as  the  electric  field  is  moving  past. 

If,  now,  we  consider  a  toroid  such  as  that  represented  by  Fig.  7  the 
magnetic  field  produced  by  it,  when  carrying  a  current,  will  be  practically 
limited  to  the  space  within  the  toroid,1  which  space  is  not  far  removed 

1  This  statement  is  not  strictly  true,  because  there  is  actually  some  magnetic  field 
outside  of  the  toroid  as  long  as  the  current  is  changing.  As  this  is  an  extremely  small 


CLOSED  AND  OPEN   FIELDS 


699 


utttttttttt 


mtttttffm 


FKJ.  8. — Two  closely  adjacent  charged  plates  illus- 
trate well  a  closed  electric  field. 


from  the  conductors  of  the  toroid.  It  is  plain  that  if  the  current  is  reduced 
to  zero  the  field  collapses  arid  in  so  doing  it  moves  with  respect  to  the 
conductors  on  the  toroid  and  induces  an  electromotive  force  therein, 
thus  producing  an  electric  / 

field.  In  this  case,  since  the 
magnetic  field  is  very  near 
to  the  conductors,  the  mo- 
tion of  all  of  the  magnetic 
field  with  respect  to  the  con- 
ductors takes  place  at  the 
same  time,  all  of  the  energy 
given  to  the  field  is  returned 

to  the  circuit,  and  no  phenomena  take  place  other  than  the  well-known 
one  of  electromagnetic  induction. 

Similarly  Fig.  8  represents  the  two  plates  PI  and  Pi  of  a  condenser. 
The  charging  of  the  condenser  produces  an  electric  field,  which  is  limited 
practically  to  the  space  between  the  plates.  If  the  condenser  plates  are 

short  -  circuited, 
the  electric  field 
will  collapse  and 
here,  as  in  the 
case  of  the  to- 
roid, since  the 
electric  field  is 
p  very  close  to  the 
plates ,  practically 
all  of  the  energy 
in  the  field  will 
be  returned  to 
the  circuit. 

If,     on     the 
other   hand,  we 


K  /> 

Elebtqc  lines 


Magnetic 

FIG.  9. — A  pair  of  wires  disposed  as  shown  here,  excited  by  a  high 

frequency  alternator,  illustrates  what  are  called  open  magnetic  and  nanging  I  tig- 
electric  fields;  these  fields  reach  out  (with  appreciable  strength)  netic  and  elec- 
to  distances  greater  than  the  dimensions  of  the  circuit  itself.  trie  fields  which 

are     distributed 

to  comparatively  great  distances  away  from  the  seat  of  these  fields, 
we  meet  with  a  new  phenomenon,  i.e.,  radiation  of  electromagnetic 
waves.  Thus,  consider  the  case  of  the  two  conductors  of  Fig.  9,  to 
which  there  is  connected  the  high-frequency  alternator  A .  The  voltage 

part  of  the  total  magnetic  field,  however,  it  may  generally  be  neglected  without  much 
error. 


700  ANTENNA  AND   RADIATION  [CHAP.  IX 

of  the  alternator  is  rapidly  changing,  and  hence  the  charges  on  the 
conductors  BC  and  DF  are  changing  both  in  value  and  in  sign;  the 
result  is  that  a  rapidly  changing  current  is  flowing  through  the  wires,  and 
the  potential  difference  between  the  wires  is  also  rapidly  changing.  In 
view  of  the  above  the  conductors  are  producing  a  rapidly  changing 
magnetic  field,  the  lines  of  force  of  which  are  circles  concentric 
with  the  wires  and  having  planes  perpendicular  to  the  wires,  and,  in 
addition,  a  rapidly  varying  electric  field,  the  lines  of  force  of  which  are 
somewhat  as  shown  in  the  figure. 

It  is  evident  at  first  sight  that  this  case  is  quite  different  from  that 
of  either  the  toroid  or  the  two-plate  condenser,  for,  while  in  the  latter 
the  field  (either  magnetic  or  electric)  was  existent  only  (at  least  practically) 
in  a  small  space  near  the  seat  of  the  fields  and  all  of  it  could  quickly 
return  its  energy  to  the  electric  circuit,  in  the  case  of  the  antenna  both 
the  electric  and  magnetic  fields  extend  outward  in  all  directions  and  to 
distances  as  great,  or  greater,  than  the  dimensions  of  the  oscillating  system. 
It  is  plain,  then,  that  here  we  must  consider  the  time  necessary  for  the 
field  to  reach  a  certain  point. 

It  is  a  matter  of  common  knowledge  that  a  disturbance  or  change  of 
either  an  electric  or  a  magnetic  field  travels  through  air  or  vacuum  with 
the  velocity  of  light.  Consider  then  a  point  such  as  P  at  a  distance  d 
from  the  antenna,  and,  for  the  sake  of  simplicity,  in  the  equatorial  plane. 

Let  f  =  frequency  of  alternator  in  cycles  per  second ; 

X  =  wave-length  in  cms. 

We  will  first  confine  our  attention  to  the  electric  field.  Assume  that 
the  potential  difference  between  the  wires  is  on  the  point  of  starting  from 
zero  towards  a  maximum  positive  value  and,  therefore,  the  electric  field 
is  on  the  point  of  doing  the  same.  The  electric  field  at  P  will  follow  the 
variations  of  the  potential  difference  between  the  wires,  except  that 
the  variations"  at  P  will  take  place  later,  on  account  of  the  appreciable 
time  necessary  for  the  strain  in  the  medium  to  travel  the  distance  d.  The 
line  of  action  of  the  field  at  P  will  be  vertical  and  represented  by  the  line 
£.  in  Fig.  9.  We  must  not  fail  to  remember  at  this  point  that  an  electric 
field  means  energy  and  therefore  a  certain  amount  of  energy  per  cubic 
centimeter  is  present  at  the  point  P  (due  to  the  electric  field)  and  the 
value  of  this  energy  is  growing. 

At  some  time,  depending  upon  the  frequency,  the  potential  difference 
across  the  wires  will  reach  a  maximum  and  begin  to  diminish;  and  this 
will  be  followed,  though  at  a  definite  time  interval,  by  corresponding 
changes  in  the  electric  field  at  the  point  P,  which  will  reach  a  maximum 
and  then  diminish.  Since  the  electric  field  about  the  conductors  is 
now  decreasing  it  follows  that  the  energy  present  in  this  field  must  be 


ELEMENTARY  ANALYSIS  OF   RADIATION  701 

given  back  to  the  conductors,  where  it  will  appear  as  energy  associated 
with  the  magnetic  field  set  up  by  the  current  caused  by  the  collapsing 
electric  field.  It  is  evident  then,  that  the  energy  which  had  at  first  moved 
from  the  oscillator  out  towards  P  must  now  return  towards  the  con- 
ductors. However,  not  all  of  the  energy  given  to  the  electric  field  at 
the  point  P  and  beyond  will  reach  the  conductors  before  the  potential 
difference  across  them  begins  to  build  up  in  the  opposite  direction,  thus 
again  sending  out  energy,  in  the  form  of  an  electric  field,  in  the  opposite 
direction.  There  is  then  left 1  at  the  point  P  a  certain  amount  of  energy 
in  the  form  of  an  electric  field  in  the  direction  indicated  by  L,  Fig.  9,  and 
this  energy  is  unable  to  return  to  the  conductors  since  they  are  already 
sending  out  more  energy  in  the  form  of  an  electric  field  in  the  opposite 
direction  to  that  of  £.,  Fig.  9. 

The  energy  left  at  P  or  at  any  other  point  in  the  field  cannot  remain 
stationary,  but  must  travel  outward.  This,  however,  could  not  happen 
were  it  not  that,  at  the  same  time  and  for  the  same  reason  that  a  certain 
amount  of  energy  is  left  detached  at  any  point  in  the  form  of  an  electric 
field,  an  equal  amount  of  energy  in  the  form  of  a  magnetic  field,  acting 
in  a  horizontal  direction  as  shown  by  H,  Fig.  9,  also  remains  at  each  point. 
These  two  energies,  moving  outward  with  the  velocity  of  light,  can  now 
sustain  each  other  and  are  completely  independent  of  the  conductors 
wherefrom  they  issued.  For,  it  must  be  here  remembered  that,  as  pointed 
out  on  p.  697,  a  moving  electric  field  produces  a  magnetic  field  and  vice 
versa.  That  the  energies  of  the  two  fields  must  be  equal  at  all  points 
and  times  follows  from  the  fact  that,  if  one  were  larger  than  the  other, 
the  difference  could  not  exist  by  itself  while  moving  in  space;2  for,  in  so 
doing,  it  would  produce  the  other  type  of  energy,  hence  it  would  either 
have  one-half  of  itself  transformed  into  the  other  type  of  energy,  both 
of  which  would  continue  to  move  together,  or  else  it  would  be  absorbed 
by  the  medium  or  some  conductor  in  the  path. 

In  the  brief  discussion  given  above  we  have  considered  energy  in  the 
form  of  a  varying  electric  field  acting  in  a  certain  direction  to  be  detached 
from  the  antenna;  but,  of  course,  in  a  similar  manner  energy  is  also 
detached  in  the  form  of  an  electric  field  acting  in  the  opposite  direction, 
so  that  the  electric  field,  equivalent  to  the  energy  which  is  detached  from 
the  antenna,  is,  at  any  point,  varying  continually  in  value  and  direction 
similarly  to  the  antenna  current.  If  this  is  harmonic  the  variation  of 
the  detached  field  will  at  any  point  be  harmonic.  Furthermore,  since 

1  In  trying  to  picture  radiation  in  this  elementary  fashion,  statements  are  neces- 
sarily made  which  will  appear,  to  the  mathematical  physicist,  rather   crude  and  arti- 
ficial. 

2  This  same  idea  holds  good  for  water  waves  also ;   when  the  two  types  of  energy 
associated  with  the  wave  become  unequal  the  wave  "breaks." 


702 


ANTENNAE  AND   RADIATION 


[CHAP.  IX 


it  takes  time  for  the  field  to  travel  any  distance,  it  follows  that  the  phase 
of  the  field  will  be  different  at  each  point;  in  other  words  we  shall,  as 
already  outlined  in  Chapter  III,  have  a  wave  constituting  an  electro- 
magnetic disturbance  in  the  medium,  so  that  while  at  a  certain  instant 
of  time  the  electric  field  in  a  certain  portion  of  the  space  may  be  repre- 
sented by  (a)  Fig.  10,  the  maximum  intensities  occurring  at  1,  2,  3,  a  little 
later  the  electric  field  will  appear  as  at  (6),  the  maximum  intensity  now 
occurring  at  1',  2',  3',  and  the  wave  of  electric  disturbance  having  traveled 
the  distance  from  1  to  1'.  The  above  also  applies  to  the  magnetic  field, 

123 


Electric  field 


b    > 


I 
Direction  of  motion  of  wave 

2 


Magnetic  field 

d 
^. 

FIG.  10. — Electric  and  magnetic  fields  associated  with  a  wave  of  radiation  at  two  suc- 
cessive instants  of  time;  magnetic  field  c  occurs  with  electric  field  a,  dense  magnetic 
field  occurring  where  dense  electric  field  is  and  vice  versa — The  magnetic  and  electric 
fields  are  in  time  phase  and  space  quadrature. 

the  latter  acting  in  a  direction  perpendicular  to  the  electric  field,  and 
both  moving  together  in  a  direction  perpendicular  to  both.  Thus,  at  a 
certain  instant  the  magnetic  field  in  the  portion  of  the  space  for  which  the 
electric  field  is  given  in  Fig.  10  (a)  and  (b)  will  be  represented  by  (c)  and 
(d)  Fig.  10,  which  will  correspond  to  (a)  and  (b)  respectively.  Since, 
as  already  stated,  a  moving  electric  field  produces  a  magnetic  field  propor- 
tional to  its  own  intensity,  and  vice  versa,  it  follows  that  the  intensities 
of  the  two  fields  are  in  time  phase,  though  in  space  quadrature. 
From  p.  696  we  have 

I  =VHXl()~8 (3) 


H=aVl 


(4) 


ELEMENTARY  ANALYSIS   OF   RADIATION  703 

Since  in  the  case  under  discussion  the  electric  field  is  produced  by  the 
motion  of  the  magnetic  field  and  the  latter  is  produced  by  the  motion 
of  the  electric  field,  it  follows  that  the  H  and  fc  of  Eq.  (3)  are  the  same 
as  the  H  and  fc.  of  Eq.  (4),  and  may  be  substituted  therein.  Thus,  from  (3) 

tf  =4x108, 
and  substituting  in  (4) 

108Xy-=aF, 

10s 

a=^2> 

and  of  course  the  second  equation  becomes  the  same  as  the  first,  i.e., 

ti   —~ 


or 

In  our  case  V,  the  velocity  of  magnetic  field  and  of  the  electric  field,  is 
the  velocity  of  light;  since  the  velocity  of  light  is  3X1010  cms.  per  sec. 
we  may  substitute  this  in  Eq.  (3)  and  thus  obtain 

1=300  H  ..........     (5) 

From  this  relation  we  conclude  that  a  magnetic  field,  of  intensity 
represented  by  one  gauss,  when  moving  with  the  velocity  of  light,  gener- 
ates an  electric  field,  at  right  angles  to  itself  and  to  the  motion,  of  the 
intensity  of  300  volts  per  centimeter. 

From  our  brief  qualitative  consideration  of  the  phenomena  around 
an  antenna  carrying  an  alternating  current  it  follows  that  we  may  consider 
the  space  about  an  antenna  as  occupied  by  two  components  of  electric 
and  magnetic  fields.  One  of  these  is  continually  moving  backwards  and 
forwards  from  the  antenna,  so  that  energy  is  alternately  given  to  it  by 
the  antenna  and  returned  by  it  to  the  antenna.  Because  of  this  back- 
wards and  forwards  motion  the  average  displacement  of  this  component 
of  either  field  is  zero,  and  may  therefore  be  known  as  the  "  stationary  " 
component,  also  known  as  the  "induction"  field;  it  is  this  component 
with  which  students  of  electrical  engineering  are  more  familiar,  in  so  far 
as  it  is  this  which  produces  the  well-known  phenomena  of  induction 
(either  magnetic  or  electrostatic). 

The  other  component  of  either  field  is  the  one  which,  once  having 
left  the  antenna,  is  prevented  from  returning  to  it  and  is  thereafter  urged 
away  from  the  antenna  and  continually  travels  outward  from  this  with 
the  velocity  of  light.  This  component,  while  fundamentally  of  the  same 
nature  as  the  stationary  component,  it  is  yet  very  different  in  so  far  as 


704  ANTENNAE  AND   RADIATION  [CHAP.  IX 

it  is  completely  detached  from  the  antenna.  It  is  known  as  the  "  radia- 
tion "  field  and  represents  energy  which  is  transferred  by  the  antenna 
to  the  medium  around  it,  which  energy  is  never  again  returned  to  the 
antenna.  At  any  given  point  in  space  the  induction  fields  (magnetic 
and  electric)  are  out  of  time  phase  by  90°;  at  the  instant  one  of  them  is 
a  maximum  the  other  is  zero.  The  two  components  of  the  radiation 
field,  on  the  other  hand,  are  in  time  phase  with  one  another;  at  a  given 
point  in  space  the  two  components  rise  and  fall  simultaneously. 

Both  of  the  above  types  of  the  fields,  i.e.,  induction  and  radiation 
exist  at  any  point  at  any  distance  from  the  antenna;  but  at  points  near 
it  the  induction  field  is  much  greater  than  the  radiation  field,  while  at 
points  far  away  from  the  antenna  the  radiation  field  is  so  much  greater  than 
the  induction  field  that  the  latter  may  be  said  not  to  exist.  The  reason 
for  this  is  that  the  amplitude  of  the  induction  field  at  any  point  varies 
inversely  as  the  square  of  the  distance  while  that  of  the  radiation  field 
varies  inversely  as  the  first  power  of  the  distance.1  Thus  any  effects 
of  the  field  near  the  antenna  are  mostly  due  to  the  induction  field,  while 
at  great  distances  from  the  antenna  they  are  mostly,  and  practically 
wholly,  due  to  the  radiated  field.  Hereafter  when  speaking  of  the  field 
about  an  antenna  we  will,  unless  otherwise  specified,  mean  to  refer  to 
the  radiation  field,  since  this  is  the  one  by  means  of  which  intelligence 
is  transmitted  to  great  distances  without  wires. 

The  radiation  component  of  the  field  is  most  important  when  the 
currents  in  the  antenna  are  of  high  frequency ;  but  it  must  not  be  under- 
stood that  no  radiation  component  exists  at  low  frequencies;  for  a  radi- 
ation component  exists  at  any  and  all  frequencies.  Since,  however,  the 
very  reason  for  the  existence  of  such  a  component  is  to  be  found  in  the 
inability  of  the  energy  given  to  a  rapidly  changing  field  to  return  in  its 
entirety  to  the  circuit  giving  out  the  energy,  it  follows  that,  for  slowly 
changing  fields,  this  effect  is  negligible,  and  hence  the  radiation  field  is 
practically  non-existent  and  is  never  considered  in  low-frequency  circuits. 

It  must  not  be  concluded,  as  a  result  of  the  foregoing  elementary 
analysis,  that  there  are  actually  two  different  fields  to  be  considered,  one 
induction  and  one  radiation.  At  any  point  in  space  in  the  neighborhood 
of  a  radiating  system,  the  magnetic  and  electric  fields  both  go  through 
harmonic  variations.  Close  to  the  radiator  these  two  fields  are  both  of 
intense  amplitude  (comparatively)  and  they  are  very  nearly  90°  out 
of  time  phase;  as  the  distance  from  the  oscillator  increases  both  of  these 
fields  fall  off  in  intensity  and  with  increasing  distance  the  phase  difference 
is  diminished  until  at  very  great  distances  (perhaps  a  wave-length  from 
the  radiator)  the  electric  and  magnetic  field  are  in  phase. 

1  See  "Principles  of  Radio  Transmission  and  Reception  with  Antenna  and  Coil 
Aerials,"  by  J.  H.  Dellinger.  Proceedings  A.  I.  E.  E.,  October,  1919. 


ELEMENTARY  ANALYSIS  OF  RADIATION 


705 


This  point  is  illustrated  in  Fig.  11;  in  (a)  are  shown  the  magnitudes 
of  the  actual  electric  and  magnetic  fields  at  various  distances  from  the 
radiator  (points  supposed  in  the  equatorial  plane)  and  in  (6)  and  (c)  are 
shown  the  induction  and  radiation  components  of  the  actual  field.  The 
electric  and  magnetic  fields  are,  for  all  conditions,  in  space  quadrature  (i.e., 
at  right  angles  with  one  another)  but  the  time  phase  between  the  two 
fields  varies  as  indicated  in  the  diagram. 


Actual  fields,  at  first  decreasing  rapidly  with  distance, and 
then  more  slowly;  time  phase  between  E  andvH  decreases 
from  nearly  90°at  (1)  to  0°at  (5) 


Induction  fields  decreasing  rapidly  with  distance,  time 
phase  between  E  and  H  for  all  points=90° 


H 

Radiation  fields  decreasing  slowly  with  distance,  time, 
phase  between  E  and  H  for  all  points  =0° 


Increasing  distance  from  antenna 


FIG.  11. — Actual  electric  and  magnetic  fields  at  different  points  in  the  vicinity  of  an 
antenna  shown  in  a;  these  actual  fields  decrease  in  magnitude  with  distance  from 
the  antenna  and  at  the  same  time  come  more  nearly  into  time  phase.  The  compo- 
nents of  the  fields  which  are  90°  out  of  phase  (in  time)  are  called  the  induction 
fields,  shown  at  b,  while  the  components  which  are  in  time  phase  with  each  other 
constitute  the  radiation  fields;  the  latter  decrease  with  the  first  power  of  the  dis- 
tance while  the  former  decrease  with  the  second  power  of  the  distance. 

The  above  discussion  has  been  given  on  the  basis  of  the  antenna  and 
counterpoise  represented  by  Fig.  1,  but  it  applies  equally  well  no  matter 
what  the  counterpoise  and  no  matter  what  the  nature  of  the  source  which 
produces  alternating  currents  in  the  antenna. 

Radiated  Field  at  any  Distance  from  Antenna. — Before  taking  this 
up  we  will  discuss  very  briefly  the  distribution  of  the  current  in  an  aerial. 
In  the  case  of  the  aerial  shown  in  Fig.  12  it  is  plain  that,  since  the  current 
in  the  wire  CD  flows  only  to  charge  the  capacity  of  the  wire,  the  effective 


706 


ANTENNAE  AND  RADIATION 


[CHAP.  IX 


value  of  the  current  at  C  will  be  a  maximum  and  at  D  it  will  be  zero, 
for  the  current  at  C  represents  the  electricity  flowing  through  that  point 
which  goes  to  charge  the  rest  of  the  wire,  while  at  the 
point  D  no  electricity  whatever  flows,  since  there  is 
nothing  to  which  it  can  flow. 

On  the  other  hand,  if  a  metallic  plate  or  a  system 
of  conductors  be  arranged  at  the  end  of  the  wire  CD, 
as  at  FG,  Fig.  13,  and  if  FG  has  a  very  large  surface 
as  compared  with  that  of  CD,  it  is  plain  that  the  effect- 
ive value  of  the  current  at  D  will  then  be  only  slightly 
smaller  than  that  at  C,  since  the  current  at  D  must  be 
FIG.  12.— A  simple  sucn  as  *°  charge  the  large  capacity  FG.     Under  such 
vertical    wire  conditions  the  effective  values  of  the  current  in  all  parts 
grounded  antenna,  of  the  vertical  wire  of  the  antenna  will  be  sensibly  equal 
and   will   be   considered  as  such  in  the  following  dis- 
cussion.    Consider  then,  the  aerial  as  represented  in  Fig.  14  where  the 
counterpoise  is  represented  by  a  horizontal  system  of  conductors,  F'G', 
laid  near  the  ground  but  insulated  therefrom,  being  in  every  way  similar 
to  the  system  of  conductors  at  the 
top  of  aerial  FG.     The  current  in 
the  vertical   part  of  the  aerial  CD 
will  be  assumed  to  have  the  same 
effective  value  throughout,  so  that  at 
every  point  of  CD  we  will  have  for 
the  equation  of  the  current: 

i  =  Im  sin  co£, 
where 

i—  instantaneous  value  of  aerial 

current  in  amperes; 
Im  -  maximum  value  of  aerial  cur-  FIG.  13. — If  the  antenna  has  a  consider- 
rent  in  amperes ;  a°le  network  of  wires  above  the  current 

co  =  angular   velocity  of  current 

vector  in  radians /sec.; 
t  =time  in  seconds. 


in  wire  CD  will  be  nearly  the  same  in 
amplitude  at  all  points  of  the  wire. 


Under  these  conditions  it  may  be  shown  that  the  radiation  component 
of  the  magnetic  field,  at  any  point  in  the  equatorial  plane  of  the  aerial, 
is  given  by  :  l 


1  The  normal  development  of  the  equation  of  radiation  field  requires  more  mathe- 
matical background  than  the  average  radio  engineer  possesses  and  it  is  not  thought  well 
to  introduce  it  here;  a  short  analysis  of  the  problem  is  given  in  Berg's  "Electrical 


OF   RADIATION 


707 


where  h  =  instantaneous  value  of  magnetic  field  in  gausses; 

I  =  height  of  antenna  in  centimeters; 

y  =  velocity  of  light  in  centimeters  per  second  ; 

d  =  distance  of  point  in  question  from  antenna  in  centi- 

meters. 

The  above  equation  shows  that  the  radiation  magnetic  field  is  a  function 
similar  to  the  antenna  current  (in  this  case  a  harmonic  function),  and  that 


F' 


f—Jm  sin  wt 


•  Equatorial  plam 


'lOVd 


FIG.  14. — With  uniform  current  in  wire  CD  the  magnetic  field  due  to  this  current,  is 

given  as  above. 

the  phase  angle  is  different  for  points  at  different  distances  since  this  angle 
is  equal  to  co  ^.     Substituting  w  =2irf  and  V  =  X/  we  have: 

phase  angle  =—-  (X  being  measured  in  cm.), 

A 

whence,  Eq.  (6)  becomes: 

?  COS   (  (j^t  — 


Since  the  "  radiation  "  component  of  the  electric  fields  bears  a  fixed  rela- 
to  the  "  radiation  "  component  of  the  magnetic  field  as  given  by  Eq.  (5), 
we  may  write: 


€=300/i= 


where 


e  =  instantaneous  value  of  electric  field  in  volts  per  centi 
meter. 


From  Eqs.  (7)  and  (8)  we  obtain  the  effective  values  of  the  radiation  com- 
ponents of  the  two  fields.  Thus,  if: 

Engineering,  Advanced  Course,"  p.  278  et  seq.  Eq.  (20),  p.  289,  of  that  volume  is 
the  same  as  the  Eq.  (6)  given  above,  it  being  noted  that  Berg  has  used  h  to  signify 
one-half  the  length  of  the  oscillator. 


708 


ANTENNA  AND  RADIATION 


[CHAP.  IX 


H  =  effective  value  of  magnetic  field  in  gausses; 
£.  =  effective  value  of  electric  field  in  volts  per  centimeter, 


H  = 


lOXd 


(9) 


(10) 


where 


/=  effective  value  of  the  current  in  aerial,  in  amperes. 


Eqs.  (9)  and  (10)  show  that  the  effective  value  of  either  field  varies 
directly  with  the  effective  value  of  current  in  the  aerial  and  with  the  height 
of  the  aerial  and  inversely  as  the  wave-length  and  distance  from  the  aerial. 

Now  consider  the  case  represented  by  a  loop  of  wire  as  shown  in  Fig. 
15.  Assume,  similarly  to  the  previous  case,  that  the  capacity  of  the  con- 


FIG.  15. — In  the  case  of  a  coil  antenna  the  magnetic  field  at  P  is  calculated  by  adding  the 
two  fields  due  to  CD  and  FG,  it  being  noted  that  the  currents  are  opposite  in  direc- 
tion. 

denser,  P\-Pzj  is  so  large  as  compared  with  the  distributed  capacity 
of  the  loop  CDGF  that  the  latter  has  the  same  effective  value  of  current 
throughout  its  length. 

Consider  the  magnetic  field  at  a  point  P  at  a  distance  d  from  vertical 
wire  CD  and  a  distance  s+d  from  vertical  wire  GF.  Assume  the  positive 
direction  of  current  to  be  as  shown  by  the  arrows.  Then  the  field  at  P 
must  be  equal  to  the  difference  of  the  field  due  to  CD  and  that  due  to  FG. 


Let 


hi  =  instantaneous  value  of  magnetic  field  at  P  due  to  CD] 
h,2  =  instantaneous  value  of  magnetic  field  at  P  due  to  FG. 


Then,  from  Eq.  (7)  we  have 


(H) 


10X(d+s) 


(12) 


LAWS  OF   RADIATION 


709 


It  will  be  noted  that  the  amplitude  of  these  two  fields  is  practically  the 
same,  since,  for  great  distances,  d  is  practically  equal  to  d-\-s,  but  the 
phases  of  the  fields  are  different  by  the  amount 

27TS 

TT — —  radians. 
The  resultant  field  (h)  is  given  by: 


lOXd 


cos 


(co£ ^-J— COS  (co£  — 


From  which  the  effective  values  of  the  resultant  magnetic  and  electric 
fields  are  given  by 

4-jrlI        TTS 
//=T7^-isin— (14) 


lOXd 

,    _    12007T/7      ,       7T.S 

L  —     TTT:   r~"  Sin  — — . 


(15) 


sin 
X 


OA=  field  at  P  due  to   CD 

OB:= FG 

OC= resultant  field,  obtained 
by  adding  (yectorially)  OB 
toOA 


FIG.  16. — The  field  due  to  wire  CD  is  shown  by  vector  OA ;  that  due  to  FG  is  shown  by 
OB'  nearly  180°  out  of  phase  with  OA.     The  actual  field  is  obtained  by  adding 

vectorially  OB'  and  OA,   it  being  noted  that  they  differ  in  phase  by  {*•  —  — -) . 

The  vector  addition  of  HI  and  fa  by  which  Eq.  (14)  is  obtained  is 
shown  in  Fig.  16.  These  equations  show  that  the  effective  value  of  the 
resultant  field  is  equal  to  twice  that  due  to  either  wire  multiplied  by  the 
sine  of  an  angle  which  varies  with  the  distance  between  the  two  wires. 

Thus  if  a  =  X 


.        ITS 

sm  —  =  sin  TT  =  0 

A 


and  if  s=s 


.       ITS          .       7T 

sin  y  =sm  ^  =  1. 


710 


ANTENNA   AND   RADIATION 


[CHAP.  IX 


•Y 


It  may  then  be  seen  that  if  the  distance  between  the  two  wires  of  the 
loop  is  exactly  equal  to  one  wave-length,  the  resultant  field  at  all  points  in 
the  plane  of  the  loop  is  zero,  while  if  the  distance  between  the  two  wires  is 

one-half  a  wave-length  the  resultant 
field  in  the  plane  of  the  loop  is  equal 
to  twice  that  of  one  wire.  In  other 
words  the  resultant  at  any  one  point 
is  due  to  fields  of  the  same  amplitude 
but  different  phase,  the  latter  depend- 
ing upon  the  distance  between  the 
wires,  since  in  one  case  the  field  has  to 
travel  a  greater  distance  than  in  the 
case  of  the  other  wire.  Thus,  if  the 

two  wires  were  close  together  the  resultant  field  at  any  point  would  be 
zero. 

Again,  if  a  point  be  chosen  such  as  F,  Fig.  17,  in  a  plane  perpendicular 


o 

Wire  Q-D 


Wite  P-@ 
o 


FIG.  17. — At  a  point  Y  in  the  equatorial 
plane  of  the  coil,  equidistant  from 
both  wires  C-D  and  FG  the  radiation 
field  is  zero. 


FIG.  18. — The  distribution  of  radiation  field  in  the  equatorial  plane  of  a  coil  antenna. 

to  the  plane  of  the  loop  and  equidistant  from  both  wires,  it  is  plain  that 
the  fields  at  F  due  to  either  CD  or  FG  must  be  180°  out  of  phase,  since 
they  have  to  travel  the  same  distance,  and  the  result  is  that  the  resultant 


EXCITATION   OF  ANTENNA 


711 


High  frequency  alternator 


'Poulsen  arc 


Tube  oscillator 


field  at  Y  is  zero.  For  points  other  than  those  such  as  point  Y  of  Fig. 
17  and  point  P  of  Fig.  15  the 
maximum  value  of  the  field  for 
a  certain  distance  from  the  aerial 
varies  from  zero  at  Y  to  a  maxi- 
mum at  P. 

If  a  curve  were  plotted  to 
polar  coordinates,  showing  the 
effective  values  of  the  magnetic  | 

field  intensity  at  all  the  points 

around    the   circumference   of  a  FIG.  19.— Excitation  of  antenna  by  magnetic 
circle  having  the  loop  as  a  center,  couPlin^  to  ^enerator- 

we  would  obtain  a  diagram  as 

shown  in  Fig.  18,  the  intensity  of  the  field  at  any  point  P  along  the  cir- 
cumference PQR  being  represented  by  the  line  Oa.     It  may  be  easily 

shown  that  the    intensity  of   the  field 

varies  harmonically  from  zero  at  points 
R  and  R'  to  maxima  at  points  T  and  T', 
and,  therefore,  the  curves  OBC  and  ODF 
should  be  circles  with  a  diameter  equal 
to  the  intensity  of  the  field  in  the  direc- 
tion TT'.  Such  a  loop  will,  then,  radi- 

mos"t  energy  in  the  direction  TT'  in 

the  plane  of  the   coil   and   practically 
FIG.  20 —Simplest  scheme   for   spark  none  m  tne  direction  RR' '. 

telegraphy  excitation.  Methods  of  Producing  Current  in 

the  Antenna. — So  far  we  have  dis- 
cussed simple  antennae  energized  by  means  of  an  alternator  placed  directly 
in  series  with  the  aerial;  but  it  has  already  been  stated  that  an  antenna 
may  be  energized  by  means 
other  than  this  one.  Thus 
the  diagrams  of  Figs.  19,  20, 
and  21  give  various  methods 
of  energizing  the  antenna, 
all  of  which  methods  have 
already  been  studied.  Fig. 
19  shows  the  alternator  in- 
ductively coupled  to  the 
antenna  circuit,  instead  of  pIGi  21.— Ordinary  scheme  of  excitation  for  spark 
having  the  alternator  directly  telegraphy, 

in  the  antenna  circuit.     This 

has  the  advantage  of  eliminating  some  of  the  harmonics  of  the  alter- 
nator, so  that  the  current  in  the  antenna    is    now  nearly  harmonic.     It 


712 


ANTENNJE  AND  RADIATION 


[CHAP.  IX 


is  to  be  noted  that  instead  of  a  high-frequency  alternator,  a  tube  gen- 
erator or  a  Poulsen  arc  may  be  used,  and,  in  every  case  the  antenna 
current  will  be  nearly  harmonic  and  undamped. 

On  the  other  hand,  the  arrangements  of  Figs.  20  and  21  are  meant 
to  produce  trains  of  damped  currents  in  the  antenna.     In  Fig.  20  the 


Umbrella  type 
FIG.  22. — Umbrella  antenna. 

spark  gap  is  directly  in  the  antenna,  while  in  Fig.  21  the  spark  gap  is 
placed  in  the  so-called  closed  oscillating  circuit.  The  disadvantage  of 
placing  the  spark  gap  directly  in  the  antenna  is  due  to  the  fact  that  such 
a  gap  has  considerable  resistance,  especially  in  the  case  of  high-power, 
high-voltage  sets  where  the  gap  distance  must  be  large,  and  when  so  used 
will  make  the  decrement  of  the  antenna  proper  very  high,  which  is 


"T"  type 


FIG.  23. — Antenna  of  the  T  type. 

objectionable.  Hence,  with  very  few % exceptions,  i.e.,  low-power  sets, 
all  modern  sets  place  the  spark  gap  in  the  closed  oscillating  circuit,  instead 
of  in  the  antenna. 

The  methods  outlined  above  are  only  typical,  and  there  are  several 
other  ways  of  energizing  the  antenna,  which  have  already  been  taken  up 
in  Chapters  III,  VI  and  VIII. 


TYPES  OF  ANTENNAE 


713 


Various  Types  of  Antennae. — It  was  stated  on  p.  706  that  if  a  single 
vertical  wire  be  used  for  antenna  the  effective  value  of  current  at  the  base 
of  the  wire  will  be  maximum,  while  at  the  top  it  will  be  zero.  Since,  the 
intensity  of  the  field  radiated  by  an  antenna  is  directly  proportional  to 
the  current  therein  (on  the  basis  of  a  constant  current  throughout  the 


FAN  TYPE 


FIG.  24. — Antenna  of  the  inverted  L  type. 

antenna)  it  is  plain  that  a  single  vertical  wire  with  non-uniform  current 
will  not  radiate  as  well  as  if  it  had  a  capacity  at  the  top  end,  when  the  cur- 
rent would  be  more  nearly  uniform,  and  also  larger,  for  a  given  voltage 
impressed  by  the  power  source.  Such  a  capacity  is  used  at  the  top  end 
of  an  antenna  in  actual  practice,  the  capacity  being  in  the  form  of  wires 
stretching  outward  from  the  antenna  proper.  Depending  on  how  these 
wires  are  arranged  we  have  sev- 
eral types  of  antennas,  known  as : 
umbrella,  T-type,  inverted  L- 
type,  "  Fan  or  Harp "  type, 
"  Multiple-tuned  "  type,  "  Coil  " 
type. 

These  various  types  are  shown 
in  the  conventional  diagrams  of 
Figs.  22-27,  respectively. 

The  characteristics  of  these 
various  types  of  antennas  will 
now  be  discussed. 

Umbrella  Type. — Since  the  top 
wires  are  symmetrically  arranged 

all  around  the  central  radiator  it  is  easily  inferred  that  at  a  given  distance 
from  the  aerial  the  intensity  of  the  field  all  around  the  radiator  is  the 
same,  that  is,  the  curve  of  distribution  of  field  intensity  around  the  radiator 
should  be  a  circle.  It  must  be  noted  that,  while  in  the  case  of  a  single 
wire  or  of  a  Hertzian  double  for  a  radiator,  vertical  wires  only  are  used 
to  radiate  energy,  in  the  umbrella  type  aerial  the  inclined  top  wires  radiate 


FIG.  25. — Fan  or  harp  antenna. 


714 


ANTENNJS  AND  RADIATION 


[CHAP.  IX' 


COIL  TYPE 


FIG.  26. — Coil  antenna. 


a  certain  amount  of  energy  in  the  direction  perpendicular  to  the  wires 
themselves.  Thus,  while  in  the  former  case  we  would  likely  find  the 
intensity  of  the  field  directly  over  the  top  of  the  antenna  practically  nil, 

in  the  latter  case  (the  umbrella  an- 
tenna) the  field  directly  over  the 
top  might  be  of  considerable  strength 
and  is  successfully  used  to  signal  to 
aeroplanes,  even  though  they  be  di- 
rectly over  the  antenna. 

On  the  other  hand,  the  top  spread- 
ers subtract,  to  a  certain  extent, 
from  the  radiating  ability  of  the 
central  vertical  wire,  for  the  follow- 
ing reason.  We  have  already  stated 
that  the  ability  of  the  vertical  wire 
or  wires  as  a  radiator  of  energy 
depends  upon  the  fact  that  in  view 
of  its  very  configuration  it  is 
capable  of  setting  up  a  field,  mag- 
netic and  electric,  which  extends 

to  very  great  distances  from  the  wire  and  is  not  mainly  confined  to 
a  space  near  the  wire;  thus  we  have  seen  that  in  the  case  of  the 
two-plate  condenser  of  Fig.  8  the  energy  stored  in  the  electric  field 
is  mainly  in  the  space  between  the  plates,  which  constitute  a  "  closed 
electric  circuit."  If  ^  ^  ^  r.  r_ 

we  were  to  imagine 
an  umbrella  aerial 
with  a  very  large 
number  of  spreaders 
reaching  nearly  to 
ground,  as  shown  in 
Fig.  28,  it  is  plain 
that  these  spreaders 
would  act  like  one 
plate,  and  the  ground 
like  the  other  plate, 
of  a  closed  electric 
circuit,  and  practi- 
cally no  energy  could 

then  be  radiated  because  the  electric  field  of  the  antenna  would,  for 
the  most  part,  be  confined  in  the  space  under  the  spreaders,  and 
there  would  be  little  likelihood  of  any  energy  being  detached  from  the 
antenna.  ;  The  radiation  from  such  an  arrangement  would  of  course 


Multiple  tuned  antenna 
FIG.  27, — Multiple-tuned  antenna. 


TYPES  OF  ANTENNAE 


715 


Umbrella  antenna  \v£h  electric 
field  nearly  "closed" 


Poor  radiator 


J^^%^^^ 

FIG.  28. — Umbrella  antenna  of  this  form  is  a  poor  radiator;  the  spreaders  come  to  low. 

be  very  small.  In  an  actual  umbrella-type  antenna  the  spreaders  do 
not  reach  to  anywhere  near  ground,  hence  they  do  not  seriously  interfere 
with  the  radiation  though  they  do  so  to  a  certain 
extent. 

Another  reason  for  the  spreaders  interfering 
with  radiation  is  to  be  found  in  the  fact  that,  at 
any  time,  the  direction  of  the  current  flowing 
through  the  vertical  wire  is  opposite  to  that  flow- 
ing in  the  spreaders;  that  is,  if  the  current  in  the 
vertical  wire  is  upward  that  in  the  spreaders  is 
downward.  In  the  extreme  case  where  the  spread- 
ers might  be  considered  as  being  close  to  the  ver- 
tical wire,  as  in  Fig.  29,  the  portion  of  the  vertical 
wire  AB  would  be  seriously  limited  in  its  radiating 
action,  since  the  action  of  the  current  in  the  vertical 
wire  is  opposed  by  that  of  the  spreaders. 

However,  the  total  interference  of  the  spreaders 
with    radiation   from    the  vertical  wire  is  less  than 
what  they  contribute  towards  increasing  the  radia-  FIG.  29.— If  thespread- 
tion  through   causing  a  more  uniform   current  and,      er  wires  are  brougnt 
for  the  same  voltage,  a  larger  current,  to  flow  through 
the  vertical  wire.      Several    large  antennae  of   this 
type  have  been  used  for  long  distance  transmission. 
In     the    smaller    sizes    they    are    very    convenient 
for   portable   sets    where   the    spreaders,    anchored   through   insulating 
clamps  to    the   ground,  serve    the    purpose  of  holding  the  central  sup- 


down  very  close  to 
the  antenna  proper 
the  radiation  is  prac- 
tically zero. 


716  ANTENNA  AND  RADIATION  [CHAP.  IX 

port,  in    addition    to    increasing  the    capacity  at  the    top   end  of  the 
vertical  wire. 

The  effect  of  the  spreaders  may  be  looked  upon  as  if  the  height  of  the 
vertical  wire  had  been  diminished  and  it  may  be  shown  that  the  "  effective 
height  "  of  an  umbrella  antenna  is  aproximately  given  by 


where  h  =  effective  height  ; 

hi  and  fa  =  the  heights  as  represented  in  Fig.  22. 

Fig.  30  shows  the  arrangement  of  spreaders,  vertical  wire  and  vertical 
support,  insulation,  etc.,  for  a  small  umbrella  aerial,  where  aaabbb  repre- 
sent insulators  and  cd  the  vertical  radiating  wire.  The  spreaders  are 
generally  made  long  enough  to  extend  about  two-thirds  the  length  of  the 
mast.  A  large  piece  of  wire  netting  (called  a  ground  mat)  may  serve 
as  a  counterpoise  for  the  oscillating  system. 

*'T"  Type.  —  Since  the  top  wires  are  on  this  type  unsymmetrically 
arranged,  i.e.,  extending  outward  from  the  vertical  wire  in  two  directions 
only,  it  would  seem  at  first  as  if  the  field  produced  by  such  an  aerial  would 
not  be  quite  the  same  all  around  the  antenna.  This  is  probably  the  case 
at  comparatively  short  distances  from  the  aerial,  but  it  is  not  found  to 
be  so  at  large  distances  away,  in  view  of  the  tendency  of  the  field  to  become 
uniform  as  it  spreads  out  in  all  directions  away  from  the  aerial. 

Here,  as  in  the  case  of  the  umbrella  type,  some  energy  is  also  radiated 
in  a  direction  directly  above  the  antenna.  Antennae  of  this  type  are  very 
widely  used  on  shipboard  where  the  flat  top  is  easily  suspended  between 
two  masts;  also  for  portable  sets  an  aerial  of  this  type  is  easily  suspended 
between  two  trees. 

Inverted  "L"  Type.  —  The  main  difference  between  this  type  and  the 
"  T  "  type  is  that  the  "L"  type  has  a  more  pronounced  directional  effect, 
that  is,  it  is  capable  of  producing  a  greater  intensity  of  radiation  in  one 
direction  than  in  any  other.  This  action,  in  the  case  of  the  "L"  antenna, 
is  not  yet  very  fully  understood  and  it  is  by  some  stated  to  be  too  small 
to  actually  claim  for  this  type  of  antenna  directional  ability.  However, 
this  type  of  antenna  is  used  by  the  Marconi  Co.  for  the  large  transatlantic 
stations  and  has  actually  been  found  to  develop,  even  at  considerable 
distance  from  it,  a  field  stronger  in  the  direction  of  the  arrow  Fig.  31  than 
in  any  other.  This  effect  depends  especially  upon  the  length  of  the  flat 
top,  BC,  as  compared  with  the  vertical  wire  AB.  The  longer  BC  is  made 
relative  to  A  B  the  greater  seems  to  be  the  directional  effect  of  the  antenna. 
It  is  probable  that  this  is  due  to  an  interfering  action  of  some  sort,  between 


TYPES  OF  ANTENNA 


717 


the  currents  in  the  vertical  and  horizontal  portions  of  the  antenna,  which 
occurs  on  one  side  of  the  antenna  to  a  much  greater  extent  than  on  the 
other.  This  would,  of  course,  take  place  to  a  greater  extent  the  larger 


M 


the  horizontal  portion  of  the  aerial  relative  to  the  vertical  portion.  The 
Clifden  station  of  the  Marconi  Co.  has  a  vertical  portion  about  60  meters 
high  and  a  horizontal  portion  about  2000  meters  long;  it  is  said  to  have 
a  large  directional  effect.  In  "  L"  type  aerials  as  used  on  board  ships, 
however,  the  horizontal  portion  is  never  very  much  longer  than  the  verti- 


718 


ANTENNAE  AND  RADIATION 


[CHAP.  IX 


Inverted"  IT  is  somewhat  directive 


Maximum 


radiation 


cal  portion  and  it  is  doubtful  if  in  this  case  any  appreciable  directional 
effect  is  present,  even  at  short  distances  from  the  aerial. 

A  directional  effect  is  noted  in  the  case  of  aeroplanes  carrying  a  long 
vertical  wire  weighted  at  one  end  and  dangling  beneath  the  aeroplane 

c proper;  this  wire, 

when  the  aero- 
plane is  in  flight, 
bends  somewhat 
as  shown  in  Fig. 
32  and  very  much 
in  the  form  of 
an  inverted  "  L" 
^^^^^^  aerial.  The 

FIG.  31. — An  inverted  L  antenna  is  somewhat  directional  giving  Sreatest  field  in- 
maximum  radiation  in  the  direction  shown  above.  tensity  IS   in  the 

direction  of  flight 

or    away   from    the   horizontal  portion   of  the   aerial;   in  this  case  the 
framework  of  the  plane  is  the  counterpoise. 

Not  only  are  "  inverted  L"  aerials  used  in  large  transatlantic  stations 
but  they  are  also  favorites  on  board  ships,  where  they  are  as  easily  installed 
as  the  "  T  "  type.  They  are  also  widely  used  for  small  stations  and  by 
amateurs.  As 
regards  their  use 
on  board  ships 
it  is  customary 
to  install  them 
where  the  dis- 
tance between 
the  masts  does 
not  exceed  about 
30  meters ;  for 
over  30  meters 
the  "  T  "  type  is 
used. 

"Fan  Type" 

Aerial. — In  this 
case  a  large  num- 
ber of  vertical  or 

nearly  vertical  wires  in  multiple  are  used,  the  top  ends  of  these  wires 
being  perhaps  free,  that  is  not  connected  electrically  to  any  other  wires. 
In  such  an  arrangement  the  effective  value  of  the  current  at  the  base  of 
each  wire  is  a  maximum  while  it  is  zero  at  the  top,  or,  in  other  words  the 
current  distribution  is  very  far  from  uniform,  and  in  this  respect  the 


Flight 


Weight 


FIG.  32.- 


An  aeroplane  antenna  is  directional,  sending  out  most 
power  in  the  direction  of  flight. 


TYPES  OF  ANTENNAE  719 

arrangement  is  objectionable.  On  the  other  hand,  the  capacitance  of 
the  aerial  is  very  large,  in  view  of  the  capacitance  of  so  many  wires  con- 
nected in  multiple;  in  fact  the  whole  arrangement  may  be  thought  of  as 
a  single  wire  having  a  capacity  equal  to  that  of  all  the  wires.  The  current 
through  the  combination  of  all  the  wires  may,  because  of  the  large  capacity, 
be  made  very  large  without  excessively  high  voltages.  Another  advantage 
of  this  type  of  aerial  as  compared  with  the  others  previously  discussed 
is  that  there  are  no  horizontal  or  inclined  wires  to  interfere  with  the  radi- 
ation from  the  vertical  wire.  As  a  matter  of  fact  such  an  arrangement 
is  considered  one  of  the  best  and  most  efficient  radiators.  In  spite  of 
this,  however,  the  fan  type  is  not  very  widely  used  because  of  the  dif- 
ficulty of  installing  it,  especially  in  the  case  of  ships  where  such  a  multi- 
tude of  vertical  wires  would  be  in  the  way  of  some  of  the  projecting  parts 
of  the  ship. 

''Multiple  Tuned  "  Type. — This  type  is  of  recent  conception  and  has 
been  used  for  the  New  Brunswick,  N.  J.,  station.  It  consists,  as  shown 
in  the  diagram  Fig.  27,  of  a  horizontal  top  similar  to  the  top  of  "  T  ' 
antenna,  fed  at  one  end  by  means  of  the  alternator  A  connected  in  series 
with  the  tuning  inductance  LI,  and  the  vertical  wire  B\C\,  and  in  addition 
of  a  number  of  vertical  wires  attached  to  the  horizontal  top  at  suitable 
points  and  each  separately  connected  to  ground  through  a  tuning  induc- 
tance. The  result  of  this  is  that  each  of  the  vertical  wires  acts  as  a  vertical 
antenna,  the  whole  arrrangement  constituting  a  number  of  vertical  anten- 
nae connected  in  multiple,  and  hence  radiating  as  if  they  were  a  single 
antenna.  The  advantage  lies  in  the  fact  that,  since  each  vertical  wire 
is  independently  connected  to  ground,  it  follows  that  all  the  ground  resist- 
ances are  connected  in  multiple,  and  hence  the  total  ground  resistance  is 
very  much  less  than  would  be  found  to  be  the  case  with  any  other  type 
of  antenna  of  the  same  power  capacity,  thus  giving  a  very  high  efficiency.1 

Of  course  it  is  hardly  necessary  to  mention  that  the  phases  of  the 
currents  must  be  adjusted  so  that  all  the  vertical  wires  will  be  radiating 
in  phase  with  one  another  in  order  to  obtain  maximum  radiation;  the 
tuning  coils  Li,Z/2,  .  .  .  L*>  are  used  for  the  purpose  of  making  this  adjust- 
ment. 

On  the  other  hand,  if  the  vertical  wires  be  suitably  spaced  and  if,  in 
addition,  the  phases  of  their  currents  be  suitably  adjusted  it  is  said  to  be 
possible  by  means  of  this  type  of  antenna  to  obtain  greater  radiation  in 
one  direction  than  in  another  thus  producing  directional  transmission. 

1  It  must  be  pointed  out  here  that  the  radiation  resistance  of  each  vertical  wire  of 
the  multiple-tuned  antenna  cannot  be  calculated  as  though  the  wire  stood  alone,  using 
e.g.  Eq.  (21),  p.  737.  The  presence  of  the  other  vertical  wires,  also  carrying  current, 
will  affect  this  radiation  resistance,  the  amount  of  this  effect  depending  upon  the  prox- 
imity of  the  various  vertical  wires,  and  upon  the  relative  phases  of  their  currents. 


720  ANTENNAE  AND  RADIATION  [CHAP.  IX 

Thus,  in  the  case  of  the  multiple-tuned  antenna  the  intensity  of  the  radiated 
field  at  any  point  is  the  resultant  of  the  fields  due  to  each  of  the  vertical 
wires  and,  if  suitably  designed  and  adjusted,  the  resultant  field  in  certain 
directions  may  be  made  a  minimum  and  in  others  a  maximum,  thus  pro- 
ducing a  directional  effect.1 

An  elementary  analysis  shows  the  normal  operation  of  this  antenna  to 
be  but  slightly  directive,  the  maximum  radiation  taking  place  at  right 
angles  to  the  length  of  the  antenna.  If  directive  radiation  is  obtained  by 
phase  shifting  in  the  different  vertical  wires,  the  radiation  resistance  of 
the  antenna  as  a  whole  falls  to  a  small  fraction  of  its  normal  value. 

"  Coil  Antenna."  —  This  has  already  been  discussed  on  p.  708,  where 
it  was  shown  that  such  an  aerial  has  a  very  decided  directional  effect, 
and  that  the  intensity  of  the  field  in  the  plane  of  the  coil,  where  it  is  a 
maximum,  is  a  function  of  the  distance  between  the  two  vertical  sides 
of  the  coil  and  is  greatest  when  this  distance  is  equal  to  one-half  a  wave- 
length. A  comparison  may  here  be  made  of  the  single  vertical  wire 
with  uniform  current  throughout  and  of  the  coil  antenna  with  uniform 
current  throughout.  Thus,  from  Eqs.  (9)  and  (14)  on  pp.  708-709  for 
the  effective  values  of  the  intensity  of  the  magnetic  field  at  any  distance 
from  antenna  we  have: 


for  single  wire 

TT      4iirll    .    ITS 
and  ff=sm 


for  coil  of  one  turn.     Of  course,  if  the  coil  aerial  has  more  turns  than 
one  the  intensity  of  the  field  is  directly  proportional  to  the  number  of  turns, 
provided  that  the  current  is  uniform  throughout. 
If  N  =  number  of  turns 

rr      4-jrNlI    .     ITS 

5in—       (14a) 


for  coil  of  N  turns. 

If  7,  /,  X,  and  d  are  the  same  for  the  two  types  of  antennas  we  may 
obtain  the  ratio  of  the  magnetic  fields  due  to  the  coil  and  to  the  single 
wire  by  dividing  (14a)  by  (9).  Thus, 

^ee  paper  by  E.  F.  W.  Alexanderson,  "Transatlantic  Radio  Communication," 
A.  I.  E.  E.,  Proceedings,  Oct.,  1919.  In  reading  this  paper  the  student  should  bear 
in  mind  that  the  quantitative  results  predicted  (magnitudes  of  currents,  etc.)  do  not 
hold  good  for  the  transient  state  which,  in  an  antenna  of  this  kind,  may  be  a  large  frac- 
tion of  the  duration  of  a  "dot," 


TYPES  OF  ANTENNAE 
Ratio  of  field  of  coil  to  that  of  single  wire 


721 


. 

A 


In  order  to  make  the  two  fields  the  same  we  must  have 


.    TTS  _   1 

Sm  Y  ~2N' 


or 


_x  .    _!_!_ 

~7rsm       2N' 


Below  is  given  a  table  showing  the  value  of  s  for  different  values  of  N. 

TABLE  I 

Distance  between  sides  of  a  coil  aerial  of  the  same  height  as  a 
corresponding  single  vertical  wire  aerial  necessary  to  make  the 
fields  from  the  two  aerials  alike. 


,N 

s 

1 

0.17  X 

2 

0.08  X 

3 

0.053  X 

5 

0.032  X 

10 

0.016  X 

100 

0.0016  X 

It  is  understood  that  the  coil  aerial  field  has,  in  the  above  discussion, 
been  considered  which  exists  in  the  plane  of  the  coil,  i.e.,  the  plane  of 
maximum  field  intensity.  The  above  table  shows  that  for  a  single  turn 
coil  aerial  the  width  must  be  as  large  as  0.17X  in  order  for  it  to  have  an 
effect  equivalent  to  that  of  a  single  wire  of  the  same  height.  But  with 
a  larger  N  the  width  may  be  made  much  smaller,  so  that  with  a  100 
turns  the  width  need  only  be  a  few  meters,  even  with  large  wave-lengths. 
However,  with  a  large  number  of  turns  the  question  of  the  capacity 
between  turns  and  the  effective  resistance  of  the  coil  plays  an  important 
part. 

If  the  capacity  from  turn  to  turn  is  large  (i.e.,  the  turns  close  together) 
the  current  will  not  be  uniform  throughout,  and,  furthermore,  the  phase 
of  the  current  at  every  point  will  be  different,  a  condition  which  is  not 
conducive  to  best  results  as  regards  radiation.  Hence  the  turns  should 
be  separated  by  a  considerable  distance  from  one  another.  This  may  be 
stated  by  saying  that  the  capacity  of  the  coil  itself  should  be  such 
^s  to  make  the  fundamental  wave-length  of  the  coil  no  larger  than 


722 


ANTENNA   AM)    RADIATION 


[CHAP.  IX 


about  one-third  of  the  wave-length  to  be  used.  The  effective  resistance 
of  the  coil  antenna  is  taken  up  on  page  737  of  this  chapter. 

As  examples  of  coil  antennae  which  seem  satisfactory  for  receiving 
purposes  it  may  be  noted  that  for  a  600-meter  wave  a  square  coil,  120 
cm.  on  a  side,  of  10  turns,  spaced  about  0.5  cm.  from  each  other,  requires 
a  tuning  condenser  somewhat  less  than  .001  nf. 

By  installing  the  coil  (or  "  loop  "  as  it  is  more  frequently  called)  as 
indicated  in  Fig.  33,  it  may  be  used  with  the  D.  P.  D.  T.  switch  down, 


For  600  meters 
10  turns  120  cm.  square 


About  .0006/u/ 


.OOOOSy"/ 


.OOOOSyU/ 


-  To  detector 
-and  amplifier 


FIG.  33. — Use  of  a  coil  receiving  antenna;  by  throwing  the  switch  down  the  coil  acts 
as  a  simple  antenna,  the  coil  L  being  used  for  tuning.  When  it  is  desired  to  get 
the  directional  effect  of  the  coil  the  switch  is  thrown  up. 

for  general  reception,  the  loop  merely  acting  as  a  low  antenna,  tuning 
being  accomplished  by  the  variometer,  L.  When  the  desired  signal  is 
received  the  switch  may  be  thrown  upwards  and  the  directive  effect  of 
the  coil  thus  be  obtained. 

For  wave-lengths  from  10,000-20,000  meters  a  square  coil  about 
6  meters  on  a  side  with  50  turns  spaced  4  cm.  apart  is  suitable. 

Because  of  the  comparatively  low  receptive  power  of  loop  antennae 
the  receiver  (detector)  used  must  be  the  most  sensitive  available;  the 
use  of  such  a  detector  with  a  good  amplifier  is  possible  because  of  the  com- 
paratively low  intensity  of  the  "  strays  "  picked  up  by  a  loop. 


TYPES  OF  ANTENNA 


723 


metal  work 
f  ship,  carefully 
connected  to- 
gether 


Aeroplane  and  Airship  Antennae. — The  aerial  system  of  aircraft  comes 
nearest  to  approximating  the  conditions  represented  by  the  simple  aerial 
system  of  the  Hertzian  double  (see  Fig.  1),  in  so  far  as  the  counterpoise 
is  not  the  ground,  and  furthermore  the  antenna  and  counterpoise  are 
at  considerable  distance  from  the  ground,  so  that  the  electromagnetic 
waves  generated  by  such  a  radiating  system  travel  outward  in  space 
without  coming  in  contact  with  the  ground  except  at  considerable  distance 
from  the  radiating  system. 

The  various  types  of  radiating  systems  used  may  be  classified  into 
two  general  headings: 

(1)  Those  which  may  be  used  only  when  the  ship  is  in  flight. 

(2)  Those  which  may  be  used  at  any  time  whether  the  ship  is 
.    in  flight  or  not. 

The  first  class  includes  by  far  the  most  effective  type  of  aircraft  aerial ; 
in  this  case  the  aerial  is  a  trailing  wire  dangling  from  the  aircraft  while 
the  counterpoise  consists 
of  all  the  metal  parts  of 
the  craft  electrically  con- 
nected together.  The  trail- 
ing wire  is  made  up  of  a 
length  of  phosphor  bronze 
or  silver  bronze  wire  rang- 
ing between  150  and  300 
feet  with  a  weight  attached 
at  its  free  end  and  dang- 
ling from  the  aircraft  some- 
what as  shown  in  Fig.  32. 
The  transmitting  or  receiv- 
ing apparatus  is  connected 
between  the  trailing  an- 
tenna wire  and  the  metal 

parts  of  the  craft  which,  as  already  stated,  form  the  counterpoise;  this  is 
schematically  shown  in  Fig.  34;  when  the  aircraft  approaches  ground 
the  aerial  wire  is  reeled  in,  the  reeling-in  apparatus  being  operated  either 
by  hand  or  by  a  small  electric  motor.  < 

Such  an  arrangement  as  the  one  above  described  has  been  used  with 
success  on  practically  all  types  of  aircraft,  including  lighter  than  air 
ships.  Its  only  disadvantage  seems  to  lie  in  the  fact  that  in  the  case 
of  a  forced  landing,  and,  more  especially,  in  the  case  of  an  aeroplane 
being  compelled  to  dive  or  to  "  loop-the-loop  "  the  presence  of  the  trailing 
antenna  wire  might  prove  disastrous  unless  it  were  reeled  in  very  quickly. 


Receiving  or 
transmitting  set 


Trailing 
wite 


I  Weight 


FIG.  34. — Arrangement  of  apparatus  on  aeroplane 
antennae. 


724 


ANTENNAE  AND  RADIATION 


[CHAP.  IX 


Again,  it  may  be  easily  understood  that  such  an  arrangement  cannot 
be  used  unless  the  aeroplane  is  in  flight. 

It  is  reported  that  transmitting  ranges  up  to  600  nautical  miles  have 
been  obtained  with  trailing  antenna  wires  on  the  large  U.  S.  Navy  N.  C. 
flying  boats  of  the  type  which  crossed  the  Atlantic,  although  one  must 
judge  from  the  results  of  that  test  that  operation  over  even  one-tenth 
of  this  distance  is  problematical.  Signals  may  be  received  by  means  of 
such  antennae  at  almost  any  distance  from  high-power  transmitting 
stations. 

The  second  class  of  aircraft  aerials  comprises  various  types  which 
enable  signals  to  be  sent  out  or  received  even  while  the  craft  is  on  the 
ground.  The  following  types  have  been  used: 

(a)  Skid-fin  aerials  for  aeroplanes. 
(6)  Coil  aerials  for  aeroplanes. 
(c)  T-antenna  for  airships. 

(a)  The  skid-fin  antenna  is  nothing  more  than  an  inverted  "  L-an- 
tenna  "  the  top  of  which  is  mounted  a  few  feet  above  the  uppermost 

plane  and  covers  in  length 
and  width  practically  the 
entire  wing,  somewhat  as 
shown  by  A  BCD  in  Fig. 
35,  where  the  wire  DF  is 
the  leading-in  wire  and 
connects  directly  to  the 
transmitter  or  receiver; 
the  counter-poise  consists 
as  usual  of  all  the  metal 
parts  electrically  connect- 
ed together.  Such  an 
antenna  has  been  exten- 
FIG.  35. — Aer  >plane  antenna  of  the  skid-fin  type.  sively  used  by  U.  S. 

Navy  aeroplanes.    It  must 

be  understood  that  because  neither  the  length  of  the  leading-in  wire 
nor  that  of  the  top  wires  can  be  made  very  large,  and  also  because 
of  the  small  separation  between  the  antenna  proper  and  the  counterpoise 
the  aerial  is  not  a  very  good  radiator,  and,  in  general,  aircraft  carrying 
a  skid-fin  antenna  also  carry  a  trailing  wire  antenna.  It  may  be  said, 
in  a  general  way,  that  the  transmitting  range  of  a  skid-fin  antenna  is 
about  one-half  that  of  a  dangling  wire  antenna  for  the  same  aircraft  and 
transmitting  apparatus. 

When  the  metal  work  of  a  ship  is  used  for  counterpoise  it  must  be 


Wire  net  work 
A  B  C  D  suitably 
insulated  from 
rest  of  aeroplane 


TYPES  OF  ANTENN2E 


725 


all  very  carefully  bonded    together,  otherwise   sparks  may  occur,  when 
transmitting,  which  are,  of  course,  an  unnecessary  fire  risk. 

(6)  Coil  aerials  have  been  used  more  especially  for  receiving  purposes, 
in  view  of  their  ability  to  detect  the  direction  from  which  the  waves  may 
be  coming.  They  are  made  up  of  several  turns  and  of  such  dimensions 
as  will  enable  them  to  fit  in  between  the  two  wings  of  a  biplane,  some- 
what as  shown  diagrammatically  by  B,  Fig.  36.  In  this  case  no  counter- 
poise is  necessary.  When  the  coil  is  used  as  a  transmitter  the  greatest 
radiated  field  will  be  in  the  plane  of  the  coil,  similarly  if  the  coil  is  used 
for  receiving  it  will  respond  most  vigorously  to  signals  coming  from  the 
direction  of  A  or  C.  In  order  to  either  send  or  receive  in  certain  direc- 
tions the  coil  may  be  rotated  or  else  the  aeroplane  itself  may  be  veered 
around  until  the  plane  of  the  coil  points  in  the  desired  direction.  In 
order  to  avoid  either  one  or  the  other  of  these  operations  another  coil 
may  be  used  with  its  plane  at  right  angles  to  the  first,  in  which  case  the 


•Upper  wing 


-Lower  wing 


FIG.  36. — Coil  type  antenna  installed  between  the  wings  of  an  aeroplane:   the  coil  sides 
are  placed  behind  the  struts  between  the  wings. 

operator  need  do  no  more  than  move  small  coils  within  his  easy  reach; 
this  will  be  more  fully  explained  later,  in  the  section  on  direction  finders, 
p.  766. 

The  range  of  transmission  of  coil  antennae  is  small,  but  they  are  used 
for  receiving  from  very  great  distances.  Some  aeroplanes  carry  a  trailing 
wire  for  long-distance  transmission  while  in  flight,  a  skid-fin  antenna 
while  stationary,  and  a  coil  aerial  for  directional  reception. 

(c)  The  T-aerial  for  airships  is  schematically  illustrated  in  Fig.  37, 
where  AB  is  the  leading-in  wire  and  CD  the  top  of  the  "  T."  The 
counterpoise  consists  of  the  metal  parts  of  the  suspended  car,  including 
engine,  etc.  Such  an  antenna  has  practically  the  same  transmitting 
characteristics  as  a  "  T  "  antenna  of  the  same  dimensions  used  on  the 
ground;  and  because  the  wire  AB  is  quite  long  and  the  wires  CD  may 
be  made  very  long  as  well,  the  range  of  the  antenna  is  comparatively 
large.  It  need  hardly  be  stated  that  the  construction  of  such  an  aerial 
is  such  as  to  permit  it  to  be  used  with  equal  effectiveness  whether  the  air- 


726 


ANTENNJ:  AND  RABIATION 


[CHAP.  IX 


ship  is  in  flight  or  not,  and  is  a  great  improvement  over  the  trailing  wire 
antenna  at  first  used  on  such  ships.  Care  must,  of  course,  be  observed 
regarding  the  fire  risk  of  the  installation. 

Underwater  Antennae. — The  problem  of  underwater  antennae  is 
especially  important  in  connection  with  submarines.  Up  to  a  few  years 
ago  communication  by  radio  with  a  submarine,  while  submerged,  was 
considered  very  unsatisfactory,  because  use  was  being  made  of  antennae 
similar  to  ground  antennae  such  as  the  "  T  "  type  or  inverted  "L." 
These  antennae,  even  if  made  of  heavily  insulated  wire,  are  more  or  less 
likely  to  be  short-circuited  by  the  water  (particularly  salt  water)  more 
especially  because,  as  will  be  made  fully  discussed  on  p.  752,  the  highest 
potential  is,  when  transmitting  with  such  antennae,  present  at  the  very 
end  of  the  wires,  where  it  is  most  difficult  to  guard  against  the  short- 


FIG.  37. — In  a  dirigible  balloon  a  T  type  antenna  is  used,  the  counterpoise  consisting  of 
all  the  metal  work  around  the  engines,  etc. 

circuiting  effect  of  the  water.  Aside  from  these  considerations  which 
are  not,  however,  so  very  serious  when  using  the  antenna  for  receiving 
purposes,  the  more  serious  handicap  was  the  fact  that  such  an  antenna 
projects  too  far  above  the  topmost  part  of  a  submarine,  even  above  the 
periscope  and  made  it  necessary  for  the  submarine  to  submerge  more 
deeply  than  would  otherwise  have  been  the  case  or  else  to  use  a  short 
ineffective  antenna. 

Real  progress  was  made  in  submarine  radio  transmission  by  the  intro- 
duction of  the  loop  antenna;  in  the  application  to  submarine  work  the 
loop  is  made  up  somewhat  as  shown  in  Fig.  38.  The  wires  A  BCD  and 
QNML  are  grounded  at  A  and  Q,  and  insulated  from  the  boat  everywhere 
else.  Thus  the  loop  may  be  diagrammatically  represented  as  in  Fig.  39, 
which  should  be  compared  with  the  diagram  of  the  simple  loop  discussed 
on  p.  708,  and  reproduced  in  Fig.  40  for  the  sake  of  convenience. 

In  the  simple  loop  the  wires  FG  and  F'G'  radiate  most  effectively 
when  the  distance  between  them  is  one-half  a  wave-length  and  the  strongest 
field  is  produced  by  the  loop  in  its  own  plane.  Similarly  in  the  case  of 


TYPES  OF  ANTENNAE 


727 


the  submarine  loop  the  wires  AB  and  A  B'  are  the  radiators  while  CD 
and  C'Df  radiate  very  little  energy  since  they  are  very  close  together  and 
the  fields  created  by  them  practically  neutralize  each  other;  of  course 


FIG.  38. — Arrangement  of  loop  antenna  in  a  submarine. 

the  best  distance  between  AB  and  A'BJ  is  one-half  a  wave-length,  and, 
again,  as  in  the  simple  loop,  the  submarine  loop  will  radiate  best  in  its 
own  plane. 


c'  c 


A' 


D' 


FIG.  39. 


FIG.  40. 


FIG.  39.— Electrical  circuit  of  the  installation  of  Fig.  38. 

FIG.  40. — As  wires  CD  and  C'D'  of  Fig.  39  radiate  no  appreciable  power  this  arrangement 
is  equivalent  to  the  single  turn  coil  here  shown  in  wires  AB  corresponding  to  FG 
and  A'B'  to  F'G'. 

Another  arrangement  used  for  submarines  is  a  coil  antenna  consisting 
of  a  large  number  of  turns  and  enclosed  in  a  water-tight  container  which 
is  supported  above  the  deck  of  the  submarine.  The  dimensions  of  such 
a  coil  are  necessarily  small  (perhaps  one  meter  square),  and  its  effective- 


728  ANTENNAE  AND   RADIATION  [CHAP.  IX 

ness  as  a  transmitter  is  consequently  low,  hut  it  has  been  used  to  receive 
from  very  great  distances  with  considerable  success. 

A  word  should  here  be  said  regarding  the  transmission  of  electro- 
magnetic waves  in  water.  It  was  already  pointed  out  in  Chapter  II 
that  electromagnetic  waves  may  be  transmitted  through  any  medium 
to  more  or  less  extent  depending  more  especially  upon  the  electrical  con- 
ductivity of  the  medium.  An  electromagnetic  wave  will,  on  striking  a 
wall  of  ordinary  conducting  material,  be  partly  reflected  and  partly 
absorbed  in  the  production  of  currents  in  the  material,  so  that  practically 
no  electromagnetic  field  would  be  found  at  even  a  small  depth  below  the 
surface  of  the  material.  On  the  other  hand  if  the  material  is,  as  in  the 
case  of  salt  water,  only  a  partial  conductor  the  electromagnetic  waves 
are  able  to  penetrate  into  it  for  considerable  distance  before  the  energy 
represented  by  them  is  completely  absorbed  by  currents  produced  in  the 
water.  It  is  a  well-known  fact  that  the  greater  the  frequency  (the  smaller 
the  wave-length)  of  a  magnetic  or  electric  field  the  smaller  is  the  depth 
to  which  it  will  penetrate  into  a  conducting  or  semi-conducting  medium; 
therefore  in  the  case  of  electromagnetic  waves  in  water  the  extent  to  which 
they  penetrate  below  the  surface  is  very  much  dependent  upon  the  wave- 
length. 

The  equation  for  penetration  of  an  electromagnetic  wave  into  a  con- 
ducting medium  was  given  on  p.  115.  Although  there  given  as  the  pene- 
tration of  a  current  the  same  formula  holds  if  written  to  express  either 
electric  or  magnetic  fields.  Thus  we  may  write 


HZ=H0€    ^    »  '-, (15) 

in  which  HQ  —  intensity  of  magnetic  field,  of  the  electromagnetic 

wave,  just  at  the  surface  of  the  ocean; 
Hx  =  intensity  of  magnetic  field  x  cm.  below  surface; 
co  =  2ir  X  frequency ; 

M  =  permeability  of  sea  water  =  unity; 
p  =  resistivity  of  sea  water  in  abohms  per  cm.3  =  approxi- 
mately 1011. 

If  we  assume  a  signal  detectable  if  Hx  is  only  1  per  cent  of  HO,  then 
the  depth  at  which  the  signal  should  be  detectable  is  obtained  from 


For  a  wave-length  of  10,000  meters  the  value  of  x  calculated  from 
this  relation  is  about  1500  cm.  or  15  meters. 

As  an  example  of  the  effect  of  wave-length  it  has  been  stated  that 
signals  have  been  received  by  submarines  with  loop  antennae  with  the 
top  of  the  loop  16  feet  below  the  surface  of  the  water  at  a  wave-length 


TYPES  OF  ANTENNAE  721) 

of  6000  meters  and  200  miles  from  the  transmitting  station,  while  for 
a  wave-length  of  2500  meters  and  the  same  distance  signals  could  only 
be  heard  with  the  top  of  the  loop  8  feet  below  the  surface  of  water. 

If  we  assume  that  the  loop  was  such  that  the  "  mean  depth  "  was 
5  feet  lower  than  the  top  of  the  loop,  so  that  in  one  case  the  effective 
depth  was  21  feet  in  the  first  case  and  13  feet  in  the  other  the  experimental 
results  agree  very  well  with  those  predicted  from  Eq.  (15).  Thus  we  have 


Again,  in  case  the  submarine  is  transmitting  while  submerged,  the 
transmitting  range  is  very  small  because  the  electromagnetic  waves  are 
practically  entirely  absorbed  in  their  passage  through  the  water  and  issue 
therefrom  with  very  feeble  strength.  Thus,  it  has  been  found  that  a 
submarine  when  submerged  so  that  its  loop  antenna  was  only  a  few  inches 
below  the  surface  could  only  transmit  to  a  distance  of  about  9  miles  with 
a  wave-length  of  about  1000  feet  and  an  antenna  current  of  6  amperes; 
while  it  could  transmit  50  miles  or  more  when  on  the  surface.  Probably 
better  transmission  through  the  water  would  be  expected  if  the  wave- 
length were  much  larger  (10,000  or  more  meters);  but  a  large  wave- 
length implies  an  antenna  of  dimensions  too  large  to  be  carried  by  a  sub- 
marine. 

It  has  been  found  possible  to  send  radio  signals  to  trains  when  they 
were  in  long  tunnels,  a  hundred  feet  underground. 

It  is  to  be  remembered  that  the  question  of  reflection  at  the  surface 
of  the  water  is  to  be  considered  when  analyzing  communication  possi- 
bilities from  a  surface  station  to  a  submerged  boat  or  vice  versa;  this 
has  not  been  attempted  here.  It  may  generally  be  stated  that  the  present 
state  of  the  art  does  not  permit  a  submerged  submarine  to  transmit  to 
any  greater  distances  than  about  10  to  20  miles,  while,  on  the  other  hand, 
enabling  it  to  receive  from  almost  any  distance  provided  it  is  not  too 
deeply  submerged. 

Ground  Antennae. — This  is  the  name  given  to  an  antenna  consisting 
of  an  insulated  wire  laid  on  the  ground  but  insulated  therefrom  as  shown 
by  Fig.  41.  In  the 

fe  /To  receiver 

figure  the  transmit-  f  / 

ter    or    receiver    is  S~ 

shown  connected  to 


the    middle     of    the   FIG.  41. — Use  of  a  wire  laid  on  the  ground  (but  insulated 

wire,  but   it  may  be  from  it)  for  an  antenna. 

connected  at  either 

end.     In  the  former  case  such    an    arrangement  will    resemble  a   "  T  " 

antenna  and  in  the  latter  an  inverted  "  L"  with  a  very  short  "  lead-in  " 

wire.     Since  it  is  the  height  of  the  lead-in  wire  which  determines  the 


730 


ANTENN.K  AND   RADIATION 


[CHAP.  IX 


To  receiver 


^ 


intensity  of  the  field  radiated  it  is  plain  that  an  antenna  of  this  type  is 
a  very  poor  radiator.     It  has,  however,  been   used   as  a  receiver  very 

successfully  1  in  connection 
with  vacuum-tube  detecting 
devices. 

As  a  matter  of  fact,  as  far 
as  receiving  is  concerned,  use 
has  been  made  of  a  wire  on  a. 
wire  fence,  in  which  case  one  of 

FIG.  42.— Even  a  fence  wire  serves  as  a  fairly' good  the  wires  has  been  opened  at  a 
antenna;  it  is  opened  and  the  receiving  appara-  point  such  as  A  (Fig.  42)  and 
tus  put  in  the  break.  the  receiver  inserted  therein. 

Again,  a  living  tree  has  been  used  as  an  antenna  for  receiving.  The 
receiver  is,  in  this  case,  shown  connected  as  in  Fig.  43,  where  A  is  a  nail 
driven  into  the  trunk  of  the  tree  as  high  up  as  possible.  It  seems  as  if, 
here,  the  actual  receiving  of  the  waves  was  mostly  effected  by  the  leading- 
in  wire  AB,  while  the  upper- 
most parts  of  the  tree  serve 
to  increase  the  capacity  of  the 
antenna  and  also  to  intercept, 
to  a  slight  extent,  electro- 
magnetic waves  which  induce 
currents  in  the  electrically 
conducting  juices  of  the  tree  as 
well  as  in  the  leading-in  wire. 
In  general  it  may  be 
stated  that  almost  any  sys- 
tem of  electrical  conductors 
more  or  less  removed  from 
ground  and  insulated  there- 
from is  capable  of  ab- 
sorbing energy  from  an 
electromagnetic  wave  pass-  FIG.  43.— A  tree  has  been  recommended  for  an  an- 
ing  by  it  and,  when  used  tenna;  experiments  seem  to  show,  however,  that 
in  connection  with  the  mod-  the  tree  is  practically  nothing  but  a  support  for 

ern  highly  sensitive  vacuum-      <**  uPPer  end  °/  ^  wirc' thc  real  recciving  being 

.,          done  by  wire  A-B> 
tube  detectors,  may  be  easily 

made  to  detect  the  presence  of  waves. 

Law  of  Radiation  of  Power  from  an  Antenna.2 — Upon  consulting  thc 
literature  there  will  be  found  many  formulae  which  are  supposed  to  give 

1  See  articles  by  A.  H.  Taylor,  I.  R.  E.,  Vol.  7,  Nos.  4  and  6. 

2  For  a  thorough  mathematical  discussion,  see  Pierce,  "Electric  Oscillations  and 
Electric  Waves." 


To  receiver 


LAW  OF  RADIATION  731 

the  power  radiated  from  an  antenna,  in  terms  of  the  height,  wave-length, 
etc.,  but  in  general  they  do  not  agree,  and  it  is  difficult  to  appreciate  the 
derivation  of  some  of  them.  The  derivation  given  below  yields  a  result 
different  from  those  given  by  accepted  authorities,  but  it  undoubtedly 
represents  the  true  state  of  affairs  as  well  as  any  of  them. 

Practically  all  analyses  start  from  the  theory  of  the  Hertzian  doublet, 
supposedly  modifying  it  properly  to  make  it  apply  to  the  groundeu  antenna. 
In  some  derivations  the  amplitude  of  the  current  in  the  antenna  is  supposed 
constant  (i.e.,  the  effective  value  of  the  current  the  same  at  the  top  of 
the  antenna  as  at  the  grounded  end),  and  in  others  the  amplitude  is  sup- 
posed to  vary  in  some  prescribed  manner.  Some  formulae  use  as  the 
height  of  the  antenna  the  actual  height  and  others  use  a  certain  "  effective 
height,"  measured  to  the  "  center  of  gravity  "  of  the  capacity  of  the 
antenna. 

We  shall  consider  the  energy  per  cu.  cm.  at  a  point  P  (Fig.  44),  in  the 
equatorial  plane  of  the  oscillator  and  distant  from  it  several  wave-lengths, 


Top  wires  of  antenna 


Equatorial  plane 
d 


Earth 

FIG.  44. — The  energy  radiated  from  an  antenna  is  to  be  calculated  from  the  law  given 
the  strength  of  magnetic  field  at  P,  in  terms  of  the  antenna  constants. 


so  far  that  the  induction  field  is  negligible.  Our  first  assumption  is  that 
the  effective  value  of  the  amplitude  of  the  current  in  the  vertical  part 
of  the  antenna  is  at  all  points  the  same ;  this  is  nearly  true  for  the  ordinary 
antenna,  in  which  the  capacity  of  the  vertical  wire  is  small  compared  to 
the  capacity  of  the  network  of  wires  generally  used  for  the  top  of  the 
antenna.  This  assumption  will  give  us  a  radiation  somewhat  greater 
than  the  true  value.  The  next  assumption  we  make  is  that  the  actual 
height  of  the  antenna,  /,  represents  the  distance  between  the  positive 
and  negative  charges  of  the  antenna,  the  flow  of  which  causes  the  antenna 
current  7.  In  case  of  a  ship  antenna  the  height  I  is  from  the  water  to 
the  top  of  the  antenna.  In  case  of  a  land  antenna,  with  possibly  a  poor 
ground,  it  is  likely  that  the  average  distance  between  the  charges  of  the 
antenna  is  greater  than  the  distance  from  the  top  of  the  antenna  to  the 
ground,  so  that  it  might  seem  that  in  this  case  we  should  take  a  distance 
greater  than  the  actual  height,  if  the  theory  of  the  doublet  is  to  be  appli- 
cable. 


732 


ANTENNA  AND  RADIATION 


[CHAP.  IX 


This  is  indicated  in  Fig.  45;   it  may  be,  for  such  a  ground  condition, 
that  the  distance  V  (average  distance  between  charges)  is  considerably 

greater  than  /.  We 
shall  neglect  this  ex- 
tra height  (l'  —  l),  how- 
ever, as  it  is  not  only 
indeterminable,  but  it 
contributes  but  little 
to  the  radiation  reach- 
ing the  distant  point, 


Surface  of  earth 


Dry  +  "*"  +   earth 


+  ++ 


Moist 

4- 


earth 


+ 

+     4- 


P;  the  electromag- 
netic energy  sent  off 
from  this  subterrane- 
an part  of  the  antenna 

FIG.  45. — In  an  actual  antenna  there  is  undoubtedly  a  verti-  cou\^  on}y  reach  P 
cal  motion  of  the  charges  in  the  earth  under  the  antenna;  fo  travelj  th  h 
this  subterranean  current  will  contribute  practically  no  ^  e 

radiation  at  distant  points  because  of  absorption  in  the  tne    earth  S 
earth's  surface.  which  case  the  atten- 

uation is  so  rapid  that 

the  amount  of  energy  arriving  at  P  by  this  path  will  be  negligible  compared 
to  that  reaching  P  from  that  part  of  the  antenna  specified  by  the  height  I. 
We  shall  therefore  assume  that  Eq.  (9)  represents  accurately  the  radi- 
ation field  at  point  P,  the  symbols  having  the  definite  meaning  given 
below. 

Hm  = 


in  which          Hm  =  maximum  value  of  magnetic  field  at  P,  in  gilberts 

per  cm.; 
1=  actual  height  of  antenna,  in  cm.,  from  ground  to  top, 

for  flat-topped  antenna; 

Im=  maximum  value  of  current  (in  amperes)  in  antenna, 
this  value  being  assumed  the  same  throughout  the 
height  of  the  antenna; 
X  =  wave-length  radiated,  in  cm.; 
d=  distance  from  antenna  to  point  P,  in  cm. 

Now  the  energy  per  cu.  cm.  at  P,  due  to  this  magnetic  field,  is  equal 
to  Hm2/&jr,  and  as  the  electric  field  set  up  at  P  by  this  moving  magnetic 
field  must  be  of  such  magnitude  that  it  represents  the  same  energy  per 
cu.  cm.  as  that  possessed  by  the  magnetic  field,  the  total  energy  per  cu. 
cm.  (maximum  value)  must  be  Hm2 /4ir.  As  the  electromagnetic  wave 
travels  past  point  P  with  the  velocity  of  light,  the  electric  and  magnetic 
fields  at  this  point  both  go  through  sinusoidal  variations,  so  that  the 


LAW   OF   RADIATION 


733 


average  value  of  the  energy  per  cu.  cm.,  in  terms  of  the  maximum  value 
of  magnetic  intensity,  must  be  equal  to  one-half  of  the  maximum  energy, 

Or  #2  /Sir. 


If  we  now  consider  the  effective  value  of  the  magnetic  field  at  the  point 
P,  we  have  (as  Hm2=2H2,  H  being  the  effective  value)  the  average 
energy  of  the  radiation  field  at  P  equal  to  H2/4ir,  the  energy  being  in 
ergs  per  cu.  cm. 

This  energy  of  radiation  travels  past  point  P  with  the  velocity  of 
light,  V,  so  that  the  energy  streaming  past  P  per  sq.  cm.  (plane  of  the 
sq.  cm.  being  perpendicular  to  distance  d)  per  second  is  equal  to  H2V  '/4r. 
Using  now  Eq.  (9)  to  express  H  and  substituting  /  (effective  current)  for 
Im,  we  get 


cos  9 


(2irlI\2V       irI2l2V 
WXd)  4^=102X2(F 

In  calculating  the  total  radiation  from  the  antenna  we  must  assume 
some  law  of  variation  in  the  value  of  H,  as  the  point  P  is  moved  ove 
the  surface  of  a  sphere  of 
radius,  d.  In  the  ideal 
case  the  distribution  of 
H  over  the  surface  fol- 
lows a  sine  law  as  indi- 
cated in  Fig.  46;  it  has 
a  maximum  value  in  the 
equatorial  plane  of  the  os- 
cillator and  zero  directly 
above  or  below  the  an- 
tenna.1 As  the  power 
per  sq.  cm.  varies  with 
the  second  power  of  H, 
and  as  H  has  a  sinusoidal 
variation  with  respect  to 
6,  Fig.  46,  it  is  evident 

that  the   average  power 

,1 
per    o(j.    GUI.    uv"i     LUC 


G-  ^6-  —  ^n  calculating  the  total  energy  sent  off  from 

an  antenna  we  assume  a  sinusoidal  distribution  of  H, 
.     ,  ...        . 

in  the  meridian  plane. 


whole  imaginary  sphere  is 

7T/6  times  as  great  as  at  the  equatorial  plane,  or  putting  7r/6  =  \  we  have 

l/7T/2/2F\ 

Average  power  per  square  centimeter  =-(         2  2) 

£  \  1CPA  d  / 

1  This  statement  neglects  the  radiation  from  the  horizontal  currents  in  the  upper 
wires  of  the  antenna  and  in  the  earth.  The  amount  of  this  radiation  may  be  consider- 
able and  should  be  calculated  in  getting  the  total  radiation  from  the  antenna.  As 
the  problem  lends  itself  at  best  to  approximate  treatment  only,  due  to  earth  conditions, 
etc.,  it  is  not  thought  worth  while  to  include  the  calculation  of  this  up-and-down  radi- 
ation, 


734 


ANTENNAE  AND   RADIATION 


[CHAP.  IX 


The  area  of  the  sphere  is  4wd2  so  we  have,  for  the  total  radiation  from 
the  oscillator 

Total  radiation,  in  ergs  per  second 


Or  we  have,  watts 


102X2 

72/2 


(17) 


In  this  formula  /  is  measured  in  amperes  (effective)  and  /  and  X  are 
measured  in  any  convenient  unit,  providing  it  is  the  same  for  both. 

It  will  be  noticed  that  in  this  derivation  the  treatment  does  not  agree 
with  that  ordinarily  given  l  in  that  the  radiation  is  considered  as  occurring 

over  a  whole  sphere  instead 
of  only  a  hemisphere. 
It  will  be  appreciated 
that  this  way  of  look- 
ing at  the  question  is 
correct  if  any  analogous 
problem  in  radiation  is 
considered.  Thus  imagine 
an  upright  incandescent 
filament  sending  out  light 
as  indicated  in  Fig.  47. 
The  filament  is  supposed 

FIG.  47.— The  radiation  of  light  from  an  incandescent  to     have     its    lower     end 

filament  standing  in  a  partially  reflecting  surface  is  resting  on  a  surface  which 

exactly  analogous  to  the  radiation  of   radio  waves  absorbs  part   of  the   inci- 

from  an  antenna.  dent  Ught  and  reflects  tne 

rest. 

Let  us  suppose  that,  by  use  of  accepted  formulae,  we  have  obtained 
the  intensity  of  illumination  at  P,  due  to  light  traveling  from  the 
filament  directly  to  P.  (This  excludes  light  arriving  at  P  after  being 
reflected  from  surface  A.)  Suppose  further  that  we  know  the  law  for  the 
distribution  of  radiation,  with  respect  to  the  angle,  6,  this  law  represent- 
ing the  distribution  in  a  homogeneous  medium,  i.e.,  exclusive  of  any  such 
reflecting  surface  as  we  have  at  A.  From  this  law  we  can  obtain  the 
average  lumens  per  sq.  cm.  which  would  exist  over  the  surface  of  a  sphere 
through  P  if  the  reflecting  surface  A  were  not  present.  To  get  the  total 
radiation  it  is  evident  that  we  must  multiply  this  average  illumination 
^ee  Berg,  "Electrical  Engineering,"  advanced  course,  p.  292 


LAW    OF   RADIATION 


735 


by  the  whole  surface  of  the  supposed  sphere  if  we  are  to  get  the  total 
radiation  from  the  filament.  To  be  sure,  the  lower  half  of  the  sphere 
(below  the  surface  A)  actually  gets  inappreciable  illumination,  due  to 
reflection  at  the  surface  and  to  absorption  in  the  material  below  A,  but 
this  fact  in  no  way  alters  the  radiation  from  the  filament,  it  merely  redis- 
tributes the  lumens  after  they  have  left  the  filament,  and  increases  to  some 
extent  the  illumination  in  the  upper  hemisphere.  The  surface  of  the  earth 


Distribution  of  H 
cos  0  in  meridian  plane 


Distribution  of  H 
in  equatorial  plane 


FIG.  48.—  In  calculating  the  power  radiated  from  a  coil  we  assume  a  sinusoidal  distribu- 
tion of  //  in  both  equatorial  and  meridian  planes. 

acts  in  the  same  way  towards  the  radio  waves  as  does  the  surface  A  to 
the  light  rays  striking  upon  it. 

In  the  case  of  a  coil  the  formula  for  radiation  may  be  at  once  obtained 
by  using  the  proper  value  for  H  in  the  previous  deduction  for  the  ordi- 
nary antenna.  We  suppose  a  coil  of  one  turn  the  length  of  whose  vertical 
sides  is  I,  and  the  width  between  these  sides  is  s;  the  value  of  H  in  the 
equatorial  plane  is 

4M       .    ITS 


If  the  coil  has  N  turns  of  course  this  value  of  H  must  be  multiplied  by  Ar. 


736  ANTENNA  AND   RADIATION  [CHAP.  IX 

The  formulation  of  the  total  radiation  for  the  coil  requires  the  knowl- 
edge of  the  distribution  in  the  meridian  plane  as  well  as  the  equatorial 
plane.  Assuming  both  these  distributions  sinusoidal,1  as  indicated  in 
Fig.  48,  we  find  the  average  value  of  H2  and  thus  we  get  the  total  radiation 
from  the  coil 


2  s 


Watts  =  1207r2-  sin2     .......     (18) 


In  the  case  the  coil  is  so  narrow  that  sin  ?-  =  ?-  we  have 

A         A 


72/2  S2 

Watte*  120r*,    ........    (19) 


and  if  the  coil  is  square  so  that  s  =  I  we  have 


Watts  =1207r4/2^V  ........     (20) 


It  was  mentioned  when  calculating  the  radiation  from  an  ordinary  antenna 
that  the  horizontal  parts  of  the  antenna  give  off  considerable  radiation, 
which  was  neglected  in  getting  the  total  radiation.  It  must  be  noticed 
that  in  the  case  of  the  coil  antenna  this  omission  causes  a  very  large 
error,  because  by  its  very  form,  the  coil  radiates  as  much  from  its  hori- 
zontal sides  as  it  does  from  its  vertical  sides,  if  the  coil  is  a  square.  In 
case  the  coil  is  not  square  its  radiation  due  to  the  horizontal  sides  may 
be  obtained  at  once  by  interchanging  the  symbols  s  and  /  in  Eq.  (14). 
Taking  this  extra  radiation  into  account  it  would  seem  that  the  total 
power  radiated  from  a  square  coil  is  twice  the  value  given  by  Eq.  (20). 

All  of  the  foregoing  formulae  for  radiation  have  been  obtained  on  the 
assumption  that  the  current  was  uniform  in  amplitude  throughout  the 
length  of  the  radiating  portion  of  the  antenna.  If  it  is  evident  that  when 
such  is  not  the  case  (as,  for  example,  a  straight  vertical  grounded  wire)  the 
average  value  of  the  current  must  be  approximated  and  this  value  used 
in  the  proper  formula.  Thus,  for  the  single  wire  just  referred  to,  if  con- 
siderable loading  is  used,  the  average  current  is  one-half  the  value  of  cur- 
rent at  the  ground  end  of  the  antenna  and  the  radiated  power  would 
be  one-quarter  o£  the  value  given  by  Eq.  (17).  If,  on  the  other  hand, 
the  wire  was  oscillating  at  its  fundamental  (l  =  \/4)  the  average  current 
would  be  2/-7T  of  the  current  at  the  base  and  the  power  would  be  (2/7r)2 
or  41  per  cent  of  the  value  given  by  Eq.  (17). 

Both  Eqs.  (17)  and  (18)  show  that  the  power  radiated  by  either  a 
coil  or  a  simple  antenna  is  a  direct  function  of  the  square  of  the  height 

1  As  noted  before,  the  treatment  of  radiation  given  here  is  elementary  and  approx- 
imate only;  the  student  is  referred  to  Chapter  IX  of  Pierce's  "  Electric  Oscillations 
and  Electric  Waves  "  for  a  full  treatment  of  the  subject. 


LAW  OF  RADIATION  737 

and  the  square  of  the  current,  and  an  inverse  function  of  the  square  of 
the  wave-length. 

We  will  illustrate  the  influence  of  the  wave-length  upon  the  power 
radiated  by  means  of  an  example.     Assume  a  simple  antenna  for  which 

I  =  10,000  cms.  =  100  meters 
I  =  20  amperes 
then  if  X  =  1000  meters  (/  =  300,000  cycles  per  sec.) 

Power  =  607T2  X  —j^?  ^  2400  watts, 

while,  if  X  =  100,000  meters  (/=  3000  cycles  per  sec.) 

Power  =  607T2  X  ~~  =  0.24  watt. 


Thus  it  may  be  seen  that  it  is  impossible  to  radiate  power  to  any  great 
extent  at  low  frequencies  and  it  must  also  be  remembered  that  this 
hypothetical  case  of  20  amperes  supplied  to  an  antenna  at  3000  cycles  is 
impossible  of  realization. 

Radiation  Resistance.  —  Radiation  resistance  is  a  fictitious  resistance 
the  value  of  which  is  such  as  will  absorb  the  same  power  as  is  radiated 
for  the  same  current  as  flows  in  the  antenna. 

From  the  definition  the  radiation  resistance  may  be  found  by  divid- 
ing the  power  radiated  by  the  square  of  the  antenna  current.  Thus, 
from  Eqs.  (17)  and  (19)  we  find 

Radiation  Resistance  for  simple  antenna 

=60^1  ..........    (21) 

Radiation  Resistance  for  single  turn  coil  having  a  width  equal  to  s, 
small  compared  to  one-half  a  wave-length 


(22) 


The  radiation  resistance  is  used  as  a  measure  of  the  ability  of  an  antenna 
to  radiate  power.  An  antenna  with  a  high  radiation  resistance  is  a  good 
radiator,  and  vice  versa. 

As  previously  pointed  out  the  values  of  resistance  obtained  from  Eqs. 
(17)  and  (19)  may  be  far  from  correct  for  an  actual  antenna.1  A  single 

1  The  fact  that  a  few  experimental  results  give  values  of  resistance  equal  to  that 
calculated  from  certain  formulae  does  not  substantiate  the  formulae  by  any  means;  the 
conditions  obtaining  in  the  experimental  work  are  far  different  from  those  assumed 
in  the  theory. 


738 


ANTENNA  AND   RADIATION 


[CHAP.  IX 


vertical  wire  (no  top  wires)  will  have  a  resistance  only  41  per  cent  of  the  value 
given  by  Eq.  (17)  when  oscillating  at  its  natural  period  and  if  much  load- 
ing is  used,  so  that  the  amplitude  of  current  decreases  uniformly  from  base 
to  top  of  antenna  the  radiation  resistance  will  be  but  25  per  cent  of  the 
value  calculated  from  Eq.  (17). 

In  the  case  of  the  coil  antenna,  radiating  up  and  down,  as  well  as 
horizontally,  the  radiation  resistance  is  probably  much  greater  than  the 
value  given  by  Eq.  (18),  for  a  square  coil  perhaps  twice  as  much. 

Current  in  Receiving  Antenna. — It  is  important  to  be  able  to  cal- 
culate the  current  in  the  receiving  antenna,  because  the  value  of  this 
current  determines  whether  or  not  it  is  possible  to  hear  the  signals  which 
cause  such  a  current  to  flow  in  the  receiving  antenna.  It  must  be  here 
stated  that  were  it  not  for  the  interference  of  the  so-called  "  strays  " 
(see  p.  193)  it  would  be  possible,  due  to  the  extreme  refinement  and  sensi- 
tiveness of  modern  detecting  apparatus,  to  hear  signals,  no  matter  how 


B           J 

E 

le< 

tuc 

ie 

Id 

0 

'  i 

it:r 

sit 

'  6 

f     Oncoming 

wave   ** 

A           > 

FIG.  49. — Wave  with  electric  gradient,  £_,  approaching  a  receiving  antenna. 


small  the  currents  in  the  receiving  antenna.  In  view  of  the  "  strays," 
however,  which  also  produce  currents  in  the  receiving  antenna,  the  signal 
currents  must  be  larger  than  would  otherwise  be  necessary,  so  that  the 
"  strays  "  may  interfere  with  the  signals  as  little  as  possible;  since  the 
"  strays  "  currents  have  considerable  magnitude  it  follows  that  attention 
must  be  paid  to  making  the  signal  currents  large.  Hence  the  importance 
of  knowing  the  factors  affecting  the  signal  current  in  the  receiving  antenna. 
We  will  determine  this  for  a  simple  antenna  and  for  a  coil  antenna. 

Received  Current  in  Simple  Antenna.1 — Consider  the  antenna  repre- 
sented by  Fig.  49  in  the  path  of  electromagnetic  waves  moving,  as 

1  In  an  article  by  Bennett,  in  the  Journal  of  the  A.  I.  E.  E.,  for  Nov.  and  Dec.,  1920, 
various  properties  of  antennae  are  analyzed  and  exact  expressions  for  them  derived. 
Among  other  things,  he  shows  that  an  antenna  having  negligible  resistance  (other 
than  radiation),  the  amount  of  power  which  can  be  abstracted  by  a  receiving  antenna  is 
equal  to  about  6%  of  the  amount  flowing  through  an  area  (parallel  to  the  wave  front) 
equal  to  (X)2  square  meters,  X  being  in  meters. 


MAGNITUDE   OF  RECEIVED   CURRENT  .      739 

shown  in  a  direction  perpendicular  to  the  antenna  lead-in  wire  A-B. 
The  electric  field  will  act  in  a  direction  parallel  to  AB,  hence  there  will 
exist  a  difference  of  potential  across  AB  which  will  be  equal  to  its  length 
multiplied  by  the  intensity  of  the  electric  field.  Thus,  if: 

£.  =  effective  value  of  intensity  of  electric  field  at  AB,  in 

volts  per  cm.  ; 

1T=  height  of  receiving  antenna,  in  centimeters; 
Ir=  effective   value   of  current   in   receiving  antenna,   in 

amperes  ; 
R=  effective    resistance   of   the   antenna,    this   of   course 

depending  among   other   things    upon  the  coupling 

and   adjustments   in    the    closed    receiving   circuit, 

type  of  detector  used,  etc. 

Then,  since  the  receiving  circuit  is  always  adjusted  to  resonate  to  the 
frequency  of  the  incoming  waves,  it  follows  that  the  reactance  will  be 
zero  and  current  in  this  circuit  will  be  given  by:  1 


(23) 


It  now  becomes  necessary  to  substitute  for  i.  its  value  in  terms  of  the  trans- 
mitting antenna  constants. 

From  Eqs.  (10)  and  (15)  we  have: 


volts  per  cm.  for  a  simple  antenna; 

1207TNII  TTS 

l=—u-slux> 

for  a  coil  of  N  turns  and  width  s. 
Substituting  in  Eq.  (23),  we  have: 


r       \dR  ....     ..... 

for  a  simple  transmitting  antenna; 

TTS 

sm        .......    (25) 


for  a  coil  transmitter  of  N  turns  and  a  width  s  with  the  receiving  antenna 
in  the  plane  of  the  coil. 

1  These  solutions  hold  only  for  the  steady  state;   they  are  not  good  until  the  transient 
condition  is  past. 


740 


ANTENNAE  AND  RADIATION 


[CHAP.  IX 


Received  Current  in  a  Coil  Antenna. — Assume  the  single  turn  coil 
of  Fig.  50  placed  in  the  path  of  incoming  electromagnetic  waves,  the  wave 
front  and  plane  of  the  coil  being  perpendicular  to  each  other  and  the 
electric  field  of  the  wave  being  parallel  to  conductors  AB  and  A  'B' . 


Oncoming 


wave 


FIG.  50.  —  Wave  approaching  a  coil  antenna. 

Then,  if  D  and  D'  represent  the  assumed  positive  direction  of  the  poten- 
tial difference  established  across  A  B  and  A'B'  and,  if: 

L  =  effective   value   of  intensity   of  electric   field  at   AB,  in 

volts  /cm.; 
Li  =  effective  value  of  intensity  of  electric  field  at  A'B',  in 

volts  /cm.; 
sr  =  width  of  coil  in  cms., 


we  have: 


i  =  effective  value  of  potential  difference  across  AB', 
=  effective  value  of  potential  difference  across  A  'B', 

=  phase  difference  between  lr^.  and  lri.i  in  radians. 


The  total  electromotive  force  witliin  the  entire  coil  is  equal  to  the  vector 
difference  of  l£.  and  lrLi.  Since  AB  and  A'B'  are  at  practically  the  same 
distance  from  the  radiating  antenna,  the  values  of  l£_  and  l£.i  will  be  the 
same,  but  their  phases  will  differ.  Hence,  total  electromotive  force  within 
the  coil  is  obtained  by  taking  the  vector  difference  of  the  e.m.f.'s  in  the 
two  sides  of  the  coil,  as  shown  in  Fig  51. 
We  then  have 

2/£.  sin  -     =  electromotive  force  in  coil 


MAGNITUDE   OF  RECEIVED   CURRENT 


741 


and  effective  value  of  current  on  the  assumption  of  a  tuned  receiving 
circuit  is  given  by: 


(26) 


for  a  single  turn  coil. 

In  case  the  receiving  coil  has  Nr  turns  Eq.  (26)  becomes 


_ 

r-     R      sm   x 


(27) 


for  a  coil  of  Nr  turns. 

And  substituting  for  £.  the  expressions  obtained  from  Eqs.  (10)  and 
(15)  we  finally  have  the  following: 


TTSr 


(28) 


AO=e.ra.f.  induced  in  A-B=  Zr« 
OB=     «•  "          "   A'-B'=lre, 

OC= vector  difference  of 
OB  and  OA  =  e.m.f. 
acting  in  the  coil. 

=  2l£    sin  —^ 


FIG.  51.  —  The  effective  induced  e.m.f.  of  a  receiving  coil  antenna  is  obtained  by  subtract- 
ing vectorically  the  e.m.f.  's.  induced  in  the  two  sides. 

for  current  received  in  a  coil  antenna  from  a  simple  transmitting  antenna 
lying  in  the  plane  of  the  receiving  coil;  and 


24QirNNrllrI       •       7TS 


(29) 


for  a  transmitter  coil  of  width  5  and  placed  with  its  plane  in  that  of  the 
receiving  coil. 

For  the  sake  of  convenience  all  receiving  formulas  are  collected  below; 
it  is  assumed  that  :  the  vertical  wires  of  the  receiving  antenna  are  parallel 
to  the  electric  field  of  the  oncoming  wave,  that  the  transmitting  antenna 
current  is  undamped  and  of  uniform  amplitude  throughout,  that  there 
is  no  energy  absorption  by  the  medium,  that  the  receiving  circuits  are 
tuned  to  the  transmitting  frequency,  and  that  the  planes  of  the  coils 


742  ANTENNA  AND   RADIATION  [CHAP.  IX 

(either  transmitters  or  receivers)  are  directed  towards  the  other  antenna 
or  coil. 

Antenna  to  antenna 

188&7 

IT  =  ' 


\dR  ' 
Coil  to  antenna 


sin^ (31) 

A 


7«J  I  VAi  f  r^T'*-         •         TfSr  /•«-»<-»  \ 

r=-w^-sm— r (32) 


Antenna  to  coil 

T     37QNrllrI    .    ' 

I     — cin   

X' 
Coil  to  coil 

,         752NNrllTI      .       WSr      .      7TS 

Ir=— lag—  SinTSmX-' 


In  case  the  angle  —  is  sufficiently  small  that  the  angle  may  be  sub- 
X 

stituted  for  its  sine  these  formulae  become  somewhat  simpler  in  form. 
We  have 

Coil  to  antenna  or  antenna  to  coil 


Coil  to  coil 

T._74WNNrttrssrIl 


In  every  one  of  the  preceding  formulae  it  is  to  be  noted  that  the  received 
current  is: 

A  direct  function  of  receiving  and  transmitting  antenna  heights, 

and  the  transmitting  antenna  current. 
An  inverse  function  of  the  wave-length,  to  the  first,  second,  or  third 

power,  the  distance  and  the  resistance  of  the  receiving  antenna 

circuit. 

Returning  to  the  matter  of  the  effect  of  "  strays  "  it  is  apparent  that 
if  the  received  signal  current  is  made  large  by  suitably  arranging  the 
receiving  antenna  constants,  then  the  "  strays  "  current  will  at  the  same 
time  be  made  large,  and  thus  reception  may  be  poor.  On  the  other  hand, 
if  the  receiving  antenna  constants  are  poor  and  the  transmitting  antenna 
constants  very  good,  then  the  received  signal  current  will  be  large  while 
the  "  strays  "  current  will  be  small,  with  consequent  improvement  in 

1  It  is  to  be  pointed  out  that  whereas  the  constants  in  these  formulae  are  given  to 
the  third  significant  figure,  the  actual  received  current  may  differ  from  the  predicted 
value  greatly;  refraction  and  reflection  of  the  waves  play  an  important  role  in  trans- 


COMPARISON   OF  ANTENNA   TYPES  743 

reception.  This  explains  the  modern  tendency  towards  radiating  systems 
of  very  large  dimensions  and  receiving  systems  of  small  dimensions. 

In  using  a  coil  antenna  for  reception  of  signals,  a  regenerative,  or 
"  feed-back  "  connection  of  some  sort  should  be  used,  to  reduce  the 
resistance  of  the  coil  as  much  as  possible.  Such  a  scheme  involves  a 
connection  similiar  to  the  connection  of  the  closed  circuit  of  Fig.  127,  p.  514, 
where  it  must  be  supposed  that  the  coil  L%  of  the  diagram  represents 
the  coil  antenna  used  for  receiving. 

The  reception  Equations  (30)  to  (35)  should  be  modified  by  multi- 
plying by  suitable  factors  when  the  transmitting  antenna  current  is 
damped,  when  there  is  absorption  of  energy  by  the  medium  and  when 
the  plane  of  the  coil  is  not  parallel  to  the  direction  in  which  the  waves 
are  being  propagated.  The  factors  are  as  follows: 

When  the  transmitting  antenna  current  is  damped  1 

Factor  is 


5  +  d'' 
When  there  is  absorption  2 

-  0.000047— ^— 

Factor  is  e  ^x . 

When  the  plane  of  coil  is  not  parallel  to  the  direction  in  which 
the  waves  are  being  propagated 

Factor  is  cos  a, 

where       5  =  decrement  of  receiving  antenna  circuit ; 
6'  =  decrement  of  transmitting  current ; 
d  =  distance  between  station  in  meters; 
\  =  wave-length  in  meters ; 
a  =  angle  made  by  plane  of  coil  with  the  direction  of  propagation 

of  the  waves ; 
e  =  base  of  natural  logarithms. 

Comparative  Merits  of  Different  Types  of  Antennae. — At  the  trans- 
mitting station  it  will  probably  always  be  necessary  to  use  a  high  antenna, 
directive  or  not  as  desired,  but  for  receiving  a  signal  it  is  scarcely  ever 
advantageous  to  use  the  same  high  antenna  as  used  for  transmitting. 

The  readability  of  a  signal  depends  not  upon  the  actual  strength  of 
the  signal,  but  upon  the  ratio  of  signal  strength  to  that  of  the  disturbing 
noises  also  present.  As  static  interference  comes  from  all  directions 

1  See  Bellinger's  paper  on  "Radio  Transmission,"  Proc.  A.  I.  E.  E.,  Oct.,  1919. 

2  See  Scientific  Paper  No.  226  of  the  Bureau  of  Standards.    This  absorption  coefficient 
holds  good  only  over  the  ocean,  in  daylight.     Over  land,  and  over  either  land  or  ocean 
at  night  time  the  transmission  is  too  erratic  to  make  a  formula  worth  while. 


744  ANTENNAE  AND   RADIATION  [CHAP.  IX 

the  ratio  of  signal  to  static  may  evidently  be  increased  by  using  a  direc- 
tional receiving  antenna;  also,  as  it  seems  probable  that  most  of  the 
energy  of  strays  may  be  considered  to  exist  in  the  form  of  highly  damped, 
long-wave  signals,  the  best  antenna  will  be  one  that  absorbs  but  little 
energy  from  waves  greater  than  that  for  which  it  is  tuned.  A  coil  antenna 
satisfies  both  of  these  requirements  better  than  the  ordinary  high  antenna, 
it  being  directional  and  having  induced  in  it  a  voltage  inversely  propor- 
tional to  the  wave-length,  for  an  oncoming  wave  of  fixed  value  of  electric 
field,  £.;  the  induced  voltage  in  the  ordinary  antenna  under  the  same  con- 
ditions is  independent  of  wave-length.  (The  statement  regarding  the 
coil  antenna  presupposes  a  coil  width  s,  small  compared  to  the  wave- 
length, practically  always  the  case.) 

It  is,  of  course;  true  that  the  intensity  of  signal  received  by  the  coil 
antenna  will  be  only  a  small  fraction  of  what  it  would  be  with  the  other 
antenna  but  the  static  interference  will  be  even  a  smaller  fraction.  Hence 
by  a  good  amplifier  the  signal  may  be  brought  up  to  readable  intensity 
and  (if  the  amplifier  increases  static  and  signal  equally)  the  amplified 
weak  signal  from  the  coil  will  be  more  easily  read  than  an  equally  loud, 
unamplified,  signal  from  the  high  antenna. 

The  validity  of  the  above  argument  depends  to  some  extent  upon 
the  actual  ratio  of  radiation  resistances  of  the  two  antennas;  if  e.g., 
the  coil  has  an  induced  signal  current  only  0.0001  as  much  as  that  of 
the  high  antenna,  then  it  will  be  necessary  to  use  an  amplification  of 
10,000  times  (in  volts)  to  make  the  coil  signal  as  loud  as  that  from  the 
other  antenna.  In  the  present  state  of  the  art  it  is  likely  that  such  an 
amplifier  would  generate  in  itself  sufficient  noises  (due  to  microphonic 
resistances,  "  dirt  "  on  hot  filament,  etc.,  see  p.  875,  Chapter  XI)  to  make 
the  signal  unreadable. 

Limitation  of  Transmission  Formula. — It  is  important  at  this  point 
to  make  certain  qualifications  as   to  the  expressions  previously  given 
regarding  the  intensity  of  the  field  at  a  distance  from  the  antenna,  the 
power  radiated  by  a  transmitting  antenna,  and  the  current  received  by 
a  receiving  antenna.     Since  the  expressions  for  the  power  transmitted 
and  for  the  current  received  are,  in  turn,  directly  based  upon  that  for  the 
intensity  of  the  field  at  a  distance  from  the  radiating  system  we  will  dis- 
cuss this  latter  expression  first,  and  the  results  of  the  discussion  will  be 
applicable  to  the  expressions  for    power    transmitted    and  for  current 
received.     The  intensity  of  the  field  radiated  by  an  antenna  as  given 
on  p.  706  is  derived  from  the  theory  of  a  doublet,  the  application  of  this 
theory  requiring  for  the  actual  grounded  antenna  the  assumptions 
(a)  That  there  is  no  absorption  between  the  two  stations, 
(6)  That  the  effective  value  of  the  antenna  current  is  the  same 
throughout  the  entire  antenna  height; 


COUNTERPOISES  745 

(c)  That  the  receiving  antenna  is  in  the  equatorial  plane  of  the 

transmitting  antenna; 

(d)  Refraction  and  reflection  effects  are  negligible. 

None  of  these  assumptions  is  fully  warranted.  Hence,  since,  in  most 
cases,  there  is  some  absorption,  and  the  current  is  not  uniformly  disirib- 
uted,  and  the  two  stations  are  far  from  being  on  each  other's  equatorial 
plane  it  is  evident  that  Formulae  (30)-(35)  must  be  considered  as  rough 
approximations  only,  giving  as  close  a  solution  of  the  problem,  however, 
as  is  possible  to  obtain  under  the  circumstances. 

Experiments  have  been  made  to  determine  experimentally  the  value 
of  the  received  current  and  the  results  check,  roughly,  the  values  cal- 
culated by  means  of  the  formulae  on  p.  742  j1  keeping  in  mind  the  large 
number  of  uncertain  factors  entering  in  both  the  transmission  and  recep- 
tion, and  that  in  the  present  stage  of  the  art  it  is  not  necessary  to  prede- 
termine results  any  closer  than  even  50  per  cent,  it  is  safe  to  consider 
the  accuracy  of  the  formulae  for  power  transmitted,  current  received  and 
field  radiated  within  the  limits  of  present-day  practice. 

Counterpoises. — It  has  already  been  stated  that  an  antenna,  other 
than  a  loop  or  coil  aerial,  must  necessarily  consist  of  a  so-called  aerial, 
which  radiates,  and  a  counterpoise,  which  may  or  may  not  radiate.  In 
the  simple  Hertzian  double  the  counterpoise  radiates,  and  this  is  also 
true  to  a  certain  extent  of  the  counterpoise  used  in  aircraft,  made  up, 
as  it  is,  of  the  metal  parts  of  the  craft.  In  most  cases,  however,  the  counter- 
poise is  the  ground  itself. 

Sometimes  when  the  ground  is  dry  and  therefore  a  poor  conductor 
the  counterpoise  consists  of  a  network  of  wires  laid  on  the  ground  (in 
some  cases  insulated  from  it)  directly  underneath  the  top  of  the  antenna 
proper.  In  every  case  it  must  be  understood  that  the  purpose  of  the 
counterpoise  is  to  enable  charges  of  electricity  to  be  transferred  to  and  fro 
between  itself  and  the  aerial  with  as  little  loss  (due  to  heat  development) 
as  possible,  and  for  this  reason  it  must  have  low  resistance  and  it  must 
also  have  sufficient  capacity.  The  metallic  surface  of  the  counterpoise 
should  be  at  least  equal  to  that  of  the  antenna  and  is  in  most  cases  larger. 

A  counterpoise  having  a  small  surface  has  the  same  effect  as  a  small 
capacity  connected  in  series  with  the  aerial ;  that  is,  it  makes  the  antenna 
capacity  very  sir  .all.  In  order  to  make  such  a  low  capacity  aerial  resonate 
at  desirable  frequencies  it  will  probably  be  necessary  to  use  a  large  loading 
inductance,  which  is  generally  accompanied  by  a  large  resistance;  hence 
the  power  lost  and  the  decrement  of  such  an  aerial  are  very  large.  As 
a  matter  of  fact  it  is  generally  attempted  to  make  the  counterpoise  of  as 
large  a  surface  and  as  low  a  resistance  as  possible.  As  a  rule,  when  the 

1  See  note  on  p.  196,  for  later  experimental  evidence  regarding  transmission  formula. 


746  ANTENNA  AND  RADIATION  [CHAP.  IX 

ground  underneath  the  antenna  is  a  good  conductor  (wet,  soft  earth) 
the  ground  itself  is  used  as  a  counterpoise  and  connection  is  made  with  it 
by  means  of  copper  plates  or  network  of  wires  sunk  into  the  ground  at 
various  places  within  the  area  underneath  the  antenna.  These  buried 
conductors  should  be  put  deep  enough  so  that  the  earth  around  them 
is  permanently  moist. 

Antenna  Resistance.  —  An  antenna  or  coil  transmitter  absorbs  power 
when  supplied  with  high-frequency  currents  by  an  alternator  or  some 
other  generator  of  such  currents.  Some  of  this  power  is,  as  has  already 
been  pointed  out,  radiated  in  the  form  of  an  electromagnetic  field, 
and  represents  useful  power,  while  the  rest  is  consumed  in  various 
ways  and  represents  a  complete  loss,  in  so  far  as  it  contributes  nothing 
towards  radiation. 

In  dealing  with  the  power  absorbed  by  a  circuit  such  power  is,  for 
the  sake  of  simplicity,  looked  upon  as  if  it  were  expended  in  a  resistance 
of  such  a  value  as  would  consume  the  actual  power  expended  in  the  cir- 
cuit for  the  same  current  as  flows  therein.  This  fictitious  resistance  is 
known  as  "  effective  resistance."  1 

Since  the  total  power  expended  in  an  antenna  is  partly  radiated  and 
partly  "  lost  "  due  to  various  causes  we  may  divide  the  "  effective  resist- 
ance "  of  an  antenna  in  two  parts,  i.e.: 

(a)  Radiation  resistance. 
(6)  Loss  resistance. 

The  radiation  resistance  has  already  been  defined  on  p.  737,  and  the 
expressions  therefor  have  been  derived  for  a  simple  antenna  and  for  a 
coil  transmitter;  these  expressions  are,  for  convenience,  rewritten  below: 


.....     ...     (19) 

for  simple  antenna 

72.2 

-         ........        (20) 


for  single  turn  coil  having  a  width  s  small  compared  to  X. 

The  loss  resistance  is  due  to  a  number  of  losses  which  are  enumerated 
and  discussed  below  : 

(1)  Loss  in  poor  dielectrics  in  the  neighborhood  of  the  aerial. 

(2)  Loss  in  the  resistance  of  the  aerial. 

(3)  Loss  in  the  resistance  of  the  counterpoise,  generally  the  ground. 

(4)  Loss  due  to  eddy  currents  in  neighboring  conductors. 

(5)  Loss  due  to  leakage  over  insulators,  etc. 

(6)  Loss  due  to  corona. 

1  See  pp.  112  et  seq. 


COMPONENTS  OF  ANTENNA  RESISTANCE  747 

(1)  The  loss  in  poor  dielectrics  is  due  to  the  hysteresis  1  phenomenon 
taking  place  in  all  dielectrics,  and  most  especially  in  poor  dielectrics  such 
as  wood,  concrete,  masonry,  trees,  etc.,  which  may  happen  to  be  in  the 
vicinity  of  the  aerial  and  hence  acted  upon  by  the  electrostatic  field  about 
the  aerial.     This  loss  resistance  is  analogous  to  that  due  to  magnetic 
hysteresis  in  iron  and  is  an  inverse  function  of  the  frequency  or  a  direct 
function  of  the  wave-length  as  discussed  on  p.  169.     The  effective  resist- 
ance due  to  dielectric  loss  must,  therefore,  increase  as  the  wave-length 
increases  or  as  the  frequency  diminishes.     This  loss  is  one  of  the  most 
important  2  taking  place  in  a  radiating  system  and  should  be  reduced 
to  a  minimum  by  keeping  the  field  of  the  antenna  free  from  unnecessary 
obstructions  wherein  a  dielectric  loss  is  likely  to  take  place.     As  the  highest 
electric  gradient  occurs  near  the  end  of  an  1  or  T  antenna,  especial  care 
must  be  taken  to  keep  poor  dielectrics  away  from  this  part  of  the  antenna. 

In  the  case  of  a  ship's  antenna  much  loss  may  occur  in  the  "lead-in" 
insulator  where  it  enters  the  radio  room;  in  case  the  radio  room  is  wood, 
no  metal  (except  the  wire  itself)  should  be  used  in  this  insulator.  When  the 
radio  room  is  metal  or  where  the  "lead-in"  wire  has  to  go  through  metallic 
bulkheads,  a  considerable  power  loss  occurs  in  the  insulator. 

(2)  The  loss  in  the  ohmic  resistance  of  the  aerial  wire  should  be  kept 
low  by  making  the  wire  of  large  cross-section  and  good  conducting  material. 
The  large  useful  cross-section  may  be  obtained  by  using  a  large  number 
of  very  fine  wires  which   are  insulated  from  one  another  in  order  to  pre- 
vent the  skin  effect  increasing  the  resistance.3     The  material  is  generally 
some  bronze  (phosphor  or  silicon  bronze),  since  this  combines  fair  con- 
ductivity with  great  tensile  strength;  mechanical  considerations  generally 
determine  the  kind  of  cable  to  use,  in  that  many  times  a  seven-strand 
cable  is  used  which  has  practically  as  much  skin  effect  as  solid  wire. 

(3)  The  loss  in  the  resistance  of  the  counterpoise  necessarily  occurs 
because  there  are  currents  flowing  therein  which  must  produce  a  Joulean 
loss  of  power  as  they  encounter  a  resistance.     A  counterpoise  should  be 
made  of  the  smallest  possible  resistance.     Where  the  ground  is  the  counter- 
poise it  is  important  that  connection  be  made  thereto  by  means  of  a  large 
number  of  copper  plates  buried  all  around  the  antenna  in  soft,  moist  soil. 
It  was  already  pointed  out  how  the  multiple  tuned  antenna  may  be 
employed  in  order  to  diminish  as  much  as  possible  the  ground  resistance. 

(4)  Loss  due  to  eddy  currents  in  neighboring  conductors  may  be  di- 
minished by  eliminating  as  much  as  possible  all  metal  masses  from  the 
neighborhood  of  the  antenna.     Of  course  this  is  quite  impossible  in  so  far 
as  metallic  masts  are  generally  used  to  support  the  antenna,  and,  besides, 

1  See  pp.  166  et  seq. 

2  See  Bureau  of  Standards  Scientific  paper  No.  269,  by  J.  M.  Miller. 

3  See  pp.  122  et  scq. 


748  ANTENNAE  AND   RADIATION  [CHAP.  IX 

if  these  masts  were  replaced  by  wooden  or  concrete  masts  the  latter  might 
suffer  considerable  dielectric  loss. 

Since  eddy  currents  and  the  loss  due  thereto  increases  with  an  increase 
of  the  frequency  it  follows  that  the  effective  resistance  representing  this 
loss  increases  with  the  frequency  or  decreases  with  an  increase  of  the  wave- 
length. 

(5)  The  loss  due  to  the  leakage  currents  flowing  between  the  aerial 
and  the  counterpoise  should  be  kept  down  by  using  suitable  insulators 
between  the  antenna  wires  and  the  supports  and  also  between  the  lead-in 
wire  and  any  walls  through  which  it  passes  so  that  the  resistance  of  the 
leakage  paths  may  be  made  as  high  as  possible.     The  resistance  of  the 
leakage   paths  is,  of  course,  very  much   diminished  in  wet  weather  and, 
especially,  where  sprays  from  a  rough  sea  reach  the  aerial.     It  has  already 
been  pointed  out  that  in  the  case  of  submarines  the  ordinary  antenna  is 
very  inefficient,  except  on  a  smooth  sea,  because  of  the  salt-water  sprays 
producing  large  leakage  currents  to  ground  and  thus  absorbing  the  largest 
part  of  the  energy  given  to  the  antenna. 

Since  the  loss  due  to  leakage  is  a  direct  function  of  the  (voltage)2 
and  the  latter  is  inversely  proportional  to  the  frequency  (for  a  given 
current)  it  follows  that  the  effective  resistance  correponding  to  leakage 
loss  varies  inversely  as  the  square  of  the  frequency  and  directly  as  the 
square  of  the  wave-length. 

(6)  The  loss  due  to  corona  takes  place  at  high  voltages  and  is  due 
to  the  partial  ionization  of  the  air  about  the  antenna  wires,  which  causes 
the  air  to  become  a  partial  conductor  and  carry  a  current.     At  night  the 
corona  effect  is  visible  through  the  glow  which   accompanies   it.     The 
corona  does  not  begin  to  take  place  except  at  a  certain  definite  voltage, 
which,  however,  varies  with  the  shape  and  size  of  the  conductors;   this 
critical  voltage  is  smallest  where  the  conductors  are  small  and  at  points 
and  corners.     Once  the  critical  voltage  has   passed,  a   large  amount  of 
energy  loss  may  take  place  due  to  corona.     As  a  matter  of  fact  this  phenom- 
enon is  to  a  certain  extent  a  limitation  upon  the  amount  of  power  which 
may  be  radiated  by  an   antenna  in  so  far  as,  for  an   antenna  of  certain 
dimensions,  the  greater  the  power  given  thereto  the  greater  must  be  the 
voltage  and  hence  the  greater  the  corona  loss;  thus,  for  a  certain  antenna 
there  is  a  limit  to  the  power  input,  beyond  which  it  is  inadvisable  to  go 
because  a  large  amount  of  power  is  wasted  due  to  corona  loss,  and  little 
is  gained  as  far  as  power  radiated  is  concerned. 

This  limit  is  reached  when  the  voltage  at  the  ends  of  the  antenna  is 
in  the  neighborhood  of  150,000  volts.1  This  is  one  reason  why  the  use 
of  very  large  radiating  systems  for  large  stations  is  imperative  in  order 

1  As  mentioned  before  this  limit  depends  upon  how  well  the  antenna  conductors  are 
kept  free  from  sharp  points  and  edges. 


COMPONENTS  OF  ANTENNA  RESISTANCE 


749 


that  the  large  capacity  resulting  therefrom  may  keep  the  voltage  below 
the  limit  of  corona  loss  even  for  large  amounts  of  power  input.  The 
effective  resistance  representing  this  loss  is  for  a  fixed  current  an  inverse 
function  of  the  frequency  and  a  direct  function  of  the  wave-length,  for 
voltages  above  the  critical  value. 

From  the  above  we  have,  then,  that  for  a  certain  antenna  and  for  a 
fixed  current  therein: 

Radiation  resistance  is  an  inverse  function  of  (X)2; 

Resistance  corresponding  to  (2)  ,  (3)  and  (4)   (eddy  currents  and 

skin  effect)  decreases  as  X  increases; 
Resistance  corresponding  to  (1),  (5)  and  (6)  (dielectric  loss,  leakage, 

corona)  increase  with  increase  in  X. 

The  above  relations  are  roughly  indicated  in  Fig.  52,  where  the  various 
components  of  the  antenna  resistance  have  been  plotted,  together  with 


Total  antennax«*sistance 
'lotal  loss 


Dielectric  loss  etc. 


Conductor  loss, 
eddy  currents  etc* 


Radiation 


Wave  length 

FIG.  52. — Various  components  of  antenna  resistance,  showing  approximately  how  they 

vary  with  wave-length. 

curves  showing  the  total  loss  resistance  and  the  total  antenna  resistance. 
From  the  component  curves  A,  B,  and  C,  we  have  obtained  the  total  loss 
resistance  curve,  by  adding  the  ordinates  of  curves  B  and  C,  and, 
finally,  the  total  antenna  resistance,  curve  H,  by  adding  the  ordinates 
of  the  curves  A,  B,  and  C.  The  important  point  brought  out  by  the 
curves  is  that,  because  some  of  the  loss  resistance  components  are  a  direct 
function,  and  others  an  inverse  function,  of  the  wave-length,  it  follows 
that  the  total  loss  resistance  has  a  minimum  value,  as  represented  by  the 
point  K  on  curve  F.  It  would  seem,  then,  as  if  from  the  point  of  view 


750 


ANTENNA  AND   RADIATION 


[CHAP.  IX 


1000  2000 

Wave  length  in  meters 


3000 


of  the  losses  the  best  wave-length  at  which  to  use  an  antenna  should  be 
that  corresponding  to  point   K,  and  in  practice  this  is  approximately 

the  most  efficient  wave- 
length at  which  to  op- 
erate an  antenna. 

The  curves  given 
above  are  purely  of  a 
theoretical  nature,  be- 
cause the  components 
of  the  antenna  resist- 
ance cannot  be  satisfac- 
torily measured  by  the 
methods  at  present 
available.  However,  to- 
tal resistance  curves 
of  actual  antennae, 
which  are  easily  ob- 
tained, are  all  found  to 
have  the  shape  of  curve 
H,  and  the  point  of 

mimimum  resistance  is  always  found  to  be  at  wave-lengths  considerably 
greater  than  the  fundamental  wave-length,  perhaps  twice  as  great. 

Some  typical  resistance  curves  of  actual  antennae  are  given  herewith  ; 
Fig.  53  shows  the  resist- 
ance for  a  ship's  antenna 
for  which  the  minimum 
resistance  takes  place  at 
a  wave-length  of  3.5 
times  the  fundamental. 
The  ordinary  land  sta- 
tion antenna  resistance 
resembles  this  curve  in 
form,  but  generally  the 
resistance  increases  with 
the  longer  wave-lengths 


FIG.  53. — Total  resistance  curve  for  a  ship's  antenna. 


" 


Trail 


Aeroplai 


tenna 


XSkidiftn 


0         600          800         1000 
Wave  length  in  meters 


1200        1400 


more  rapidly  than  does  o       200 

that   given   in    Fig.   53. 
Fig.  54  gives    the   total   FIG.  54. — Resistance  curves  for  two  types  of  aeroplane 
resistance    for   an  aero-  antenna, 

plane    antenna    of    the 

trailing-wire  type  and  one  of  the  skid-fin  type;  both  of  these  antennae  have 
about  the  same  fundamental  wave-length.  It  is  to  be  noted  that  the  trailing- 
wire  antenna  curve  shows  large  resistance  to  the  left  of  the  minimum  value, 


NATURAL   WAVE-LENGTH  OF  ANTENNA  751 

while  the  other  curve  shows  large  resistance  to  the  right  of  the  minimum 
value.  This  is  accounted  for  as  follows :  a  trailing- wire  antenna  is  a  much  bet- 
ter radiator  than  a  skid-fin  antenna,  hence  the  radiation  resistance  should 
be  larger  in  the  former  and  therefore  that  part  of  the  curve  to  the  left 
of  the  minimum,  which  is  very  much  affected  by  the  radiation  resistance, 
should  have  the  larger  ordinates  in  the  trailing  antenna  than  in  the  skid- 
fin  antenna  curve.  On  the  other  hand,  since  the  skid-fin  antenna  is  very 
close  to  the  aeroplane  structure,  the  dielectric  and  leakage-loss  resistance 
should  be  very  much  greater  than  in  the  trailing-wire  antenna,  and  hence 
the  ordinates  of  the  resistance  curve  to  the  right  of  the  minimum  value 
should  be  much  larger.  The  minimum  resistance  for  the  skid-fin  antenna 
is  seen  to  be  less  than  for  the  other  in  view  of  the  shorter  length  of  wire 
used  and  hence  less  ohmic  resistance.1 

The  very  large  land  stations  have  a  minimum  antenna  resistance 
between  1  and  2  ohms;  the  minimum  resistance  for  the  antenna  of  a 
5-kw.  set  is  generally  between  5  and  10  ohms.  Portable  field  antennae 
sometimes  have  a  resistance  as  high  as  50  ohms. 

What  has  been  said  of  the  resistance  of  an  ordinary  antenna  applies 
to  a  coil  radiator  as  well,  except,  of  course,  that  the  components  of  the 
total  resistance  are  related  to  one  another  in  a  somewhat  different  way; 
and  this  is  true,  to  a  certain  extent,  of  any  one  type  of  antenna  relative 
to  any  other.  The  most  important  thing  about  a  coil  radiator  is  that 
its  counterpoise  or  ground  resistance  is  practically  eliminated,  and  hence 
a  much  less  total  resistance  is  obtained.  Therefore,  a  certain  voltage 
will,  when  impressed  upon  a  coil  radiator,  produce  a  much  larger  current 
than  in  a  simple  antenna  having  the  same  radiation  resistance  as  the  coil; 
hence  it  is  possible  to  radiate  larger  amounts  of  power  by  means  of  the 
coil  than  one  might  at  first  think;  for  ordinary-sized  coils,  however,  the 
frequency  must  be  very  high  if  appreciable  power  is  to  be  radiated. 

Natural  Wave-length  of  Antenna. — Consider  an  antenna  in  its  simplest 
form,  i.e.,  a  long  vertical  wire  connected  to  the  alternator  as  shown  in 
Fig.  55.  The  antenna  wire  has: 

(1)  Distributed  inductance. 

(2)  Distributed  capacity. 

(3)  Distributed  resistance. 

(1)  The  distributed  inductance  is  due  to  the  ability  of  every  part  of 
the  antenna  to  develop  magnetic  lines  of  force.  Assuming  the  absence 
of  magnetic  material  near  the  antenna,  its  inductance  per  unit  length 
should  be  practically  uniform  throughout  its  height. 

1  For  a  number  of  curves  of  aircraft  antenna  resistance  see  Johnson's  paper  in  I.  R.  E., 
Vol.  8,  Nos.  1  and  2. 

Also  see  Scientific  paper  No.  341  of  Bureau  of  Standards,  bv  J.  M.  Cork. 


752 


ANTENNA  AND   RADIATION 


[CHAP.  IX 


(2)  The  distributed  capacity  consists  of  the  capacity  between  the 
wire  and  the  counterpoise,  or  earth,  and  is  in  general  different  for  different 
parts  of  the  antenna. 

(3)  The  distributed  resistance  of  the  antenna  is  due  to  radiation  and 
all  the  losses  taking  place.     This  total  resistance  per  unit  length  of  wire 

maybe  considered  to  be  about  uniform  through- 
out the  entire  antenna  height. 

The  antenna  as  a  whole  has  a  certain  value 
of  effective  inductance,  effective  capacity  and 
effective  resistance,  all  of  which,  when  defined 
in  terms  of  current  at  the  base  of  the  antenna, 
change  with  the  frequency  of  the  currents  flow- 
ing through  the  wire.  It  has  already  been 
shown  how  the  effective  resistance  changes  with 
the  frequency  or  wave-length.  The  effective 
inductance  and  capacity  change  with  the  fre- 
quency because,  as  will  be  presently  demon- 
strated, the  distribution  of  the  voltage  and 
current  over  the  antenna  changes  with  the 
wave-length  or  frequency.  Thus,  if  the  an- 
tenna inductance,  say,  is  measured  for  a  cer- 
tain value  of  X  and  some  effective  value  of 
current,  70,  at  the  alternator,  and  if,  then, 
the  wave-length  is  changed  while  the  effective 
value  of  the  current  I0  is  maintained  the  same, 
the  total  netic  flux  emanating  from  the 


resistance,  are  distributed  and  antenna  will  be  different  on  account  of  the 
must  be  so  considered  when  different  distribution  of  cu  Tent,  and  the  in- 
accurate equations  for  cur-  ductance  will  necessarily  be  different.  If,  for 
rent  and  voltage  are  desired.  instance,  the  effective  value  of  the  current 

over  the  antenna  were  as  in  a,  Fig.  56  (an 

impossible  condition)  every  part  of  the  antenna  would  be  nearly  as  effect- 
ive in  producing  magnetic  flux,  while  if  the  current  distribution  were 
as  in  6,  with  the  same  current,  I0,  at  the  alternator,  the  parts  of  the  antenna 
farthest  removed  from  the  alternator  would  not  be  very  effective  in  pro- 
ducing magnetic  flux,  thus  making  the  inductance  smaller  as  compared 
with  a. 

A  similar  thing  happens  in  the  case  of  the  capacity,  because  the  volt- 
age distribution  along  the  antenna  varies  with  the  wave-length,  and  hence 
the  ability  of  the  different  parts  of  the  antenna  to  produce  electrostatic 
lines  of  force  varies  with  the  wave-length. 

Distribution  of  Current  and  Voltage  along  the  Antenna  Wire.  —  It 
has  already  been  pointed  out  that  the  current  and  voltage  cannot  be  the 


CURRENT  AND  VOLTAGE   DISTRIBUTION 


753 


same  throughout  the  antenna  wire  of  Fig.  55.  The  current  in  such  a 
wire  exists  because  electrons  are  being  made  to  flow  alternately  into  and 
out  of  a  capacity;  at  the  very  end  of  the  wire  past  which  there  is  no  capacity 
the  current  must  be  zero  and  will  grow  in  value  for  points  farther  away 
from  the  end.  The  flow  of  this  rapidly  alternating  capacity  current 
(leading  current)  through  the  inductance  of  the  antenna  wire  produces 
an  increasing  voltage  as  we  proceed  towards  the  end  of  the  wire,  a  phenom- 


P'.'.ds 


FIG.  56. 


FIG.  57. 


FIG.  56. — If  the  current  at  the  base  of  an  antenna  is  held  constant  while  frequency  is 
changed  the  distribution  of  current  along  the  antenna  will  change;  this  will  change 
the  amount  of  magnetic  energy  associated  with  the  antenna  and  hence  will  change 
its  effective  self-induction. 

FIG.  57. — By  considering  the  leakage,  capacitance,  inductance,  and  resistance  of  a 
small  element  ds,  the  equations  for  current  and  voltage  may  be  obtained.  Even  if 
the  resistance  and  leakage  are  neglected  fairly  accurate  expressions  will  be  obtained. 

enon  which  is  well  known  to  the  electrical  engineer  in  the  case  of  long- 
distance transmission  lines.  In  order  more  fully  to  understand  the  dis- 
tribution of  current  and  voltage  we  are  giving  below  the  expressions  for 
the  current  and  voltage  in  a  simplified  antenna  or,  more  definitely,  an 
antenna  having  uniformly  distributed  inductance  and  capacity  and  no 
resistance  whatever.  Thus,  let  A  B,  Fig.  57,  represent  such  an  antenna. 

Let  E  =e.m.f.  vector  at  any  point  P,  the  effective  value  of  the  e.m.f. 

being  E', 

/  =  current  vector  at  any  point  P,  the  effective  value  of  the 
current  being  7; 


754  ANTENNA  AND  RADIATION  [CHAP.  IX 

s  =  distance  from  A  to  P,  in  centimeters; 

I  =  length  of  antenna  in  centimeters; 
LI  =  inductance  of  antenna  in  henries  per  centimeter; 
Ci  =  capacity  of  antenna  in  farads  per  centimeter; 

w  =  angular  velocity  of  alternator  e.m.f.  in  radians  per  sec.; 

x  =  inductive  reactance  in  ohms  per  centimeter  =  co  LI  ; 

6  =  capacity  susceptance  in  mhos  per  centimeter  =  coCi  ; 
Eo=  e.m.f.  vector  at  alternator  end  of  antenna; 
Jo  =  current  vector  at  alternator  end  of  antenna. 

By  suitable  mathematical   analysis  l    it  may  be  shown  that,  if  the 
antenna  resistance  is  neglected, 

70  =j  -^=Eo  tan  Vbx  I  (36) 

Vbx 

#=r—  ^=^  cos  Vbx  (I-  s)  .....     (37) 
cos  Vbxl 

=-sin  Vbx  (I-  s)  .....     (38) 


sn 


vbxl 


If  we  let  d  *=  distance  from  the  upper  end  of  the  antenna  in  centimeters, 
then 

d=l-s       ...........     (39) 

call 

a  =  Vbx.     ...........     (40) 

Substitute  (39)  and  (40)  in  Eqs.  (36),  (37),  (38)  and  we  have  the  simple 
equations  : 

/o=#otanaZ  ..........     (41) 


(42) 


7.  . 

cos  al 

1=^-,  sin  ad  ........     (43) 

sin  al 

From  Eqs.  (42)  and  (43)  we  note  that  both  E  and  I  are  trigonometric 
functions  of  the  distance  from  the  upper  end  of  the  antenna  d.  E  varies 
with  cos  ad  and  7  varies  with  —  sin  ad,  therefore  E  and  /  must  differ  by 
90°  in  "  space  phase."  In  Fig.  58  the  abscissae  of  curves  E  and  /  repre- 
sent the  values  of  the  e.m.f.  vector  and  current  vector  respectively,  at 
various  points  along  the  antenna,  obtained  by  the  application  of  Eqs. 

1  See  John  M.  Miller,  "Electrical  Oscillations  in  Antennas  and  Inductance  Coils," 
Proc.  I.  R.  E.,  Vol.  7,  No.  3. 


CURRENT  AND   VOLTAGE   DISTRIBUTION 


755 


(42)  and  (43).  At  the  end  of  the  antenna  the  current  vector  is  zero 
while  the  voltage  vector  is  a  maximum.  At  the  alcernator  end  E  and  / 
may  have  any  value,  depending  upon  the  value  of  Vbx  and  the  height 
of  antenna.  The  example  represented  by  the  curves  is  not  one  which 
is  ever  purposely  realized  in  practice,  since  the  antenna  would,  m  this 
case,  produce  a  comparatively  weak  electromagnetic  field,  in  view  of  the 
fact  that  the  current  and  voltage  are  positive  over  certain  portions  of  the 

antenna  and  negative  over  others;  hence 
the  effect  of  certain  parts  of  the  antenna 
would  be  partly  or  fully  neutralized  by 
other  parts.  The  curves,  however,  show 
a  more  or  less  extreme  possibility.  The 


FIG.  58. 


FIG.  59. 


FIG.  58. — A  possible  form  of  excitation  of  an  antenna,  at  a  frequency  much  higher  than 

its  natural  frequency. 

FIG.  59. — The  ordinary  form  of  voltage  and  current  distribution  on  an  unloaded  antenna, 
excited  at  its  natural  wave-length. 

more  usual  case  is   that   represented   by  Fig.  59;    this   case  will  be  dis- 
cussed more  fully  a  little  later. 

Again,  we  note  from  Eqs.  (42)  and  (43)  that,  since  E  and  /  are  trigono- 
metric functions  of  ad,  this  quantity  must  represent  a  space  rate  of  change 
of  angle,  as  distinguished  from  co,  which  represents  a  time  rate  of  change 
of  angle.  Now,  looking  at  the  curves  of  Fig.  58,  which  represent  nothing 


750  ANTENNAE  AND   RADIATION  [CHAP.  IX 

but  so-called  stationary  waves  of  e.m.f.  and  current,  the  distance  between 
such  points  as  B  and  D  must  be  the  length  of  the  stationary  wave  over 
the  antenna,  and  this  distance  must  be  such  as  to  make 

a\i  =  2ir, 
where 

Xi  =  wave-length  of  stationary  waves  in  centimeters, 
or 


Since 

a  =  Vbx  and  b  =  coi  x  = 


tt 

/= frequency  of  alternator  in  cycles  per  second, 
/  =  —  and  substituting  in  (45), 

(46) 

The  quantity    /          is  shown  in  electrical  engineering  texts  to  be  very 


nearly  equal  to  the  velocity  of  light  or  to  the  velocity  of  propagation  of 
electromagnetic  waves  emanating  from  an  antenna  through  the  air. 

If  V=  velocity  of  propagation  of  electromagnetic  waves  in 

cm.  /sec., 


and  substituting  in  (46) 

a-** 

y  » 

and  finally  substituting  this  expression  for  a  in  Eq.  (44)  we  have: 

Xi-j  .....  '.'....     (47) 

Thus,  the  length  of  the  antenna  stationary  waves,  Xi,  is  equal  to  the 
velocity  of  propagation  of  the  waves  divided  by  the  frequency;  but  this 
quotient  represents  the  length  of  the  electromagnetic  waves,  therefore, 
the  wave-length  of  the  stationary  antenna  waves  is  equal  to  the  wave-length 
of  the  electro-magnetic  waves  in  free  space. 

Now,  going  back  to  Eq.  (41)  on  p.  754  we  may  solve  for  the  value 

of  T—  ,  thus: 
IQ 

^  =  -^cotaZ  ........     (48) 

/o  " 


CURRENT  AND   VOLTAGE   DISTRIBUTION  757 

Since  Eo  and  7o  are  the  e.m.f.  and  current  at  the  alternator  their  ratio 
must  be  the  effective  impedance  of  the  antenna  at  the  point  where  the 
alternator  is  connected.  In  our  case  the  expression  for  this  impedance 
is  always  imaginary,  and  therefore,  represents  the  value  of  the  reactance. 
This  result  was  to  be  expected,  since  the  resistance  has  been  omitted  in 
our  simplified  discussion. 

Let  XQ  =  antenna  reactance  at  the  alternator  in  ohms. 

Then 

XQ  =  —  T  cot  al (49) 

o 

Substituting  for 


we  have 

or 

'rlcot^        (si) 

where  X  =  wave-length  of  electromagnetic  waves,  in 

centimeters. 

The  value  of  this  reactance  will  apparently  vary,  for  a  fixed  X,  as  we 
vary  the  antenna  height  I.     When  /  is  such  as  to  make  cot  —  =0,  then 

A 

the  reactance  is  zero  and  the  antenna  will  resonate  to  the  alternator  fre- 
quency.    This  will  happen  when: 


uKl       7T  O7T  /c.        .    .,  \7T  /rr»\ 

.......    (    ^ 


or  when 


x       7     ax       7     /2n+lNU 
=  -  or  Z  =  fX  or  /=  (  JX. 


And  since  X  is  also  equal  to  the  wave-length  of  the  stationary  antenna 
waves,  it  follows  that  the  antenna  will  resonate  to  the  frequency  of  the 
alternator  when  the  antenna  height  is  such  that  there  will  result  a  dis- 
tribution of  e.m.f.  and  current  vectors  which  will  produce  either  J  or  f 
or  f,  etc.,  of  a  stationary  wave. 

If  the  expression  for  XQ  as  given  by  Eq.  (50)  be  plotted  against  values 

of  alternator  frequency,1  everything  else  remaining  the  same,  we  would 

have  the  curve  shown  in  Fig.  60.     At  the  points  1,  3,  5  the  antenna  react- 

ance is  zero,  and  the  frequencies  at  1,  3,  5,  etc.,  are  in  ratios  1:3:5:7, 

1  For  experimental  curves  showing  this  effect  see  Fig.  109,  p.  109. 


758 


ANTENNAE  AND   RADIATION 


[CHAP.  IX 


etc.  Hence  the  antenna  can  be  made  to  resonate  at  the  frequency /i  and 
at  frequencies  three  times,  five  times,  seven  times,  etc.,  f\.  On  the  other 
hand,  a  little  to  either  side  of  the  points  2,  4,  6,  etc.,  the  reactance  is 
infinite  and  directly  at  the  points  2,  4,  6,  etc.,  the  resistance  of  the  antenna, 
as  measured  at  the  base,  becomes  infinite  so  that  practically  no  current 
can  be  caused  to  pass  into  the  antenna  at  the  frequencies  /2,  /4,  /6,  etc., 
which  are  two  times,  four  times,  six  times,  etc.,  the  first  resonating  fre- 
quency /i .  It  is  not  out  of  place  to  point  out  here  that  the  first  resonating 
frequency  f\  is  such  as  to  produce  one-quarter  of  a  stationary  wave  over 
the  antenna,  as  may  be  easily  seen  from  the  discussion  of  p.  757.  This 


13 


Frequency 


1° 

«< 


FIG.  60. — As  the  frequency  impressed  on  an  antenna  is  varied  the  reactance  (as  measured 
at  the  base)  goes  through  the  changes  indicated  here;  in  case  an  antenna  with  appre- 
ciable resistance  had  been  considered  the  reactance  changes  from  its  high  positive 
value  to  high  negative  value  by  going  through  zero  values  at  2,  4  and  6. 

frequency  and  the  wave-length  corresponding  to  it  are  known  as  the 
fundamental  or  natural  frequency  and  wave-length  of  antenna  respectively. 

An  antenna  if  excited  by  means  of  a  spark  gap  will  naturally  have  cur- 
rents produced  in  it  of  the  frequency  corresponding  to  zero  reactance, 
and  therefore  of  the  fundamental  frequency  and  wave-length ;  it  is  possible 
by  putting  proper  discontinuities  in  the  antenna,  to  cause  this  frequenc}^ 
to  be  three  times  and  even  five,  times  the  fundamental.  In  general,  it 
may  be  said  that,  whenever  the  simple  antenna  oscillates  freely,  no  matter 
how  excited,  it  does  so  at  the  natural  or  fundamental  wave-length. 

The  curves  of  Fig.  60  also  show  that  the  reactance  of  the  antenna  may 
be  negative  (condensive)  or  positive  (inductive),  depending  entirely  upon 
the  frequency  at  which  it  is  used. 

In  the  above  discussion  we  have  assumed  an  antenna  consisting  of 


NATURAL  WAVE   LENGTH  OF  ANTENNAE  759 

a  vertical  wire  and  having  distributed  inductance  and  capacity,  and  no 
resistance.  The  presence  of  the  resistance  makes  the  results  only  slightly 
different,  and  so  does  the  fact  that  the  capacity  is  not  quite  uniformly 
distributed. 

Consider  now  an  actual  antenna  with  a  flat  top.  If  the  top"  consists 
of  a  single  horizontal  wire  of  the  same  size  as  the  vertical  wire,  then  it 
may  be  shown  in  the  manner  already  illustrated  for  the  simplest  antenna 
that,  assuming  uniformly  distributed  capacity  and  inductance  throughout, 
the  total  length  ABC,  Fig.  61,  represents  one-quarter  of  the  fundamental 
wave-length  of  the  antenna. 

If,  on  the  other  hand,  the  top  consists  of  a  number  of  horizontal  wires, 
as  in  Fig.  62,  then  the  problem  is  somewhat  complicated,  because  the 

N.  wires 


FIG.  61.  FIG.  62. 

FIG.  61. — In  the  case  of  an  inverted  L  antenna  the  natural  wave-length  is  slightly  more, 
than  four  times  the  extreme  length  A-B-C. 

FIG.  62. — An  antenna  with  a  wide  top  has  a  natural  wave-length  considerably  greater  than 
four  times  the  extreme  length  A-B-C;  by  spreading  out  the  wire  A-B  (separating 
the  different  strands  sufficiently  and  bringing  them  down  in  a  cylindrical  form)  the 
natural  wave-length  may  be  brought  down  to  very  nearly  four  times  the  length  A  -B-C. 

capacity  and  inductance  per  unit  length  of  the  part  BC  are  different  from 
those  for  part  AB.  However,  in  view  of  the  fact  that  for  the  part  BC 
the  capacity  per  unit  length  is  kn  times  1  that  of  a  single  wire,  while  the 

inductance  per  unit  length  is  —  times  that  of  a  single  wire,  the  product 

kn 

of  these  two  quantities  remains  the  same,  and  it  is  safe  to  take  the  dis- 
tance A  BC  as  again  being  approximately  one-quarter  of  the  fundamental 
wave-length  of  the  antenna. 

The  inaccuracy  of  this  simple  rule  increases  as  the  form  of  the  aerial 
departs  from  the  simple  one  given  in  Fig.  57.  It  has  been  found  experi- 
mentally that  the  natural  wave-length  is  connected  to  the  extreme  length 

1  k  is  a  constant  less  than  unity;  it  approaches  unity  as  the  different  wires  of  the 
antenna  are  spaced  farther  apart. 


760  ANTENNA  AND  RADIATION  [CHAP.  IX 

of  the  antenna  (from  ground,  up  lead  wire  to  farthest  point  of  aerial) 
about  as  given  here 

Vertical  wire 4-4 .  II 

T  aerial  with  small  tops 4.3-    5/ 

T  aerial  with  broad  tops 5-    6Z 

Umbrella  aerial 6-  10Z 

Horizontal  wire,  1  meter  from  ground 5Z 

The  capacities  of  antennae  vary  from  perhaps  0.4X10"9  farads  to 
20X10~9  farads;  the  lower  value  being  for  small  portable  field  antennae 
and  the  higher  value  for  large  high  power  stations.  The  ordinary  ship 

antennna  has  a  capacity  between  1 X  10~9 
and  2  X10~9  farads. 

In  the  case  of  a  coil  radiator  the  capac- 
ity of  the  condenser  C,  Fig.  63,  is  gener- 
ally very  large  as  compared  with  the 
distributed  capacity  over  the  conductor 
A  BCD,  hence  the  latter  may  be  neglected 
and  the  fundamental  wave-length  of  the 

.  I,  circuit  may  be  obtained  from  the  induc- 

— ©^       1 1  tance  of  the  coil  and  the  capacity  C. 

Current  and   Voltage   Distribution   in 
FIG.  63.— The  natural  wave-length 

of  a  coil  antenna  is  seldom  used;  Antenna  for  Various  Loadings.— The  ex- 
the  wave-length  is  calculated  from  pression  "  Loading  of  an  antenna  "  applies 
the  value  of  L  of  the  coil  and  the  to  the  insertion  of  an  inductance  or  a 
amount  of  capacity  in  C.  condenser  in  series  therewith  for  the 

purpose    of    changing    the    fundamental 

wave-length  of  the  antenna  circuit.  This  is  best  understood  by 
referring  to  the  curves  of  Fig.  64,  which  give  the  reactance,  at  differ- 
ent frequencies,  for  an  antenna,  for  a  coil,  and  for  a  condenser.  The 
antenna  reactance  curve  A  is  the  same  as  the  first  section  of  the  curve 
of  Fig.  60,  the  curve  for  the  inductance  is  a  straight  line,  since  inductive 
reactance  varies  directly  with  the  frequency,  and  the  curve  for  the  con- 
denser is  an  equilateral  hyperbola,  since  condensive  reactance  varies 
inversely  as  the  frequency. 

If  the  antenna  and  the  coil  are  connected  in  series  it  is  plain  that  the 
total  reactance  will,  for  any  frequency,  be  the  algebraic  sum  of  the  two 
individual  reactances;  a  similar  thing  applies  to  the  case  where  a  con- 
denser is  connected  in  series  with  the  antenna.  The  resultant  reactance 
curves  are  shown  as  F  and  G.  Now,  considering  the  three  curves  A, 
F,  G,  it  will  be  seen  that  the  antenna  alone  has  a  natural  frequency  of  f\ , 
the  antenna  with  the  coil  in  series  has  a  natural  frequency  of  //,,  and  the 
antenna  with  the  condenser  in  series  has  a  natural  frequency  of  fc.  Thus, 


EFFECT  OF  LOADING  AN  ANTENNJS 


761 


the  effect  of  the  series  inductance  is  to  make  the  natural  frequency  of  the 
entire  antenna  circuit  smaller  (larger  wave-length)  than  that  of  the  antenna 
alone,  and  vice  versa  for  the  case  of  the  series  condenser. 

It  will  be  noted  that  by  making  the  slope  of  the  curve  B  very  great 
(large  inductance)  the  antenna  circuit  may  be  caused  to  have  a  very 
much  lower  fundamental  frequency  than  that  of  the  antenna  alone,  the 


Frequency 


A  — Antenna  alone 

B-Coil 

D  -  Condenser 

F  —Antenna  +  series  coil 

G  -Antenna  +  series  condenser 


FIG.  64. — The  diagram  of  reactances  of  an  antenna  (A),, a,  coil  (J5),  and  a  condenser 
(D),  shows  how  the  natural  wave-length  of  an  antenna  circuit  is  changed  by  adding 
loading  coil  or  shortening  condenser  in  the  base  of  the  antenna. 

limit  being  zero.  In  the  case  of  the  series  condenser  it  will  be  observed 
that  no  matter  how  large  we  make  its  reactance  (how  small  its  capacity) 
the  maximum  frequency  obtainable  is  twice  that  of  the  fundamental 
frequency  of  the  antenna  proper.  Thus,  if  an  antenna  has  a  natural 
wave-length  of,  say,  500  meters,  it  is  impossible  to  change  this  to  any- 
thing less  than  250  meters  by  placing  a  condenser  in  series  with  the 
antenna. 

The  changes  which  take  place  in  the  natural  wave-length  of  an  antenna, 
as  various  coils  or  condensers  are  used  in  series  with  it,  are  shown  in  Figs. 


702 


ANTENNA  AND   RADIATION 


[CHAP.  IX 


DWU 
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Loading  inductance  in  10  henries 
FIG.  65. — Effect  of  loading  coil  on  the  wave  length  of  a  single-wire  antenna. 1 


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[)            .2            .4                          .8           1.0          1.2          1.4          1.6          1.8         2.0 
Capacity  in  10"9  farads 

FIG,  66.— Effect  of  shunting  the  loading  coil  of  Fig.  65  by  a  variable  condenser. 


EFFECT  OF  LOADING  AN  ANTENNA 


763 


65,  66,  and  67.  A  single-wire  antenna  was  used  in  the  test,  about  175 
meters  long,  having  (unloaded)  a  natural  wave-length  of  700  meters. 
As  a  variable  inductance,  in  series  with  the  ground  connection  of  the 
antenna  was  changed,  the  natural  wave-length  of  the*  loaded  antenna 
increased  as  shown  in  Fig.  65.  Then  keeping  the  value  of  the  loading 
inductance  fixed  at  1140  ph  a  variable  condenser  shunted  around  this 
load  coil  brought  about  the  changes  in  wave-length  shown  in  Fig.  66. 

The  effect  of  putting  a  "  short-wave  "  condenser  in  series  with  the 
base  of  the  antenna  is  shown  in  Fig.  67 ;  it  will  be  seen  that  with  no  capacity 
in  series  with  the  base  of  the  antenna  (that  is,  the  lower  end  of  the  antenna 


.4  .8  1.2          1.6          2.0       _(2.4          2.8          3.2          3.6          4.0 

Capacity  in  10  "  farads 

EIG.  67. — Effect  of  putting  a  variable  condenser  in  series  with  the  base  of  the  antenna. 


merely  left  free,  connected  to  nothing)  the  natural  wave-length  decreased 
(by  extrapolation  of  the  curve)  to  half  the  natural  wave-length  of  the 
grounded  antenna. 

It  has  already  been  stated  that  an  antenna  is  generally  used  at 
frequencies  lower  than  its  fundamental,  and  therefore  antennas  have 
generally  a  loading  inductance  inserted  in  series.  The  series  condenser  is 
sometimes  used  in  the  case  of  receiving  antennas,  but  very  seldom  for 
tranmitting  antenna 

Current  and  Potential  Distribution  over  Antenna. — We  will  consider 
the  following  cases: 

(1)  Simple   antenna  (single  vertical  wire)  with  no  loading  induc- 
tance or  series  condenser. 

(2)  Simple  antenna  with  loading  inductance  in  series. 


764 


ANTENNA  AND   RADIATION 


[CHAP.  IX 


(3)  Simple  antenna  with  condenser  in  series. 

(4)  Commercial  antenna  with  large  top  and  no  loading  inductance 
or  series  condenser. 

(5)  Commercial  antenna  with  loading  inductance. 

(6)  Commercial  antenna  with  condenser  in  series. 

It  is  understood  that  in  every  case  the  antenna  circuit  is  operated  at 
the  fundamental  frequency  of  the  circuit,  for  at  this  frequency  the  react- 
ance is  zero,  the  resistance  is  a  minimum,  and  the  current  a  maximum. 

Case  (1).  Eqs.  (42)  and  (43)  of  page  754,  give 


E  = 


. 
cos  al 


cos  ad 


and 


•  IQ        .         , 

7  =  — = 7  sin  ad 

sin  at 


and  indicate  that,  since  the  antenna  height  (I)  is  equal  to  one-quarter 
of  a  wave-length,  the  voltage  and  current  curves  will  be  as  shown  in 

Fig.  59,  the  curves  being  sinusoidal;  the 
current  curve  will  be  one-quarter  of  a 
complete  sine  wave. 

Case  (2),  Fig.  68.  Here  the  X  of  the 
entire  circuit  will  be  larger  than  that  of 
the  antenna  alone,  therefore  the  antenna 
height  will  represent  less  than  one-quarter 
of  the  wave-length.  Furthermore  the  cur- 
rent through  the  inductance  will  be  con- 
stant, but  the  voltage  over  it  will  vary 
from  DK  to  AH.  Hence  the  voltage  E'Q 
at  the  beginning  of  the  antenna  wire  will 
be  much  larger  than  in  case  (1),  and  the 
insulators  at  the  point  A  will  need  to  be 
such  as  to  stand  a  larger  voltage. 

Case  (3),  Fig.  69.     Here  the   X  of  the 
entire  circuit  is  less  than  that  of  the  an- 
tenna alone;    hence    the    antenna   height 
will  represent   more  than    one-quarter  of 
FIG.  68.— Voltage  and  current  dis-  the     wave-length.       The    current    curve, 
tribution  in  simple  antenna  with  therefore,  has  its  zero  at  B,  its  maximum 
loading  coil.  at  H  and  decreases  to  70  at  F\   it  has  the 

same  value  on  both  sides  of  the  condenser. 

The  voltage  curve  is  a  maximum  at  B,  zero  at  K  and  becomes  negative 
thereafter;  however,  it  again  changes  sign  over  the  condenser. 


CURRENT  AND   VOLTAGE   DISTRIBUTION 


765 


Cases  (4),  (5)  and  (6),  illustrated  in  Figs.  70,  71,  and  72,  are  analogous 
to  cases  (1),  (2)  and  (3),  respectively,  except  that  the  distribution  of 
voltage  and  current  takes  place  over 
the  entire  antenna  length  and  not 
over  the  vertical  part  alone.  The 
result  of  this  is  that  the  vertical  part 
has  a  current  of  more  nearly  con- 
stant effective  value  over  the  entire 
height;  of  course  this  result  is  especi- 
ally desirable  in  view  of  the  better 
radiation  produced  by  a  uniform  cur- 
rent over  the  vertical  wire. 

Experimental  curves    of    voltage 
and  current  distribution  for  a  low- 
frequency  circuit,  representing  at  low 
frequency  what  an  antenna  does  at 
high  frequency,  bear  out  the  theo- 
retical predictions  already  discussed,    %^%^^^       'tmmimzzmt? 
except  that,  whereas  in  the  theoreti-   FIG.  69. — Voltage  and  current  distribu- 
cal  curves  of  Figs.  69  and  72  we  have       tion  in  simple  antenna  with  shortening 
shown  the  effective  value  of  the  volt-      condenser, 
age  to  actually  become  zero  at  points 

marked  K,  this  does  not  happen  in  the  experimental  curves.1     The  reason 
for  this  lies  in  the  fact  that  the   theoretical  curves  have  been  plotted 

on  the  basis  of  Eq.  (37), 
which  takes  no  account 
of  the  resistance  of  cir- 
cuit, while  actually  there  is 
resistance.  The  effect  of 
the  resistance  upon  the 
effective  value  of  the  volt- 
age along  the  antenna  is, 
generally,  to  make  it  im- 
possible for  it  to  become 
zero  for,  at  the  nodal  point, 
where  the  voltage  should 
FIG.  70. — Voltage  and  current  in  unloaded  inverted  be  zero,  there  is  power  flow- 
L  antenna.  mg  past  the  nodal  point  to 

supply  the  losses   for  the 

rest   of   the   antenna,  and   in   order   for  this  to  take  place  the  voltage 
must  be  greater  than  zero.     In  the  case  of  no  resistance  the  voltage  along 

1  See  Morecroft,  "Experiments  with  long  electrical  conductors,"  Proc.  I.  R.  E.;  Vol. 
5,  No.  6,  Dec.,  1917. 


766 


ANTENNAE  AND  RADIATION 


[CHAP.  IX 


the  antenna  has  different  effective  values,  but  the  same  phase  for  the 
same  half-wave  and  changes  in  phase  through  180°  at  the  point  where  it 
passes  through  its  zero  value.  On  the  other  hand,  in  the  actual  case 

the  voltage  all  along  the 
antenna  has  not  only 
different  effective  values, 
but  different  phases  as 
well,  as  may  be  shown  by 
the  vector  diagram  of  Fig. 
73  where  the  vectors  rep- 
resent voltages  at  differ- 
ent points  of  the  antenna 
of  Fig.  72,  the  numbered 
vectors  corresponding 
with  the  numbered  posi- 
tions on  the  antenna.  At 

FIG.  71— Current  and  voltage  in  inverted  L  antenna   nodal    points  the   voltage 
having  a  loading  coil.  would   be   very  small   as 

shown  at  ES;  its  magni- 
tude (for  a  given  impressed  voltage)  becomes  smaller  as  the  resistance 
of  the  upper  part  of  the  antenna  is  decreased. 

Direction  Finders. — This  is  the  name  given  to  receiving  antennas 
so  constructed  as  to  indi- 
cate the  direction  from 
which  the  signals  are  com- 
ing. The  simplest  direction 
finder  is  a  receiving  coil 
antenna;  it  has  already 
been  pointed  out  on  p.  708, 
that  such  a  coil  when  used 
as  a  transmitter  will  produce 
the  maximum  intensity  of 
field  in  its  plane  and  the 
minimum  at  right  angles 
thereto ;  in  a  similar  manner 
the  coil  will,  when  receiving, 
have  the  greatest  current 
produced  in  its  circuit  when  FIG.  72. — Current  and  voltage  in  inverted  L  antenna 
its  plane  is  in  the  plane  of  navins  «h«rtcning  condenser, 

propagation  of   the   waves 

and  the  minimum  when  its  plane  is  perpendicular  to  the  plane  of  propa- 
gation of  the  waves.  Thus,  if  the  coil  be  arranged  so  that  it  may  be 
made  to  rotate  with  respect  to  its  vertical  axis  while  signals  are  being 


DIRECTION   FINDERS 


767 


received,  then  when  the  coil  is  placed  into  a  position 
of  minimum  or  zero  strength  of  signals  the  normal  to 
its  plane  indicates  the  direction  from  which  the  waves 
are  coming. 

It  has  already  been  stated  that  in  the  case  of  aero- 
planes a  coil  antenna  is  sometimes  used  for  receiving, 
which  is  kept  fixed  in  position  with  repect  to  the  aero- 
plane while  the  aeroplane  is  maneuvered  until  mini- 
mum strength  of  signals  is  obtained. 

In  order  to  obviate  the  necessity  of  moving  the 
coil  while  obtaining  bearings  Bellini  and  Tosi  invented 
the  so-called  goniometer  which  bears  their  name.  It 
consists  of  two  similar  coil  antennas,  Fig.  74,  at  right 
angles  to  each  other,  the  antennae  being  kept  station- 
ary. Each  of  the  antennae  is  connected  in  series  with 
similar  coils  D\  and  D2  and  variable  condensers  F\,  F2, 
such  as  to  enable  the  operator  to  tune  to  the  incoming 
waves.  The  condensers  are  constructed  so  that  they 
may  both  be  varied  at  the  same  time  and  by  the 
same  amount,  in  order  for  both 
antennae  to  be  simultaneously  tuned 
to  the  incoming  waves.  The  coils 
DI  and  D2  are  constructed  in  two 
parts  as  shown  in  Fig.  75,  leaving  a 
space  in  the  middle  for  a  coil  K 
which  may  be  rotated  with  respect 
to  a  line  through  0  as  an  axis.  The 
coil  K  is  connected  to  a  tuning 
condenser  to  which  there  is  attached  the  detecting 
circuit. 

The  signal  strength  will  vary  as  the  coil  K  is  rotated. 
This  may  be  shown  as  follows:  Let  in  Fig.  76  D\,  D2 
\i if  and  K  represent  the  planes  of  the  stationary  coils  D\ 

^Ir'^P;'  and  D2  and  of  the  movable  coil  K  respectively;   also 

assume,  for  the  sake  of  simplicity,  that  the  coil  antenna? 
AI  and  A2  are  placed  so  that  the  plane  of  A i  is  parallel 
to  that  of  DI  and  the  plane  of  A2  parallel  to  that  of 
-D2.  It  is  understood  that  the  coils  DI  and  D2  together 
with  the  respective  antennas  A\  and  A2  and  the  con- 
densers FI  and  F2  (see  Fig.  74)  are  so  adjusted  that 
each  circuit  has  a  natural  wave-length  equal  to  that  of 
the  incoming  waves  and  the  same  value  of  resistance 
as  the  other  circuit;  this  means  that  the  circuits  of  the 


FIG.  73.  —  Voltage 
magnitudes  and 
phases  of  the  anten- 
na shown  in  Fig.  72 ; 
at  the  nodal  points 

.  of  such  an  antenna 
the  voltage  is  not 
zero  as  the  curves 
of  Figs.  69  and  72 
would  indicate, 
but  a  certain  small 
value  depending 
upon  the  resistance 
of  the  antenna. 


D, 


Fio.74.-Pairof  sim- 
ilar coil  antennae 
placed  at  right  an- 
gles to  each  other 
constitute  the 
Bellini-Tosi  direc- 
tion finder. 


768 


ANTENNA  AND  RADIATION 


[CHAP.  IX 


Totuning  condenser' 
and  detector 


To  Antenna  2 


To  Antenna  1 


FIG.  75. — Arrangement  of  coils  in  the  base  of  the  two  antennae;  coil  K  may  be  rotated 
and  by  the  magnitude  of  the  signal  strength  induced  in  it  the  direction  of  the  send- 
ing station  (±180°)  can  be  obtained. 


oncoming  wave 


FIG.  76. — Diagram  for  analysis  of  the  action  of  the  direction  finder. 


DIRECTION  FINDERS  760 

two   antenna   must    be    exactly  similar.       Assume   that   the  incoming 
electromagnetic  waves  are  harmonic  and  that,  therefore,  harmonic  e.m.f. 's 
will  be  induced  in  A\  and  A2  which  will,  in  turn,  produce  harmonic  currents 
in  their  respective  circuits. 
Let  «=the  angle  made  by  the  direction  of  incoming  waves 

with  the  plane  of  the  A\  antenna; 
j8  =  angle  made  by  the  normal  to  the  plane  of  the  revolving 

coil  K  with  the  plane  of  the  A\  antenna; 

11  =  instantaneous  value  of  current  in  circuit  Ai~D\-F\ 

(Fig.  74); 

12  =  instantaneous  value  of  current  in  circuit  A2-D2-F2 

(Fig.  74); 
e\  =  instantaneous  value  of  e.m.f.  induced  in  K  by  current 

in  Di; 
62  =  instantaneous  value  of  e.m.f.  induced  in  K  by  current 

in  £2; 
e  =  instantaneous  value  of  total  e.m.f.  induced  in  K  by 

the  simultaneous  action  of  D\  and  D2; 
Im  =  maximum  value  of  the  current  which  would  flow  in 

A\-D\-F\  or  A2-D2-F2  if  either  were  placed  with 

its  plane  parallel  to  the  direction  of  the  incoming 

waves ; 
co  =  angular  velocity  of  currents  flowing  in  Ai-Di-Fi  and 

A2-D2-F2', 
M  =  coefficient  of  mutual  induction  between  K  and  either 

DI  or  D2  when  the  plane  of  K  is  parallel  to  either 

Di  or  D2. 

It  was  stated  on  p.  743  that  the  effective  value  (the  same  applies  to 
the  maximum  value)  of  the  current  flowing  in  a  receiving  coil  antenna, 
whose  plane  is  inclined  to  the  direction  of  the  incoming  waves,  is  equal 
to  that  which  would  flow,  were  its  plane  parallel  to  the  direction  of  the 
waves,  multiplied  by  the  cosine  of  the  angle  which  the  direction  of  the 
waves  makes  with  the  plane  of  the  coil.  In  our  case,  therefore,  we  have: 

i\  =  Im  cos  a  sin  ut (53) 

By  imagining  that  DI  is  rotated  (counter-clockwise)  until  it  coincides 
with  position  shown  for  D2,  we  see  that  the  equation  for  current  in  coil 
D2  must  be 

ii  =Im  cos  (a +  90)  sin  ut  =  —Im  sin  a  sin  ut.        ...     (54) 

From  the  well- known  law  of  electromagnetic  induction 

ei  =  -Msm(3^ (55) 

62  =  _Mcos/3 '.     (56) 


770  ANTENNA  AND   RADIATION  [CHAP.  IX 

Substituting  in  (55)  and  (5(5)  the  values  of  it  and  i2  of  (53)  and  (54)  we 
have: 

61  =  —  uMIm  cos  a  sin  /8  cos  co<, (57) 

62  =  uMIm  sin  a  cos  0  cos  wf , (58) 

6  =61+62  =  —wMIm  cos  co/ (cos  a  sin  0  —  sin  a  cos  0).     .     (59) 

The  maximum  value  of  e  for  a  given  value  of  a  and  0  evidently  occurs 
when  cos  ut  =  1  or 

Max.  value  of  e  =  uMIm  (cos  a  sin  0  —  sin  a  cos  0).     .     .     (60) 

Since  the  maximum  value  of  the  current  flowing  in  the  coil  K  is  directly 
proportional  to  the  maximum  value  of  e,  and  since  this  latter  changes 
as  the  angle  0  is  changed,  i.e.,  as  the  position  of  K  changes,  it  follows 
that  the  signal  strength  will  vary  as  K  is  rotated  about  its  axis. 

We  may  now  find  the  values  of  0  which  will  make  the  signal  strength 
zero  or  a  maximum  respectively;  this  will  occur  when  the  value  of  the 
parenthesis  of  Eq.  (60)  is  zero  or  a  maximum. 

We  can  put      cos  a  sin  0  —sin  a  cos  ft  =sin  (/3— a)  and  then  get 

sin  (0-a)  =0  when  /3-a=0°  or  180° 

from  which  0=a  or  =  180°+a: (61) 

sin  (0-a)  =maximum  when  /3-a=90°  or  270° 

from  which  ft  =  90°+a  or  =  270°+a.     .     .     (62) 

We  may  therefore  state  that  extinction  of  the  signals  will  take  place 
when  the  normal  to  the  plane  of  the  coil  K  is  parallel  to  the  direction  of 
the  incoming  waves,  and  that  maximum  strength  of  signals  will  result 
when  the  normal  to  the  plane  of  K  is  at  right  angles  to  the  direction  of 
the  incoming  waves.  It  will  be  noted  that,  in  this  particular  case,  where 
DI  and  D2  are  parallel  to  A\  and  A%  respectively,  the  results  are  the  same 
as  if  the  whole  system  of  coils  were  reduced  to  the  coil  K  alone  used  as  a 
coil  antenna;  for,  when  the  plane  of  K  is  perpendicular  to  the  direction 
of  the  waves,  the  strength  of  signals  is  a  minimum,  and  when  the  plane 
of  K  points  towards  the  direction  of  the  waves,  the  strength  of  signals 
is  a  maximum. 

A  discussion  similar  to  the  one  given  above  may  be  applied  in  a  similar 
manner  and  with  similar  results  to  the  case  of  damped  waves.  Of  course 
it  is  plain  that  the  results  expressed  by  Eqs.  (61)  and  (62)  are  vitiated 
by  the  existence  of  any  dissimilarity  between  the  circuits  A\-D\-F\  and 
A2-D2-F2.  In  order  to  avoid  any  dissimilarity  as  much  as  possible,  even 
at  the  expense  of  sensitiveness,  the  condensers  F\  and  F2  are  often  dis- 
pensed with,  and  the  circuits  are  thus  made  aperiodic. 

By  fitting  coil  K  with  a  suitably  calibrated  dial  and  rotating  the  coil 
until  weakest  signals  are  obtained,  the  direction  of  the  incoming  waves 
may  be  determined  with  a  comparatively  small  percentage  of  error,  Use 


DIRECTION   FINDERS 


771 


has  been  made  of  the  direction  finders  for  determining  the  position  of  a 
ship  or  aircraft  of  some  kind.  Thus,  in  the  case  of  a  ship  S  which  is 
nearing  the  port,  the  ship  may  get  her  bearings  quite  accurately  in  one  of 
two  ways,  as  indicated  below:1 

(a)  The  ship  may  be  fitted  with  a  directional  receiver,  and  the  stations 
A,  B,  C,  D  may  be  fitted  with  non-directional  transmitters  continually 
sending  out  different 
identifying  letters.  The 
operator  on  board  the 
ship  is  assumed  to  know 
the  positions  of  the  sta- 
tions A,  B,  C  and  D  on 
his  chart.  He  would 
obtain  the  angles  a,  0,  7 
(see  Fig.  77)  by  mani- 
pulating his  directional 
receiver.  By  plotting 
the  points  A,  B,  C,  D 
and  the  angles  <*,  0,  7 
the  position  of  the  ship 
may  be  obtained. 

(6)  The  ship  may 
be  fitted  with  a  non- 
directional  transmitter 
continually  sending  out 
some  identifying  letter, 
and  the  stations  A,  B, 
C,  D  may  be  fitted  with 
directional  receivers. 
The  operators  at  A,  B, 
C,  D  would,  by  manip- 
ulating their  direc- 
tional receivers,  obtain 
the  angles  which  the 
lines  SA,  SB,  SC,  SD 

make  with  the  north  and  south  line  and  report  these  angles  by  telephone 
to  a  central  station  F,  where  the  angles  are  plotted  and  the  position 
of  the  ship  is  determined.  Station  F  will  then  transmit  the  position  of 
the  ship  by  radio  to  the  operator  on  board  the  ship. 

1  Ships  desiring  radio  compass  service  must  be  fitted  to  receive  on  450  meters  in 
American  ports  and  800  meters  in  European  ports;  thus  a  ship  sailing  from  American 
ports  should  now  have  receiving  equipment  calibrated  at  300  and  000  meters  (man- 
datory) as  well  as  450  and  800  meters. 


FIG.  77. — Arrangement  of  shore  station  around  a  port  to 
furnish  radio  compass  service  to  incoming  ships. 


772 


ANTENNA  AND   RADIATION 


[CHAP.  IX 


This  latter  method  is  the  one  used  in  the  port  of  New  York  and  seems 
to  be  preferable  to  the  former,  in  so  far  as  this  requires  the  presence  of  a 
skillful  operator,  capable  of  plotting  the  ship's  position,  on  board  each 
ship,  whereas  in  the  other  case  all  the  plotting  is  done  in  one  single  cen- 
tral station,  where  much  greater  accuracy  may  be  obtained. 

So  far  we  have  shown  how,  by  means  of  the  single  coil  antenna  or  by 
means  of  a  goniometer,  we  may  be  able  to  determine  the  plane  parallel 

to  which  the  electromagnetic  waves  are 
acting;  but  we  have  not  yet  determined 
the  exact  direction  of  the  incoming  waves. 
Thus,  we  have  been  able  to  find  that  the 
waves  may  be  acting  along  the  line  AB, 
but  not  whether  they  are  coming  from  A 
or  from  B;  this  determination  is  techni- 
cally known  as  the  "  elimination  of  the 
180°  uncertainty."  In  most  instances  the 
direction  from  which  the  waves  are  coming 
is  known,  especially  in  communication 
between  ship  and  shore  and  vice  versa; 
but  sometimes  this  is  not  the  case. 

In  order  to  eliminate  the  180°  uncer- 
tainty the  single-coil  antenna  or  the  double- 
coil  antenna  of  a  goniometer  is  accom- 
panied by  a  vertical-wire  antenna  located 
in  the  axis  of  the  coil  or  coils,  as  shown 
for  the  case  of  the  single  coil  antenna  of 
Fig.  78,  where  A  BCD  is  the  coil  antenna, 
FG  the  vertical-wire  antenna,  connected 
to  ground  in  series  with  the  tuning  in- 
ductance H  and  the  key  K.  The  in- 
ductance H  is  loosely  coupled  to  the  coil 
N  inserted  in  series  with  the  coil  antenna. 
The  operation  of  obtaining  the  direction  of 
the  incoming  waves  would  be  as  follows : 

(1)  With    key  K   open   and   the    coil 

uncertainty  it  is  necessary  to  use  ,   .    ,  ...  , 

antenna  turned  into  some   position  where 
a  simple  antenna  in  connection  r 

with  the  coil  antenna.  tne  signals  may  be  easily  heard,  tune  the 

coil  antenna  circuit  to  the  incoming  wave- 
frequency  by  means  of  condenser  P. 

(2)  Close  K,  and,  without  changing  condenser  P,  adjust  H  until  the 
circuit  of  the  vertical  wire  antenna  is  tuned  to  the  frequency  of  the  incom- 
ing waves,  which  will  be  denoted  by  maximum  noise  in  the  receivers  con- 
nected in  the  detecting  apparatus. 


FIG.   78. — To    eliminate 


180C 


DIRECTION  FINDERS 


773 


w 


(3)  Again  open  key  K.     Turn  the  coil  antenna  until  the  signals  dis- 
appear or  become  a  minimum.     The  normal  to  the  plane  of  the  coil  when 
in  this  position  represents  a  line  parallel  to  the  direction  of  the  incoming 
waves. 

(4)  With  key  K  still  open  turn  the  coil  antenna  90°  from  position  of 
(3).     Maximum    signal    strength  will       r 

then  be  obtained. 

(5)  With  the  coil  antenna  in  the 
position  of   (4)  depress  key  K.     The 
signal  strength  will  either  increase  or 
decrease  relative    to  that  of  (4),  de- 
pending upon  the  exact  direction  from 
which  the  waves  are  coming.      If  the 
signal  strength  decreases  upon  closing 
K  the  waves  are  coming  from  a  cer- 
tain direction,  and  if  it  increases  the 
waves  are  coming  from    the   opposite 
direction.     Whether  it  is  one  direction 
or  the  other  may  be  told  by  previously 
calibrating     the     entire      apparatus. 
Waves  are  used  for   this  calibration 
which  are    known    to    come    from   a 
definite  direction. 

The  reason  for  the  behavior  of  the 
vertical-wire    antenna   together   with 
the  coil  antenna   is   as   follows :    Con-  FIG.  79.— Direction  of  assumed  positive 
sider  Fig.  79  and  let  the  arrows  repre-       e.m.f.  induced  in  the    conductors  of 
sent  the    assumed   positive  directions      the  two  antennae  of  Fig-  78. 
of   the    electromotive    forces    in    the 

wires  AB,  FG,  CD.  Let  the  direction  of  the  incoming  waves  be  as  repre- 
sented by  W,  and  let  the  plane  of  the  coil  be  parallel  to  the  direction 
of  the  waves. 


Call 


I=  effective  value  of  e.m.f.  produced  in  wire  AB  due  to 

waves  W; 
z=  effective  value  of  e.m.f.  produced  in  wire  FG  due  to 

waves  W; 
a=  effective  value  of  e.m.f.  produced  in  wire  CD  due  to 

waves  W; 
a  =  angle  equivalent  to  distance  S\  between  AB  and  FG, 

and  between  FG  and  CD; 
E=  effective  value  of  total  e.m.f.  in  coil  antenna  due  to 

waves  W; 


774 


ANTENNAE  AND  RADIATION 


[CHAP.  IX* 


OA=OE-OEn 

FIG.  80.— The  e.m.f.  act- 


in  its  two  sides  and  s 
shown  at  OE]  current 
flowing  in  the  simple 
antenna  is  shown  at  Oh 


/2=  effective  value  of  current  produced  in 
the  vertical  wire  antenna; 

En  =  effective  value  of  e.m.f.  induced  into  N 
by  the  current  in  H. 

Since  the  waves  strike  wire  A  B  first  it  is  plain 
that  the  e.m.f.  produced  therein  will  be  ahead  of 
that  of  FG  and  CD  and,  therefore,  the  various 
e.m.f. 's  will  be  as  shown  in  Fig.  80  below,  where: 

E=Ei-Ez 


It  is   plain  that   no   matter  what   the   angle  a 
the  vector  E  will  always  be  at  right  angles  to  E2. 

ing  in  the  coil  antenna  Tne  current  I2  will,  since  the  wire  antenna  is 
(Fig.  79)  is  the  vector  tuned  to  the  incoming  waves,  be  in  phase  with  the 
difference  of  the  e.m.f.  e.m.f.  E2.  The  e.m.f.  En  induced  in  N  will  be  90° 
behind  the  current  I2  or  180°  from  the  e.m.f.  E. 
Since  the  total  e.m.f.  producing  the  current  in  the 
coil  antenna  is  E—Enj  this  e.m.f.  will,  in  this  case, 
and  this  induces  a  volt-  be  OA,  less  than  if  the  coil  antenna  alone  were 
age  in  the  coil  antenna  acting,  when  the  total  e.m.f.  would  be  E. 
equal  to  OEn.  Now  consider  the  case  when  the  waves  are 

coming   from  the   opposite  direction  to  W.     Let 

the  symbols:  E>\,  Ef2,  E's,  E',  I'2,  En'  represent  quantities  correspond- 
ing to  Eiy  E2,  Es,  E,  I2,  En,  with  the  waves  from  the  direction  opposite 
to  W.  In  this  case  the  waves  will 
strike  conductor  CD  first,  and  hence 
the  e.m.f.  produced  therein  will  lead 
the  e.m.f. 's  of  FG  and  A  B.  The 
vector  diagram  will  then  be  as  shown 
in  Fig.  81.  As  before  E' =  E'i-E's 
and  will  be  always  perpendicular  to 
E'2.  The  e.m.f.  E'n  will  now  be  in 
phase  with  E'  and  the  total  e.m.f. 
CE^+Jin)  producing  the  current  in 
the  coil  antenna  will,  in  this  case, 
be  0 A ,  larger  than  if  the  coil  anten- 
na alone  were  acting,  when  the  total 
e.m.f.  would  be  E' . 

Thus  it  has  been  shown  that  if  the 
waves  are  coming  from  TF,  Fig.  79,  the 

action  of  the  current  in  the  vertical-wire  antenna  is  to  diminish  the  current 
in  the  coil  antenna  (and  hence  the  strength  of  signals) ,  while  if  the  waves 


FIG.  81. — This  diagram  shows  how  the 
phase  relations  of  the  various  e.m.f.  of 
Fig.  80  change  if  it  is  assumed  that  the 
signal  waves  are  coming  from  the  oppo- 
site direction  to  that  assumed  in  Fig.  81. 


DIRECTION  FINDERS  775 

are  coming  from  the  opposite  direction  the  action  of  the  vertical-wire 
antenna  is  to  increase  the  strength  of  the  signals.  It  will  be  understood 
that  whether  the  signal  strength  is  increased  or  decreased  by  the  action 
of  the  vertical-wire  antenna  will  depend  not  only  upon  the  direction  of 
increasing  waves,  but  also  upon  the  direction  of  the  winding  on  the  ^eoils 
H  and  N  and  the  position  of  these  coils  relative  to  each  other.  This  is 
the  reason  why  the  entire  apparatus  has  to  be  calibrated  beforehand. 
In  the  case  of  a  goniometer  the  vertical  wire  antenna  is  coupled  to  both 
of  the  coil  antennae,  and  the  manipulation  of  the  apparatus  is  similar  to 
that  for  the  single-coil  antenna. 

Incomplete  Extinction  of  Signals. — Unless  special  precautions  have 
been  taken  coil  antennae  do  not  give  zero  signal,  in  any  position;  the 
signal  goes  to  a  minimum,  but.  is  not  extinguished.  This  effect  is  pro- 
duced by  the  coil  acting  to  some  extent  like  a  simple  antenna.  The 
two  wires  leading  from  the  coil  to  the  detecting  apparatus  unbalance  the 
coil  electrically,  one  of  them  going  directly  to  ground  (filament  circuit 
of  detecting  tube)  and  the  other  connecting  to  ground  only  through  a 
very  high  impedance.  This  asymmetry  is  sufficient  to  prevent  a  "  silent  " 
setting  to  be  made  with  the  coil,  because  the  antenna  effect  gives  an 
e.m.f.  90°  out  of  phase  with  the  coil  effect.  By  a  suitable  auxiliary  cir- 
cuit it  is  possible  bo  eliminate  this  antenna  effect,  thus  getting  a  more 
accurate  setting,  if  necessary. 

Reliability  of  Direction  Finders. — The  precision  with  which  a  direction- 
finding  receiving  coil  can  be  set  (under  laboratory  conditions)  is  probably 
less  than  1°;  in  general  an  operator  can  set  more  precisely  for  minimum 
signal  strength  than  for  maximum  unless  two  coils,  at  right  angles  to 
each  other,  are  used  and  one  of  them  arranged  for  commutation.  In 
this  scheme  the  combination  of  coils  is  so  placed  that  one  coil  (the  one 
without  the  commutator)  lies  approximately  in  the  direction  of  the 
signal,  thus  being  set  for  maximum  reception.  The  other  coil  (evidently 
set  for  minimum  signal)  is  connected  in  series  with  the  first  by  means  of 
the  commutator.  The  operator  then  orients  the  apparatus  until  the 
commutation  of  the  one  coil  makes  no  difference  in  the  signal  strength. 
The  precision  of  setting  with  this  apparatus  is  probably  much  better 
than  1°. 

It  would  seem  that  it  is  not  worth  while  to  increase  the  precision  of 
direction  finders  beyond  that  now  attainable,  because  of  the  non-linear 
propagation  of  radio  waves.  With  short  waves  there  is  not  much  devia- 
tion from  straight  line  propagation,  under  ordinary  conditions;  with  the 
long- wave-signals,  however,  the  propagation  seems  to  be  rather  erratic.1 
With  signals  from  10,000-20,000  meters  long,  an  apparent  change  in 

1  See   Bureau   of   Standards   Scientific   Paper   No.  353,  reporting  experiments  by 
A.  H.  Taylor. 


776  ANTKN.VK    AND   RADIATION  [CHAP.  IX 

direction  of  a  transmitting  station  of  as  much  as  90°  may  occur,  the  change 
occurring  quite  rapidly  (as  much  as  several  degrees  per  minute).  This 
variation  occurred  when  the  two  stations  were  less  than  200  miles  apart 
and  might,  of  course,  been  greater  if  the  distance  had  been  greater.  The 
change  in  direction  is  undoubtedly  due  to  refractions  caused  by  conditions 
of  conductivity  in  the  atmosphere,  and  surface  conditions;  one  might 
expect,  for  example,  large  deviations  when  transmitting  along  a  shore 
line. 

In  view  of  Taylor's  experiments  it  seems  hardly  advisable  to  use  highly 
directional  receiving  antennae  for  communication  between  long-wave- 
stations.  It  would  seem  as  though  many  experiments  on  attenuation 
measurement  with  long  waves  must  be  of  extremely  doubtful  value,  if 
the  receiving  antenna  was  at  all  directional. 

Setting  up  the  Steady  State  in  an  Antenna. — It  has  been  noted 
previously  that  after  the  sending  key  is  depressed  it  may  be  an  appreciable 
time  before  the  current  reaches  the  value  predicted  by  the  steady  state 
equations;  some  of  the  effects  obtained  are  shown  in  Figs.  82,  83,  and  84. 
In  getting  the  film  shown  in  Fig.  82  the  impressed  frequency  was  such  as 
to  set  the  artificial  antenna  into  quarter  wave-length  oscillation;  the 
three  curves  on  the  film  show  the  voltage  impressed,  voltage  half  way 
along  the  antenna,  and  voltage  at  the  open  end.  They  are  not  shown  in 
the  film  to  the  same  scale  as  the  voltage  at  the  open  end  measured  345 
volts,  that  at  the  middle  212  volts  while  the  voltage  impressed  was  only 
20  volts. 

It  took  this  artificial  antenna  about  20  cycles  to  obtain  its  steady 
state  values;  in  an  actual  antenna  it  may  take  100  cycles  or  more 
before  the  steady  state  is  reached,  i.e.,  before  normal  radiation  is 
established. 

By  examination  of  the  film  it  may  be  seen  that  the  voltage  at  the  base 
(a  nodal  point)  is  90°  out  of  phase  with  the  voltage  at  the  end  of  the 
antenna;  this  is  in  accordance  with  the  ideas  brought  out  in  discussing 
Fig  73 

In  getting  the  film  of  Fig.  83  the  frequency  was  increased  to  three 
times  the  value  for  quarter  wave-length  oscillation.  It  may  be  found 
from  measurement  of  the  film  that  it  took  the  first  pulse  three-quarters  of 
a  cycle  to  travel  from  the  beginning  of  the  antenna  to  the  end.  Further- 
more, it  may  be  noted  that  in  the  steady  state  the  voltage  at  C  (end  of 
antenna)  is  180°  out  of  phase  with  the  voltage  at  B,  as  predicted  in  Fig. 
73,  and  voltage  at  A  is  90°  out  of  phase  with  the  voltage  at  B. 

In  establishing  the  steady  state  it  may  happen  that  one  section  of  the 
antenna  builds  up  to  a  voltage  higher  than  it  has  in  the  steady  state; 
this  is  indicated  in  Fig.  84  in  which  the  impressed  frequency  had  no  partic- 
ular relation  to  the  fundamental  frequency  of  the  antenna. 


TRANSIENT  CONDITION  IN  AN  ANTENNA 


778 


ANTENNA  AND  11AD1AT1OJN 


[CHAP.  IX 


FIG.  83. — Here  the  artificial  antenna  was  forced  to  vibrate  at  three  times  its  fundamental 
frequency;  it  will  now  be  noted  that  the  voltages  at  B  and  C  are  in  opposite  phase 
in  the  steady  state.  From  the  film  it  can  be  seen  that  the  original  pulse  arrives 
at  C  one-half  a  cycle  after  passing  point  B. 


FIG.  84. — While  the  steady  state  is  being  set  up  some  sections  of  the  antenna  may  carry 
currents  greater  than  the  steady  state  values. 


TlU.N8iE.NT  CONDITION  IN  AN  ANTENNA 


779 


780  ANTENNAE   AND    RADIATION  [CHAP.  IX 

Efiect  of  Pulse  Excitation  of  an  Antenna. — In  Fig.  85  is  shown 
the  effect  of  putting  a  square  pulse  of  current  into  the  antenna  and  then 
disconnecting  the  antenna  from  earth;  an  oscillatory  current  is  set  up  in 
the  antenna  (as  shown  by  the  middle  curve)  the  frequency  of  which  for 
the  conditions  used  is  that  of  the  half  wave-length  oscillation  of  the  antenna. 
Thus  pulses  of  "static"  always  excite  an  antenna  to  oscillate  at  its  natural 
period. 


CHAPTER  X 
WAVE-METERS  AND  THEIR  USE 

Relation  between  Frequency  and  Wave-length. — It  has  already  born 
shown  (see  p.  183)  that  a  definite  relationship  exists  between  the  wave- 
length of  the  energy  radiated,  the  frequency  of  oscillation,  and  the  velocity 
of  propagation,  which  may  be  expressed  as  follows 

-7> 

where  X  =  wave-length  in  meters; 

V  =  velocity  of  propagation  in  meters  per  second; 
/= frequency  of  oscillations  in  cycles  per  second. 

Since  the  velocity  of  propagation  V  is  the  same  for  all  cases,  i.e., 
3X108  meters  per  second,  corresponding  to  the  speed  of  light,  the  wave- 
length may  thus  be  immediately  determined,  if  the  frequency  is  known, 
and  vice  versa. 

Principle  of  the  Wave-meter. — Therefore,  an  instrument  by  means 
of  which  the  frequency  may  be  determined  may  also  be  used  to  measure 
the  wave-length,  and  instead  of  having  its  indicating  scales  graduated 
in  frequencies,  may  have  them  calibrated  directly  to  read  the  wave-length. 
Such  an  instrument  is  called  a  wave-meter,  and  represents  the  most  use- 
ful and  important  measuring  device  employed 
in  radio-engineering.  The  instrument  consists 
fundamentally  of  a  circuit, thenatural  frequency 
of  which  is  adjustable  and  known  at  all  set- 
tings. This  circuit  is  brought  into  resonance 
with  the  frequency  to  be  measured,  which  FlG>  i._The  simplest  wave- 
may  then  be  read  at  once  from  the  setting  meter  consists  of  a  fixed 
of  the  wave-meter  (indicated  in  wave-length).  coil,  L,  of  as  low  resistance 

In  its  usual  form,  it  consists   of  a  simple      as  feasible>  in  series  with  a 

series   circuit,  containing  an   inductance  and 

.  .  denser  C,  and  a  hot-wire  am- 

capacity  and  an  indicating  device,  e.g.,  a  hot-      meter>    A)    for    indicating 

wire  ammeter,  to  show  the  resonant  condition.       resonance. 
This  circuit  is  shown  in  Fig.  1 . 

For  varying  the  natural  frequency  of  the  circuit,  the  capacity  is  usually 
made  variable,  as  being  the  more  practical  and  convenient,  while  the 

781 


782  WAVE-METERS  AND   THEIR  USE  [CHAP.  X 

inductance  is  fixed  in  value.  The  relation  between  natural  frequency, 
wave-length,  and  the  circuit  constants  has  already  been  derived  (see  page 
212)  as 

/  = -i=  cycles  per  second 

where  L  and  C  are  measured  in  henries  and  farads, 
and  X  =  1885  VLC  meters 

in  which  L  and  C  are  measured  in  microhenries  and  microfarads. 

As  the  condenser  capacity  is  varied,  a  pointer  attached  to  the  moving 
element,  moves  over  a  graduated  scale,  which  may  be  calibrated  to  indicate 
the  natural  frequency  of  the  circuit  at  the  different  settings.  Usually, 
the  scale  is  calibrated  in  wave-lengths,  as  already  mentioned,  due  to  the 
custom  of  expressing  frequencies  in  terms  of  wave-length. 

Extending  the  Wave-length  Range. — Assuming  a  coil  of  constant 
inductance  L,  the  wave-length  range  which  may  be  covered  by  the  meter 
is  limited  by  the  maximum  and  minimum  values  of  the  variable  condenser, 
and  the  internal  capacity  of  the  coil  being  used.  The  wave-meter  may 
be  required  to  measure  wave-lengths  from  very  small  values,  for  example, 
50  meters,  up  to  wave-lengths  of  10,000  meters  and  above,  and  to  attempt 
to  cover  this  range  with  one  value  of  inductance  would  require  a  very 
large  variable  condenser,  with  a  correspondingly  crowded  scale,  and  deter- 
minations would  be  difficult  and  inaccurate.  It  is  therefore  usual  to  supply 
several  coils  of  different  inductance  with  the  instrument,  the  larger  values 
of  inductance  being  inserted  in  the  circuit,  when  higher  wave-lengths  are 
to  be  determined.  Similarly,  the  smaller  inductances  would  be  used  in 
small  wave-length  measurements. 

To  increase  the  range  beyond  the  maximum  and  minimum  wave- 
lengths, which  can  be  measured  with  the  inductances  supplied  with  the 
instrument,  the  procedure  would  be  as  follows,  assuming  that  the  induc- 
tance of  the  coils  supplied  is  not  known. 

For  Wave-lengths  below  the  Minimum  Range. — Assume  the  maximum 
wave-length  which  can  be  measured  with  the  lowest  wave-length  coil 
in  circuit  as  100  meters.  Adjust  some  exciting  source  to  radiate  at  50 
meters,  the  wave-meter  being  loosely  coupled  to  the  radiating  circuit, 
which  may  be  a  transmitting  set  or  a  simple  buzzer-excited  circuit.  Esti- 
mate the  coil  inductance  as  accurately  as  possible  from  the  dimensions 
and  turns  of  the  coil  in  circuit,  and  construct  a  coil  with  approximately 
one-quarter  (or  somewhat  greater)  of  this  inductance.  Insert  this  new 
coil  in  circuit  in  place  of  the  standard  coil,  and  again  couple  loosely  to 
the  radiating  circuit,  which  is  still  adjusted  to  radiate  at  50  meters.  It 
should  be  found  that  the  wave-meter  is  now  in  resonance  with  the  variable 
condenser  adjusted  to  about  the  100-meter  graduation. 


EXTENDING  RANGE  OF  WAVE-METEH  783 

If  it  is  desired  to  have  a  definite  proportionality  between  the  readings 
obtained  with  the  new  and  old  coil  (for  example  2  to  1),  remove  turns* 
from  the  improvised  coil  until  resonance  occurs  when  the  capacity  is  set 
at  100  meters.  The  true  wave-length  being  50  meters,  a  multiplying 
factor  of  i  must  thus  be  applied  to  all  readings  obtained  when  using  the 
new  coil.  The  maximum  wave-length  of  the  new  minimum  wave-length 
coil  has  therefore  been  cut  in  half,  and  low  wave-length  determinations 
may  now  be  more  easily  and  accurately  made.  Of  course  it  is  not  neces- 
sary to  make  the  new  coil  have  such  an  inductance  as  to  cut  the  wave- 
length scale  in  two.  Suppose  that  the  new  coil  gives  resonance  with  the 
wave-meter  set  at  97  meters;  then  the  proper  wave-length  reading  for 
the  new  coil  will  be  50/97  that  for  the  smallest  wave-meter  coil. 

For  Wave-lengths  above  the  Maximum  Range.  —  For  this  case  the 
procedure  is  exactly  as  outlined  above,  with  the  exception  that  the  induc- 
tance would  be  increased  instead  of  decreased.  Thus  if  the  range  is  to 
be  doubled,  and  the  maximum  wave-length  with  the  maximum  induc- 
tance L  in  circuit  was  2000  meters,  the  inductance  to  be  added  to  the  cir- 
cuit would  be  3  L  (the  total  inductance  thus  being  4  L),  and  the  maximum 
wave-length  which  could  be  measured,  thus  doubled  to  4000  meters. 
Calibration  would  be  carried  out  by  adjusting  a  sending  set  to  radiate  at 
2000  meters,  and  then  adjusting  the  added  inductance  until  resonance 
is  indicated  at  the  1000-meter  mark.  A  multiplying  factor  of  2  must 
then  be  applied,  to  obtain  the  true  wave-length  from  that  indicated  on 
the  condenser  scale,  and  the  wave-length  range  has  therefore  been  doubled. 

If  the  inductances  of  the  coils  furnished  with  the  instrument  are 
accurately  known  (this  is  usually  the  case),  and  means  are  available  to 
construct  accurately  the  desired  additional  inductances,  the  laboratory 
calibration  described  above  would  not  be  required.  It  would  be  desirable, 
however,  to  make  a  check  measurement  in  all  cases  when  possible. 

Schemes  for  Indicating  Resonance.  —  The  wave  meter  circuit  will  be 
in  resonance  when  its  natural  frequency  coincides  with  the  frequency  of 
the  induced  e.m.f.,  or  when 


Under  this  condition,  the  impedance  of  the  wave-meter  circuit,  will 
be  a  minimum  (loose  coupling  assumed)  and  will  be  equal  to  the  effective 
resistance  R  of  the  circuit.     Thus  the  current  will  be  a  maximum  and  any 
device  whose  indications,  whether  audible  or  visible,  vary  with  the  current 
value,  may  be  used  as  a  means  of  indicating  the  resonant  condition. 
The  following  devices  are  applicable  for  this  purpose: 
a.  Hot-wire  ammeter. 
6.  Crystal  detector  and  phones. 


784 


WAVE-METERS  AND   THEIR  USE 


[CHAP.  X 


c.  Thermo-couple  and  galvanometer. 

d.  Crystal  detector  and  galvanometer. 

e.  Tube  filled  with  rarefied  gas  (neon). 
/.  Small  incandescent  lamp. 

a.  Hot-wire  Ammeter. — This  instrument  may  be  connected  directly  in 
series  in  the  circuit  as  shown  in  Fig.  1,  or  may  be  shunted  across  one  or 

more   turns   of  the  inductance,  as  shown  in 
Fig.  2. 

The  latter  scheme  is  more  usually  employed, 
due  to  the  high  resistance  of  the  ammeter. 
The  instruments  used  in  wave-meters  are 
FIG.  2.— Sometimes  the  sensi-  never  called  on  to  measure  very  large  currents, 
tive,  high-resistance,  am-  as  the  current  may  always  be  limited  by  the 
meter  used  in  a  wave-meter  coupling  between  the  wave-meter  and  the 
is  shunted  across  a  few  turns  exciti  circuit>  The  current  carrying  element 
of  the  inductance  as  this  may  *?  .  ~  &  . 

introduce  less  resistance  in  (see  below)  *  therefore  of  rather  fine  wire,  and 
the  wave-meter  circuit  than  possesses  considerable  resistance,  which,  if 
if  the  meter  were  connected  placed  directly  in  series  in  the  circuit,  would 
directly  in  series,  as  in  Fig.  1.  seriously  increase  the  meter  decrement,  as  dis- 
cussed later. 

The  ammeter  should  be  made  as  sensitive  as  possible  so  that  large 
deflections  may  be  obtained  without  coupling  the  meter  too  closely  to 
the  circuit  being  tested.  It  consists  essentially  of  a  very  thin  wire  or 
strip,  through  which  the  circuit  current,  or  portion  thereof,  passes.  The 
wire  is  under  tension  and  as  it  expands,  due  to  the  heating  effect  of  the 
current  flowing  through  it,  it  causes 
a  shaft  to  rotate.  The  pointer  of 
the  instrument  is  rigidly  attached 
to  this  shaft.  This  arrangement  is 
indicated  in  Fig.  3. 

The  heat  loss  in  the  wire,  and 
therefore  its  elongation  and  the 
meter  indication  is  evidently  pro- 
portional to  I2.  In  order  that 
the  pointer  deflections  be  truly 
proportional  to  I2,  it  is  necessary 
that  R  should  be  constant  over 
the  frequency  range  at  which  the 
instrument  will  be  used.  For  this 

reason  very  thin  wire  is  employed,  having  negligible  skin  effect.  The 
resistance,  however,  is  correspondingly  high,  and  it  is  for  this  reason 
directly,  as  already  mentioned.  A  typical  sensitive  instrument,  e.g.,  has 
a  resistance  of  8  ohms  and  gives  full  scale  deflection  with  30  milliamperes. 


Thin  wire  of 
high  expansion 
coefficient 


Fine  thread 
or  wire 


Zero  adjustment 
attached  here 


Spring 


FIG.  3. — Sketch  showing  how  the  average 
hot-wire  meter  is  constructed;  sometimes 
the  expansion  of  the  wire  is  still  further 
magnified  by  one  more  string  attach- 
ment. 


RESONANCE  INDICATORS  785 

It  should  be  noted  that  in  the  various  measurements  used  with  wave- 
meters  it  is  not  necessary  that  the  absolute  value  of  current  be  known, 
but  only  relative  values  are  required,  therefore  there  is  no  objection  to 
connecting  the  meter  in  shunt,  since  the  variations  in  frequency  are  so 
small  during  any  one  measurement  that  the  accuracy  of  the  result  is  not 
affected  (due  to  change  in  the  shunt  impedance). 

When  the  current  to  be  measured  exceeds  3  amperes,  as  for  instance 
the  antenna  current  of  a  transmitting  set,  the  size  of  the  wire  required, 
were  it  attempted  to  use  but  one  conductor,  would  be  so  large  that  its 
resistance  would  no  longer  be  independent  of  frequency.  For  this  case 
a  squirrel-cage  element,  consisting  of  a  number  of  fine  wires  or  strips  con- 
nected in  parallel,  is  used.  See  Fig.  12,  page  123. 

For  currents  larger  than  20  amperes  a  current  transformer  may  profit- 
ably be  employed.  This  transformer  may  be  air-  or  iron-cored,  the  latter 
being  used  to  the  greatest  extent,  as  it  insures  close  coupling  between  the 
primary  and  secondary  turns.  The  core  is  of  toroidal  form,  made  of  very 
thin  iron  plates,  and  at  radio  frequencies  the  current  ratio  is  given  approxi- 
mately by  the  turn  ratio,  i.e., 

!i  =  !^ 
1 2     n\ 

where,  ri2  =  number  of  secondary  turns  in  series; 

n\  =  number  of  primary  turns  in  series; 
/2  =  secondary  current  ; 
/i  =  primary  current. 

It  has  already  been  noted  that  the  deflections  of  the  hot-wire  ammeter 
are  proportional  to  72,  or  to  the  watts  (PR)  lost  in  the  instrument  itself. 
For  this  reason  it  has  been  erroneously  called  a  watt-meter,  when  the  scale 
is  graduated  in  (amperes)2  and  not  in  amperes.  The  ammeters  used  in 
modern  wave-meters  are  graduated  in  either  of  these  ways,  in  fact,  the 
(ampere)2  graduation  is  the  more  convenient  for  certain  measurements. 
It  should,  however,  be  clearly  kept  in  mind  that  the  instrument  is  not 
really  a  watt-meter  in  the  ordinary  sense;  the  scale  calibration  generally 
gives  the  watts  used  in  the  instrument  itself. 

b.  Crystal  Detector  and  Phones. — The  hot-wire  ammeter  is  applicable 
only  when  the  wave-meter  is  to  be  coupled  to  a  circuit  of  considerable 
power,  so  that  appreciable  currents  are  caused  to  flow  in  the  wave-meter 
circuit.  When  the  induced  currents  are  exceedingly  small,  as  when  the 
wave-meter  is  coupled  to  a  receiving  antenna,  or  a  buzzer-excited  wave 
generator,  only  the  most  sensitive  of  current  indicating  devices  may  be 
used.  The  crystal  detector  and  phones,  which  have  already  been  de- 
scribed in  connection  with  the  reception  of  spark  signals  (see  page  339) 


786 


WAVE-METERS  AND   THEIR   USE 


[CHAP.  X 


are  eminently  suited  for  this  purpose,  and  various  schemes  for  connecting 
these  into  the  wave-meter  circuit  have  been  tried.  These  schemes  are 
shown  in  Fig.  4,  which  also  shows  the  relative  sensibility  of  the  different 
arrangements.1 

Scheme  No.  1  is  probably  the  most  generally  used,  and  its  operation 
and  action  is  exactly  similar  to  that  involved  in  the  reception  of  spark 
signals  (see  page  339).  It  illustrates  what  is  known  as  the  "  direct  " 
connection  of  the  detector  and  phones.  Circuit  No.  4  represents  what  is 
called  the  "  unilateral  "  connection,  the  phones  and  detector  being  com- 
nected  in  a  closed  loop,  which  is  connected  to  the  wave-meter  circuit  at 
one  point  only.  This  scheme  is  not  used  to  any  great  extent,  due  to  its 
poor  sensibility,  but  possesses  an  advantage  in  that  the  calibration  of  the 
wave-meter  is  not  affected  appreciably,  by  the  character  of  the  detector- 


FIG.  4.- — Various  schemes  of  connecting  crystal  rectifier  and  telephones  for  indicating 
resonance  in  a  wave-meter  excited  by  a  very  low-powered  source. 

phone  circuit.  Thus  in  circuit  No.  1,  the  leads  going  to  detector  and 
phones  may  possess  considerable  capacity  (as  indicated  diagrammatically 
by  the  dotted  condenser),  which  capacity  is  in  parallel  with  the  wave- 
meter  condenser.  The  wave-meter  calibration  will  thus  no  longer  apply, 
since  the  circuit  capacity  has  been  augmented  by  an  uncertain  amount, 
and  the  determinations  are  therefore  inaccurate.  The  amount  of  error 
produced  evidently  depends  on  the  relative  value  of  the  variable  wave- 
meter  capacity,  and  the  external  fixed  capacity.  This  error  will  be  a 
maximum  when  the  variable  condenser  is  set  at  the  minimum  value, 
the  meter  reading  being  less  than  the  true  wave-length  which  is  being 
measured.  As  the  variable  capacity  is  increased,  the  error  decreases, 
and  may  become  negligible  at  the  larger  wave-lengths. 

With  the  "  unilateral  "  connection,  however,  the  wave-meter  circuit 
constants  are  unaltered,  regardless  of  the  characteristics  of  the  detector- 
1  Circular  of  the  Bureau  of  Standards,  No.  74,  p.  105. 


RESONANCE  INDICATORS  787 

phone  circuit,  and  any  pair  of  phones  with  associated  leads,  etc.,  may  be 
employed.  The  action  of  this  connection  is  essentially  one  of  electro- 
magnetic induction.  The  high-frequency  magnetic  field  linking  L  links 
also  the  closed  loop  of  the  phone  detector  circuit  (the  coupling  is  very 
small,  however,  and  this  probably  accounts  for  the  low  sensibility),  and 
induces  in  it  a  radio  frequency  e.m.f.,  which  will  cause  rectified  radio 
frequency  wave-trains  of  current  to  flow  in  the  loop.  Electrostatic  effects 
also  play  a  considerable  role  in  the  operation  of  this  detecting  scheme. 

The  connection  has  an  important  application  to  portable  or  field-type 
wave-meters,  which  may  thus  be  used  with  phones  whose  leads  vary  in 
length  and  other  characteristics,  i.e.,  size,  insulation,  and  configuration. 
Since  the  wave-meter  is  independent  of  these  variations,  accurate  determi- 
nations can  be  made,  if  the  audibility  requirements  do  not  necessitate 
coupling  the  wave-meter  too  closely  to  the  exciting  circuit,  while  varying 
degrees  of  error  would  occur  with  connection  No.  1,  which  requires  the 
wave-meter  to  be  used  with  the  phone-detector  circuit  with  which  it  was 
calibrated,  if  accuracy  is  to  be  obtained. 

Circuit  Nos.  2.  3,  and  5  all  operate  through  the  trapping  of  a  charge 
on  one  condenser  plate  (by  means  of  the  rectifier)  during  the  passage 
of  the  wave- train,  the  condenser  then  discharging  through  the  phones, 
giving  an  audible  click.  Thus  in  circuit  No.  2,  if  we  assume  that  the 
detector  will  permit  current  to  flow  downward,  but  not  upward,  it  is  evident 
that  a  positive  charge  will  accumulate  on  the  lower  condenser  plate  during 
the  passage  of  a  wave-train.  After  the  group  has  passed,  the  condenser 
discharges  downward  through  the  phones  (it  cannot  discharge  up  through 
the  detector)  and  up  through  the  inductance  of  the  wave-meter  circuit 
until  the  charges  on  its  plates  are  neutralized. 

The  action  of  circuit  No.  3  is  similar  to  that  of  circuit  No.  1. 
In  circuit  No.  5  the  charge  is  trapped  on  one  plate  of  the  condenser 
C  in  the  phone-detector  circuit.  If  we  again  assume  the  detector  to  be 
conducting  for  downward-flowing  current,  then  the  right-hand  plate  of 
the  condenser  will  accumulate  a  positive  charge.  Current  will  also  flow 
through  it  in  the  opposite  direction  through  the  phones,  but  with  difficulty 
due  to  greater  impedance  of  the  phones.  The  condenser  charge,  caused 
by  the  asymmetrical  flow  of  current,  is  discharged  upward  through  the 
phones  (it  cannot  pass  through  the  detector)  and  causes  the  phones  to  click 
once  per  wave-train  as  in  previous  circuits. 

Circuit  No  6  is  better  suited  to  large  currents,  the  telephone  and 
detector  being  replaced  with  a  small  hot-wire  ammeter,  when  particularly 
large  currents  are  to  be  indicated.  If  a  small  power  exciting  source  is 
coupled  to  the  wave-meter,  the  energy  transferred  from  the  wave-meter 
circuit  to  the  aperiodic  detector  circuit  is  too  small  to  give  clearly  audible 
indications,  unless  the  coupling  between  the  exciting  circuit  and  the  wave- 


788  WAVE-METERS  AND  THEIR  USE  [CHAP.  X 

meter  is  increased  to  an  excessive  value,  which  would  be  undesirable,  due 
to  obscurity  in  the  resonance  point,  and  consequent  inaccuracy.  It 
possesses  the  same  advantage  as  circuit  4,  in  that  the  wave-meter  cali- 
bration is  nearly  independent  of  the  detecting  circuit  characteristics.  These 
two  schemes  (No.  4  and  No.  6)  also  possess  the  advantage  that  the  decre- 
ment of  the  wave-meter,  upon  which  the  sharpness  of  tuning  depends, 
is  but  little  affected  by  the  detector  circuit.  In  the  other  four  arrange- 
ments, the  decrement  is  appreciably  increased,  scheme  No.  3  producing 
the  greatest  increase  (about  300  per  cent  on  the  average)  while  No.  5  pro- 
duced the  least  (about  100  per  cent  on  the  average). 

c.  Thermo-couple  and  Galvanometer. — Very  small  currents  may  be 
indicated  by  a  thermo-couple  and  sensitive  galvanometer.  The  hot- 
wire ammeter  may  also  be  used,  but  a  limit  is  reached  in  this  type,  how- 
ever, when  the  wire  becomes  so  fine  as  to  make  the  instrument  too  delicate 
for  practical  purposes,  and  for  currents  beyond  this  limit  the  thermo- 
couple and  galvanometer  are  generally  used. 

>.  £  High  frequency 

High  frequency  •  recurrent 

current 


To  galvanometer    J  Tog^ometer 

FIG.  5. — Two  types  of  thermo-couples  for  use  with  comparatively  large  currents;  the 
most  sensitive  couples  use  an  extremely  fine  welded  joint  at  the  contact,  and  are 
mounted  in  a  small  evacuated  glass  bulb. 

The  thermo-couple  consists  of  two  crossed  wires  of  dissimilar  metals, 
the  two  wires  being  lightly  soldered  or  welded  together  at  the  junction 
point.  This  junction  is  connected  into  the  circuit  in  which  the  high- 
frequency  current,  whose  value  is  to  be  determined,  is  flowing,  the  con- 
nection being  made  as  shown  in  Fig.  5,  which  illustrates  two  types  of 
couple  in  use. 

The  high-frequency  current  flowing  through  the  junction  raises  its 
temperature,  which  causes  a  unidirectional  e.m.f.  to  be  generated,  which 
in  turn  causes  a  direct  .current  to  flow  in  the  galvanometer  circuit.  This 
current,  and  therefore  the  galvanometer  indication,  is  proportional  to 
the  voltage  produced,  which  in  turn  is  proportional  to  the  temperature 
rise  of  the  junction.  The  galvanometer  deflections  are  therefore  pro- 
portional to  the  square  of  the  high-frequency  current. 

The  sensitivity  of  the  thermo-couple  depends  on  the  thermo-electric 
properties  of  the  wires  used  and  resistance  of  the  junction;  if  the  wires 
are  short,  their  length  has  some  effect  on  the  sensitivity.  The  air  pressure 


RESONANCE  INDICATORS 


789 


also  affects  the  sensitivity  as  this  determines  the  rise  in  temperature;   the 
best  couples  are  enclosed  in  an  evacuated  glass  bulb. 

The  metals  usually  used  in  the  couple  are  constantan  and  steel,  or 
constantan  and  maganin,  the  former  metal  being  a  copper-nickel  alloy 
while  manganin  represents  an  alloy  of  copper,  manganese,  and-nickel. 
The  materials  are  not  expensive  and  their  combination  possesses  perfectly 
satisfactory  thermoelectric  properties.  A  typical  cons  tan  tan-steel  thermo 
element  would  have  wires  of  about  0.02  mm.  in  diameter  and  4  mm.  long. 
Such  an  element  has  a  resistance  of  about  1  ohm  and  with  15  milliamperes 
of  high-frequency  current  flowing  through,  it  will  generate  about  40 
micro-volts.  The  resistance  of  the  galvanometer  used  with  the  couple 
should  be  approximately  the  same  as  that  of  the  couple  itself;  with  such 
a  combination  a  deflection  of  100  mm.  would  thus  be  produced  on  a  galvan- 


FIG.  6. — The  thermo-couple  may  be  connected  directly  in  the  wave-meter  circuit  or  may 
be  connected  in  the  secondary  of  a  transformer  having  suitable  ratio. 

ometer  with  a  sensitivity  of  0.25  mm.  per  microvolt,  by  15  milliamperes 
of  the  high-frequency  current. 

The  sensibility  of  galvanometers  used  with  wave-meters  is  not  as  high 
as  this  and  is  not  really  required,  as  the  high-frequency  currents  flowing 
in  the  circuit  may  be  readily  increased  by  increasing  the  coupling  of  the 
wave-meter  to  the  exciting  circuit.  Also,  the  construction  of  such  a  sen- 
sitive galvanometer  would  be  very  delicate,  and  not  applicable  for  use 
in  connection  with  the  wave-meter,  for  which  it  must  be  of  portable  con- 
struction. The  coupling  for  the  thermo-couple  and  portable  galvanom- 
eter will  in  any  case  be  very  much  less  than  that  required  by  the  direct- 
reading  hot-wire  ammeter,  and  the  sharpness  of  tuning  and  accuracy 
thus  increased. 

Fig  64  illustrates  a  wave-meter  circuit,  equipped  with  thermo-couple 
and  galvanometer.  The  sensitivity  may  possibly  be  increased  by  using 
a  current  transformer,  as  shown  in  Fig.  6J5.  This  also  increases  the 
-Affective  resistance  of  the  radio  frequency  circuit,  but  has  the  possible 


790 


WAVE-METERS  AND   THEIR  USE 


[CHAP.  X 


advantage  that  the  galvanometer  is  not  metallically  connected  to  the 
main  circuit.  This  arrangement  has  had  little  application  to  wave-meter 
circuits. 

d.  Crystal  Detector  and  Galvanometer. — This  scheme  is  similar  to  that 
indicated  in  Fig.  4,  diagram  No.  1,  except  that  a  sensitive  galvanometer 

has  been  substituted   for  the  phones, 
the    resonant    condition    thus    being 
visibly  indicated.      The    connections 
are  shown  in  Fig.  7.     This  arrange- 
ment is   equivalent    to  the    thermo- 
couple-galvanometer     scheme       dis- 
FIG.  7. — In  case  the  resonance  curve  of  cussed  above,  and    possesses    the  ad- 
the  wave-meter  is  to  be  plotted,  the  vantage  that  the  mcrease  in  effective 
phones  of  Fig.  4  may  be  replaced  by  a         .  ,  ,.    , , 

galvanometer;  this  should  be  of  about  resistance  of  the  wave-meter,  due  to 
the  same  resistance  as  the  detector,  it,  is  less  than  m  the  former  scheme 
generally  several  thousand  ohms.  For  and  the  sharpness  of  tuning  is 
suitably  low  voltages  (say  less  than  therefore  better.  It  possesses  the 
one  volt)  the  readings  of  the  galvan-  disadvantage,  however,  of  requiring 
ometer  will  be  proportional  to  the  ,  , 

square  of  the  current  in  the  wave  an  external  shunt  connection  to  be 
meter  circuit.  made  across  the  variable  condenser, 

decreasing  the  accuracy  of  the  instru- 
ment, as  has  already  been  discussed  for  the  similar  circuit  using  phones. 
The  galvanometer  indications  will  be  proportional  to  the  mean  current 
(or  d.c.  component)  flowing  through  it.  For  large  a.c.  voltages  the  cur- 
rents may  be  proportional  to  the  voltage,  while  they  are  proportional 
to  higher  powers  of  the  voltage  at  very  low  voltages,  in  fact,  proportional 
to  the  square  of  the  voltage  when  it  is 
sufficiently  low.  This  is  indicated  by 
the  curves  in  Fig.  60,  page  347. 

e.  Neon    Tube. — This   indicator    de- 
pends on  the  luminous  effect  which  oc- 
curs,whentheelectricpotentialimpressed 

on  a  gas  at  low  pressure  is  increased  to  a  FIG.  8.— When  the  wave-meter  is  used 


in  testing  a  high-powered  circuit  and 
a  resonance  indicator  (as  contrasted 
to  a  measuring  device)  only  is  re- 
quired, a  small  glass  tube  filled  with  a 
rarefiedgas,  such  as  neon,  isapplicable. 


value  where  cumulative  ionization  (by 
impact)  occurs.  The  connections  of 
the  tube  are  indicated  in  Fig.  8. 

As     the     wave-meter    circuit     ap- 
proaches resonance,  the  drop  across  the 

condenser  and  tube  increases,  and  at  resonance  become  a  maximum,  under 
which  condition  the  tube  glows  at  maximum  brilliancy.  This  scheme  is 
simple  and  determinations  are  quickly  and  easily  made.  The  accuracy 
obtainable,  however,  is  not  so  good  as  with  the  previous  circuits,  as  it  is 
difficult  to  judge  exactly  the  point  of  maximum  brightness,  especially  if 


RESONANCE  INDICATORS  791 

small  powers  are  involved,  in  which  case  close  coupling  may  be  required 
to  cause  the  tube  to  glow,  still  further  decreasing  the  accuracy  of  the 
measurement.  Actually  this  scheme  is  good  only  for  testing  on  high- 
power  sets;  a  buzzer-excited  circuit  would  not  produce  sufficient  current 
in  the  wave-meter  to  make  the  tube  glow,  no  matter  how  tight  the  coupling. 

/.  Incandescent  Lamp. — This  device,  in  its  manner  of  indicating  reso- 
nance, is  similar  to  the  neon  tube  discussed  above.  It  is,  however,  con- 
nected directly  in  series  in  the  wave-meter  circuit,  as  indicated  in  the 
diagram  of  connections  (Fig.  9).  The  lamp  is  a  low  voltage  lamp  (2- 

or  4-volt  battery  lamp)  and  is   usually  con-  r  

nected  into  the  circuit  by  means  of  an  ordinary 
small  lamp  socket,  which  is  short-circuited 
when  the  lamp  is  not  in  use. 

This  scheme  possesses  the  same  advantages  .    , 

and  disadvantages   which  were  mentioned  in 


connection  with  the  neon  tube.     It  also  pos-  pIG  9 jn  some  wave-metcrs 

sesses  the  disadvantages  of  inserting  a  con-  a  small,  low  resistance,  in- 
siderable  additional  resistance  in  the  wave-  candescent  lamp  has  been 
meter  circuit,  while  the  neon  tube  arrangement  used  as  resonance  indicator, 
has  the  disadvantage  of  connecting  a  leakage 

of  uncertain  value  across  the  wave-meter  condenser,  as  discussed  before 
in  connection  with  previous  circuits.  The  effect  of  the  parallel  connec- 
tion of  the  neon  tube  is  of  course  to  raise  the  effective  series  resistance 
of  the  wave-meter  circuit  somewhat,  the  amount  of  increase  depending 
upon  the  intensity  of  glow  in  the  tube.  There  is  little  to  choose  between 
the  lamp  and  tube. 

Classification  of  Resonance  Indicators. — The  above  schemes  for  indi- 
cating resonance  of  the  wave-meter  circuit  may  be  classified  as  to  whether 
the  results  obtained  are  quantitative  or  qualitative,  and  the  power  of  the 
circuit  to  which  the  wave-meter  is  coupled.  Those  schemes  which  permit 
a  curve  of  high-frequency  current  (or  indication  proportional  thereto)  to 
be  plotted  against  the  wave-length  readings  on  the  wave -meter  condenser, 
are  considered  as  quantitative,  while  those  which  permit  only  the  resonant 
wave-length  adjustment  to  be  obtained,  are  considered  qualitative. 

Those  schemes  which  indicate  visibly  are,  in  general,  in  the  quantitative 
class.  The  neon  tube  and  incandescent  lamp  are  exceptions  to  this  rule, 
and  are  in  the  qualitative  class.  The  hot-wire  ammeter,  the  thermo- 
couple and  d.c.  galvanometer,  and  crystal  and  galvanometer,  are  arrange- 
ments which  will  give  quantitative  results.  Audible  schemes  are  usually 
qualitative,  as  illustrated  by  the  crystal  and  phones.  It  should  be  noted 
that  this  device  may  be  made  quantitative  by  shunting  the  phones  with 
a  variable  resistance,  as  in  the  audibility  meter,  but  the  results  obtained 
are  not  accurate.  It  is  also  possible  to  obtain  quantitative  measurements 


792 


WAVE-METERS  AND  THEIR  USE 


[CHAP.  X 


by  varying  the  coupling  between  the  wave-meter  and  exciting  circuit,  so 
as  to  keep  the  note  heard  in  the  phones  at  a  fixed  loudness  as  the  wave- 
meter  condenser  is  varied.  This  method  is  also  inaccurate  and  is  seldom 
used. 

The  hot-wire  ammeter,  thermo-couple  and  galvanometer,  neon  tube 
and  incandescent  lamp  are  employed  where  the  current  in  the  exciting 
circuit  is  of  considerable  magnitude,  as  in  the  case  of  a  transmitting  set. 
For  measurements  of  low  power  circuits,  i.e.,  receiving  circuits,  the  detector 
and  phone  arrangement  is  the  most  important,  and  is  used  exclusively 
when  quantitative  results  are  not  required.  The  detector  and  sensitive 
galvanometer  are  used  when  quantitative  data  are  to  be  obtained. 

Use  of  Special  Condenser  to  Make  Wave-meter  Scale  Uniform.— 
Since, 

Ameters  =  Io85 

the  subscripts  indicating  micro  units,  where  L  is  usually  fixed  in  value 
(or  variable  in  fixed  steps  only)  this  equation  may  be  re-written  as  follows : 


Xm 


or 


FIG.   10. — With    circular    plates    the 
capacity  of  the  condenser  is  nearly 


=  1885  VaC, 

=  K  Vc,  where  K  =  1885  Va. 

In  the  usual  type  of  variable 
condenser  the  movable  element  con- 
sists of  semicircular  plates  which 
may  be  rotated,  so  that  more  or 
less  of  their  area  intersects  the  area 
of  the  fixed  element,  as  shown  in 
Fig.  10. 

Since  the  capacity  is  propor- 
tional to  the  amount  of  superim- 
posed areas,  which  in  turn  varies 
directly  with  the  angle  of  rotation, 


proportional  to  the  angle  through      tne  capacity  varies  with  the  angle   of 
which  the  movable  plates  are  rotated.      rotation,  i.e., 


c=ke, 


and  since 
it  follows 


(i) 


Thus  if  the  condenser  scale  were  graduated  to  read  directly  in  wave- 
lengths instead  of  the  capacity  value,  such  scale  would  be  crowded  at  the 
smaller  wave-lengths  and  opened  up  at  the  higher  values,  which  would 
tend  to  make  the  readings  difficult  and  increasingly  inaccurate  at  the 


SCALE  GRADUATION  OF  WAVE-METER 


793 


Capacity 

/*/*/ 

2000 


1000 
800     1000 


uneconomi- 
space    and 


400 

200 


500 


Kl/C- 


o° 


3(T 


90 


120 = 


150° 


18(T 


lower  wave-length  values.     These  conditions  are  graphically  illustrated 
in  Fig.  11. 

The  wave-length  curve  indicates  the  rapid  variation  of  wave-length 
with  capacity  (C)  at 
the  smaller  capacity 
values    (necessitat- 
inga  crowded  scale),    Meters 
and  the  very  grad-     120°    150° 
ual  change    at  the 
larger    values    (ne- 
cessitating an  open 
scale) .     This  varia- 
tion is 
cal    of 

undesirable  because 
of  the  probable  error 
it  may  introduce. 

It  may  be  desir- 
able to  design  the 
shape  of  the  mova- 
ble condenser  element  so  that  the  wave-length    shall  vary  directly  with 
the  angle  of  rotation,  i.e., 

\=ke, 

and  the  wave-length  scale  be  uniform  throughout  its  length.  The  required 
form  of  the  moving  condenser  plates  to  produce  this  relationship  may  be 
readily  derived  as  follows: 

Since 


or, 


FIG.  11. — A  condenser  such  as  that  pictured  in  Fig.  10  will,  if 
used  in  a  wave-meter,  give  a  wave-length  calibration  scale 
crowded  at  the  shorter  wave-lengths  and  opening  out  at  the 
longer  wave-lengths. 


VC=K'8  where  Kr  =-|, 


C=a02  where  a - 


The  capacity  is  also  proportional  to  the  area  intersected  by  the  movable 
and  fixed  elements ;  this  area  is  expressed  by : 

A  =  2  I  r2d6  (in  polar  coordinates).       .     .     (2) 

Now  since 

C=K"A=ad2, 
we  have, 

A  =  -  =hfl2  (3) 


794 
where 


WAVE-METERS  AND  THEIR  USE 


[CHAP.    X 


Differentiating  expressions  (2)  and 
(3)  with  respect  to  6  and  equating, 
we  obtain 


or, 
and 


ie     2 
r2=460. 


.      .     (4) 


Fig.  12  illustrates  the  form  of  the 
movable  plates  when  designed  accord- 
FIG.  12.— By  suitably  forming  the  rotat-  ing  to  thig  expression>  the  fixed    ele- 

ing  plates  and  locating  the  shaft  eccen-  ,   ,     .  n  ,  .   .        , 

tricallythe  capacity  of  the  condenser  ment  being  usually  made  semicircular 

may  be  made  to  vary  as  the  square  of  for  convenience. 

the  angle  of  rotation.  It  will  be  seen  from  the  figure  that 

the    capacity    variation    per   degree 

rotation  is  relatively  small  at  the  smaller  values  of  capacity,  thus  tending 
to  spread  the  wave-length  scale.  At  the  higher  values  of  capacity,  the 
capacity  variation  per 
degree  rotation,  is 
large,  and  tends  to 
make  the  scale  close 
up.  Actually,  the  ca- 
pacity varies  as  the 
square  of  the  deflec- 
tion and  the  wave- 
length scale  is  uniform 
over  the  entire  range. 
These  conditions  are 
indicated  in  Fig.  13. 

To  provide  clear- 
ance for  the   shaft  of 


2000 


1200  tlSOO 
1000  § 

f<  O 

£    800  a  1000 
I    600° 


400 
2CO 


500 


/ 

c 

/ 

/ 

^ 

X=K 

^^ 

£ 

•""' 

1 

^ 

^ 

/ 

^^ 

^ 

Vo 

^* 

^ 

&*•**"* 

^/. 

'^~ 

-— 

'" 

^ 

-^ 

^,- 

-  — 

** 

•^ 

^ 

—  "^ 

,  —  - 

"" 

0°          30°         60°         90°        120°       150°       180° 
FIG.  13. — With  a  condenser  of  the  form  shown  in  Fig.  12, 
the  capacity  varying  as  the  square  of  the  angle  of  rota- 
tion, the  wave-length  calibration  scale  is  uniform. 
this  moving-plate  sys- 
tem a  circular  area  must  be  cut  from  the  fixed  plates.     If  this  is  to  be 
taken  into  account,  the  equation  of  the  boundary  curve  of  the  movable 
plates  must  be  corrected    as  follows  (assuming    the    radius  of    circular 
area  cut  from  stationary  plates  equal  to  r2) : 


A==; 


AUTOPYM:  WAVE-METER 


795 


then 


or 

r  =  V4b6+r22 (5) 

This  is  the  form  of  condenser  used  in  modern  wave-meters,  having 
practically  superseded  the  semicir- 
cular form,  due  to  its  greater  con- 
venience and  accuracy  of  reading. 

A  simpler  form,  utilizing  rect- 
angular plates,  but  not  having 
commercial  application,  due  to 
space  requirements,  is  shown  in 

FIG.  14. — A  simple  form  of  condenser  in  which 

It  is  readily  seen  that  the   in-       the  capacity  varies  as  the  square  of  the 
tersected    area    of    the    fixed    and       setting  of  the  movable  plates, 
movable  elements    (and    thus  the 

capacity)  varies  as  the  square  of  the  distance  of  movement.  Thus  the 
wave-length  scale,  placed  as  shown,  would  have  a  uniform  marking, 
— r  as  in  the  case  of  the  rotating 

plate  condenser  previously  de- 
scribed. 

Autodyne  Wave-meter. — It 
has  been  previously  shown,  in 
the  description  of  the  "  beat  " 
method  of  receiving  undamped 
waves  (see  page  514),  that  the 
beat  frequency  reduces  to  zero 
when  the  incoming  and  local 
high-frequencies  are  made  equal. 
Therefore  if  the  local  high  fre- 
FIG.  15.— If  an  oscillating  tub(Tcircuit  (calibrat-  quency  is  known,  the  incoming 
ed  for  frequency  or  wave-length  of  the  closed  frequency  is  at  once  determined, 
oscillating  circuit)  is  available  it  may  be  used  This  principle  is  utilized  in  the 
as  a  autodyne  wave-meter;  when  the  beat  so.caned  autodyne  wave-meter 
note  (heard  in  the  phones)  is  reduced  to  zero,  .,,  ,  .  ^.  1  _ 

the  unknown  wave-length  is  the  same  as  that  L 

given  by  the   calibration   curve  of  the  oscil-          The    wave-meter     must    be 
lating  tube.  completely  calibrated  by  means 

of  known  high  frequencies,  and 

this  calibration  must  be  frequently  checked  as  the  constants  of  the  tube 
change  with  time.     It  will  be  noted  that  the  capacity  of  the  tube  from 


!  Circuit  in  which  oscillations 
3f  unknown  wavelength 
xre  flowing:. 


796  WAVE-METERS  AND   THEIR  USE  [CHAP.  X 

grid  to  ground  (assuming  Ca  omitted)  is  in  parallel  with  C,  and  this 
capacity  will  therefore  effect  the  wave-length  of  the  local  oscillations. 
It  has  been  shown  (see  page,  432)  that 

l^grld  to  ground  ~ (-'grid  to  filament   I    VM   '    -U' 'grid  to  plate  ' 

also  that  ju  is  changed  somewhat  when  the  filament  current  or  plate  voltage 
is  changed.  Indirectly,  therefore,  a  change  in  filament  current  or  plate 
voltage  causes  a  change  in  the  frequency  (or  wave-length)  of  the  oscilla- 
tions. 

To  limit  this  change  of  frequency  with  filament  current  or  plate  voltage 
the  grid  condenser  Cff  is  inserted  in  the  circuit.  Cff  being  small  com- 
pared to  Cg-g  (the  capacity  from  grid  to  ground),  and  fixed  in  value,  the 
capacity  in  shunt  across  C  is  practically  constant.  The  total  capacity 
of  the  oscillating  circuit  is  thus  made  more  nearly  independent  of  Cg-g, 
and  the  generated  frequency  thus  also  made  constant  and  independent 
of  variations  in  filament  current  or  plate  voltage.  It  is  also  desirable  that 
the  moving  element  of  condenser  C  should  be  on  the  ground  side.  (See 
page  635.) 

If  this  wave-meter  is  used  to  measure  the  frequency  of  an  oscillating 
tube  generator,  producing  upper  harmonics  in  addition  to  its  fundamental, 
there  exists  the  possibility  of  an  upper  harmonic  frequency,  instead  of 
the  fundamental  frequency,  being  measured.  This  should  be  avoided 
by  making  careful  determinations  over  the  entire  range  of  possible  values, 
particularly  at  the  low  wave-lengths.  The  note  obtained  when  the  wave- 
meter  is  set  to  the  fundamental  is  much  stronger  than  that  obtained  with 
the  upper  harmonics,  which  are  relatively  weak.  In  fact,  they  are  so  weak 
that  this  error  can  only  be  made  when  the  wave-meter  is  close  to  the 
source  of  power.  At  greater  distances,  only  the  fundamental  will  have 
sufficient  power  to  give  an  audible  note  in  the  wave-meter  phones. 

Actual  Method  for  Measuring  the  Wave-length  of  a  Transmitting 
Set. — The  set  is  first  carefully  adjusted  as  for  normal  operation  and  the 
wave-meter  then  very  loosely  coupled  to  the  antenna  circuit.  It  is  very 
important  that  the  meter  be  coupled  to  a  portion  of  the  antenna  circuit, 
where  the  fluxes  set  up  are  truly  representative  of  the  high-frequency 
current  flowing.  As  has  already  been  mentioned  in  Chapter  V,  page 
330,  the  complex  resultant  flux  which  links  the  oscillation  transformer 
does  not  fulfill  this  requirement  and  the  wave-meter  is  therefore  always 
coupled  to  a  portion  of  the  circuit  remote  from  the  oscillation  transformer. 
It  may  be  coupled  to  the  loading  inductance  if  this  is  connected  in  the 
circuit.  It  is  customary,  however,  since  this  loading  inductance  may 
not  be  in  service,  to  insert  in  the  circuit  a  small  inductance  of  one  or  two 
turns  only,  to  which  the  wave-meter  may  be  conveniently  coupled.  This 
coil  has  an  inductance  which  is  negligible  in  value  compared  to  the  total 


WAVE-LENGTH  DETERMINATION 


797 


inductance  of  the  circuit,  and  hence  will  not  appreciably  affect  the  char- 
acteristics of  the  set.  This  coil  may  be  arranged  for  mounting  directly 
on  the  wave-meter,  one  terminal  being  connected  to  ground,  while  the 
other  is  connected  to  the  antenna  through  the  oscillation  transformer. 

The  coupling  between  the  small  inserted  inductance,  called  a  search 
coil,  and  the  wave-meter  itself,  must  always  be  as  loose  as  possible  and 
yet  permit  definite  indications  to  be  obtained.  This  is  so  that  the  current 
in  the  wave-meter  may  not  produce  an  appreciable  reaction  back  on  the 
circuit  whose  wave-length  is  being  measured,  which  would  cause  its  own 
indications  to  be  in  error.  This  is  similar  to  the  case  of  instruments  which 
are  used  to  measure  pressure:  a  voltmeter  must  draw  so  little  current 
as  to  alter  inappreciably  the  electrical  pressure  at  the  points  to  which 
it  is  connected,  or  a  gauge,  inserted  in  a  gas  tank,  must  not  have  so  much 


Closed 
Circuit 

of 

Spark 
Transmitter 


Search 
Coil 


Link  Coils 


FIG.  16. — In  measuring  the  wave-length  of  a  transmitting  set,  a  search  coil  (gene'ally 
one  turn)  is  inserted  in  the  base  of  the  antenna,  and  the  wave  meter  coupled  very 
loosely,  to  the  search  coil.  The  Marconi  Co.  has  used  an  additional  "link"  circuit 
to  permit  easy  adjustment  of  coupling. 

space  within  itself,  as  to  decrease  materially  the  pressure  of  the  gas  which 
it  is  supposed  to  measure. 

The  simplest  manner  of  varying  the  coupling  is  to  vary  the  distance 
between  the  wave-meter  and  the  search  coil.  An  intermediate  circuit 
whose  coupling  to  the  wave-meter  and  search  coil  may  be  conveniently 
varied  is  also  largely  employed.  This  arrangement  is  shown  in  Fig.  16, 
and  is  used  by  the  Marconi  Company  in  their  station  type  wave-meter. 

It  is  very  important  that  very  loose  coupling  be  employed  when  making 
the  initial  adjustment  of  the  wave-meter,  as  otherwise  the  delicate  hot- 
wire ammeter  may  be  burned  out  when  the  resonant  adjustment  is  attained. 
The  coupling  may  easily  be  increased  when  it  is  found  that  the  value  used 
gives  deflections  which  are  too  small  for  accuracy.  The  best  adjustment 
is  that  which  results  in  definite,  readable  indication  with  minimum  coupling. 

When  the  preliminary  adjusting  of  the  wave-meter  indicates  this  con- 
dition, the  adjustment  of  the  set  should  be  carefully  repeated,  and  wave- 


798  WAVE-METERS  AND  THEIR  USE  [CHAP.  X 

length  readings  taken  at  each  position  of  maximum  current.  If  the  coupling 
between  the  antenna  and  closed  circuits  is  small,  but  one  such  point  will 
be  obtained,  indicating  that  the  energy  is  concentrated  more  or  less  into 
the  one  wave-length.  If  the  coupling  were  increased,  two  such  points 
would  be  obtained,  the  corresponding  wave-length  readings  indicating 
the  length  of  the  "  coupling  waves  "  which  now  exist  simultaneously  in 
the  circuits.  Where  a  partial  quenching  action  is  obtained,  three  such 
points  may  appear,  the  corresponding  wave-length  readings  representing 
the  fundamental  wave-length,  at  which  most  energy  is  radiated,  after 
the  quenching  action  has  occurred,  and  the  two  coupling  waves,  at  which 
most  energy  is  radiated  before  the  quenching  action  takes  place. 

The  above  covers  specifically  a  spark  transmitter,  but  the  procedure 
with  an  undamped  wave  set  is  exactly  similar.  In  this  case  only  one 
point  of  maximum  current  will  be  obtained,  and  this  point  will  be  very 
sharp  and  clearly  defined,  as  the  energy  is  radiated  at  one  wave-length 
only  (neglecting  upper  harmonics),  which  is  fixed  by  the  speed  of  the 
generator  (Alexanderson,  Goldschmidt),  or  the  circuit  constants  (Poulsen 
arc  and  vacuum  tube). 

If,  however,  the  wave-meter  be  coupled  too  tightly  to  a  low-powered 
circuit  of  the  latter  type,  e.g.,  an  oscillating-tube  generator,  the  reaction 
of  the  wave-meter  circuit  current  on  the  tube  circuit  will  cause  the  fre- 
quency of  the  tube  circuit  to  change.  It  may  raise  or  lower  the  frequency 
of  the  tube  circuit,  depending  upon  its  setting.  This  condition  is  evidently 
undesirable,  and  the  coupling  should  be  reduced  until  the  reaction  of  the 
wave-meter  on  the  tube  circuit  becomes  negligible.  If  the  hot-wire 
ammeter  is  not  sufficiently  sensitive  to  indicate  accurately  under  this 
condition,  it  should  be  replaced  by  one  of  the  more  sensitive  type  of  visible 
indicators,  e.g.,  thermo-couple  and  galvanometer. 

The  antenna  ammeter  may  also  be  used  as  the  wave-meter  indicating 
device  when  measuring  the  wave-lengths  of  a  tube  set.  Thus  assuming 
the  connections  shown  in  Fig.  16  (spark  transmitter  replaced  with  a 
tube  generator),  as  the  wave-meter  adjustment  reaches  the  resonant  value 
the  wave-meter  current  increases  suddenly  (although  this  increase  may 
be  too  small  to  deflect  the  wave-meter  hot-wire  ammeter),  and  the  losses 
in  the  wave-meter  become  a  maximum.  Since  these  losses  are  supplied 
from  the  antenna,  this  amounts  to  a  sudden  increase  in  the  antenna  resist- 
ance, and  the  antenna  current  will  therefore  suddenly  decrease,  this 
decrease  being  indicated  by  the  antenna  ammeter.  Thus,  this  dip  in 
antenna  current  is  an  indication  that  the  wave-meter  is  in  resonant  adjust- 
ment and  the  wave-length  of  the  set  is  therefore  determined. 

Energy  Distribution  of  a  Set  from  a  Wave-meter. — In  addition  to 
determining  the  wave-length  of  the  set,  i.e.,  the  wave-length  at  which 
maximum  energy  is  radiated ?  the  wave-meter  may  also  be  used  to  deter- 


DETERMINATION  OF  ENERGY  DISTRIBUTION 


799 


mine  the  distribution  of  all  the  energy  radiated  by  the  set.  The  procedure 
is  exactly  similar  to  the  foregoing,  with  the  exception  that  instead  of 
noting  only  the  wave-length  readings  at  points  of  maximum  current, 
readings  are  taken,  at  a  number  of  condenser  settings,  of  both  the  wave- 
length and  the  wave-meter  current  or  "  current  squared  "  if  the  liot -wire 
ammeter  scale  has  been  calibrated  in  this  way. 

Referring  to  Fig.  16,  as  the  variable  condenser  is  adjusted  to  the  several 
wave-lengths  in  succession,  the  current  in  the  ammeter  will  successively 
increase  as  the  resonant  adjustment  is  approached,  and  then  decrease  as 


500 


550  600  650 

Wave  Length  in  Meters 


700 


FIG.  17.- — Energy  distribution  curves  of  a  spark  transmitter,  with  three  different  coup- 
ling values  used  in  the  oscillation  transformer. 

the  adjustment  again  departs  farther  and  farther  from  that  of  resonance. 
If  the  coupling  M  between  the  antenna  and  closed  circuits  is  loose  the 
curve  plotted  between  the  ammeter  and  condenser  scale  (A)  readings  will 
have  the  form  shown  in  Fig.  17  (A)1. 

As  the  coupling  M  is  tightened,  the  energy  radiated  at  Xo,  the  wave- 
length for  which  the  set  has  been  adjusted  increases,  as  shown  in  curve 
B,  but  further  increase  of  coupling  causes  the  formation  of  the  coupling 
waves  and  a  spreading  of  the  energy  as  shown  in  curve  C.  These  curves 

1  These  curves  are  the  same  as  those  shown  in  Fig.  46,  p.  332,  and  are  here  repro- 
duced for  convenience. 


800  WAVE-METERS   AND   THEIR   USE  [CHAP.  X 

have  already  been  briefly  discussed  in  Chapter  V  (see  page  326),  and  are 
called  the  "  energy-distribution  "  curves,  since  they  show  the  amount 
of  energy  radiated  at  the  different  wave-lengths. 

Significance  of  Energy  Distribution  Curve. — Considering  the  wave- 
meter  simply  as  a  calibrated  receiving  circuit  having  a  very  small  decre- 
ment, the  curves  indicate  proportionately  the  amount  of  energy  which 
would  be  received  (and  therefore  the  strength  of  signal),  by  each  one  of 
a  number  of  such  receiving  circuits  assumed  equidistant  from  the  trans- 
mitting station,  and  each  tuned  to  a  different  wave-length.  Thus,  that 
circuit  which  is  tuned  to  Xo  (assuming  M  to  be  loose  or  medium  coupling) 
would  receive  a  maximum  amount  of  energy  and  the  strongest  signal. 
This  would  be  the  station  for  which  the  signal  is  intended.  The  other 
receiving  stations  would  also  receive  some  energy;  this  energy  would 
decrease,  as  the  adjustment  from  Xo  becomes  greater  and  greater,  and 
signals  so  received,  represent  interference  to  the  receiving  station.  If 
we  consider  /o2  as  the  energy  required  for  audibility  at  the  several  stations, 
then  Xi  to  X2  represents  the  range  of  tuning  over  which  interference  will 
occur  if  the  transmitter  coupling  M  is  loose.  Similarly,  X'i  to  X'2,  and 
X"i  to  X"2  represent  the  range  of  wave-lengths  over  which  interference 
occurs  as  the  coupling  is  tightened.  It  is  therefore  evident  that  tight 
coupling  should  be  avoided  except  under  emergency  conditions  (SOS  call), 
so  that  interference  to  other  receiving  stations,  which  may  be  tuned  to 
wave-lengths  in  the  neighborhood  of  Xo,  t^e  minimized. 

It  should  be  kept  clearly  in  mind  that  the  set  is  radiating  energy  at 
all  the  different  wave-lengths,  and  each  receiving  station  is  in  tune  with 
the  energy  which  is  causing  the  signal  to  be  heard.  That  is,  each  receiving 
circuit  picks  out  its  own  particular  wave-length  to  which  it  is  tuned, 
and  its  received  signal  is  proportional  to  the  amount  of  energy  which  the 
transmitter  is  sending  out  at  that  wave-length. 

Wave-meter  Coupling. — When  determining  the  energy  distribution 
curves  for  the  set,  the  coupling  between  the  wave-meter  and  search  coil 
should  first  be  adjusted  so  that  a  full  scale  deflection  is  obtained  on  the 
hot-wire  ammeter  when  the  resonant  condition  is  obtained  with  the  trans- 
mitter coupling  (M,  Fig.  16)  adjusted  to  its  proper  value.  This  coupling 
between  the  wave-meter  and  search  coil  should  remain  undisturbed 
throughout  the  determination  of  the  several  energy  distribution  curves. 
The  curves  obtained  will  thus  have  maximum  permissible  ordinate  values, 
making  any  error  in  their  determination  a  minimum,  and  the  energy 
radiation  under  the  different  coupling  adjustments  will  be  comparative 
in  a  quantitative  as  well  as  a  qualitative  sense. 

Energy  Distribution  for  Undamped  Wave-transmitter. — For  an 
undamped  wave-transmitter,  the  energy  is  all  radiated  at  the  fundamental 
wave-length,  neglecting  the  small  amount  radiated  by  the  upper  harmonics, 


DETERMINATION  OF  ENERGY  DISTRIBUTION 


801 


which  are  relatively  weak.  If  the  wave-meter  circuit  had  zero  decre- 
ment, that  is,  no  resistance,  the  signal  would  be  received  by  that  wave- 
meter  only,  which  is  tuned  to  Xo.  The  energy  distribution  curve  in  this 
ideal  case  would  be  a  straight  line  ordinate  at  X0  (Fig.  18). 

Since  the  wave  meter  always  possesses  a  decrement,  however  small, 
the  distribution  curve  will  appear  as  shown  by  the  curve  A,  Fig.  18. 
The  greatly  decreased  interference  is  indicated  by  the  small  difference 
between  Xi  and  X2.  Assuming  receiving  circuits  with  a  decrement  equal 
to  that  of  the  wave-meter,  only  those  tuned  within  this  range  would  receive 
interference,  while  the  set  for  which  the  signal  is  intended  receives  a  stronger 


.12 


MO 


..06 


1.04 


.02 


X2 


500 


550 


700 


600  650 

Wave  Length  in  Meters 

FIG.  18. — The  energy  distribution  curve  obtained  from  an  undamped  wave  trans- 
mitter is  very  narrow,  being  determined  entirely  by  the  decrement  of  the  wave-meter 
itself;  if  the  wave-meter  had  zero  decrement  the  energy  distribution  curve  obtained 
would  be  a  straight  vertical  line. 

signal,  due  to  all  the  energy  being  radiated  by  the  transmitter  at  the  wave- 
length (Xo)  for  which  the  wave-meter  is  tuned.  The  greater  selectivity 
and  efficiency  of  the  undamped  wave-set,  as  indicated  by  the  above 
characteristics,  are  rapidly  causing  its  increasing  use  in  the  art,  and  it 
may  eventually  supersede  the  damped  wave-set  altogether. 

Determination  of  Decrement  of  a  Spark  Transmitter  from  Energy 
Distribution  Curve  and  Known  Decrement  of  the  Wave-meter. — If  we 
consider  a  wave- meter  circuit  coupled  loosely  to  an  undamped  wave- 
generator  as  shown  in  Fig.  19,  then,  when  the  wave-meter  circuit  is  tuned 

to  resonance,  its  reactance  (Lo>  —  -^—  j  is  equal  to  zero  and  the  current 
is  limited  only  by  the  resistance  in  the  circuit,  or 


802 


WAVE-METERS  AND  THEIR  USE 


[CHAP.  X 


where  E  is  the  voltage  induced  in  the  wave-meter  circuit.  Now,  if  the 
condenser  adjustment  be  altered  from  its  resonant  value  CT}  the  react- 
ance in  the  circuit  is  no  longer  equal  to  zero,  that  is, 


High  Frequency 
Alternator 


FIG.  19. — Connection  of  wave-meter  to  a  source  of  continuous  waves  for  determination 
of  the  decrement  of  the  wave-meter  itself.  Conditions  must  be  so  adjusted  that  as 
the  wave-meter  setting  is  changed  the  current  in  the  power  circuit  shows  no  change. 

Since  Leo  =  ~ — ,  this  reactance  may  be  expressed  as, 


\          n 

j-co     Ceo 


and  the  current  is 
7  = 


E 


E 


It  may  be  shown1  that  the  decrement  is  expressed  by, 


or, 


Crco~  5  ' 


•     •     (6) 


T-> 

From  Formula  (20),  page  214,  we  have  5= — , 

2/L 


since 


{  =  — 

3        ' 


also 


=  -—-,  therefore  5  =irRCru 
cot  V 


DETERMINATION  OF  DECREMENT  803 

Substituting  this  expression  in  the  above  expression  for  current,  we 
have 


and 

E2 

P2_|_ 

I2  R2  * 


P  b*  R2 


\     C 
Solving  this  expression,  we  obtain 

f* 

5=- 


C 


The  value  of  6  so  obtained  is  the  decrement  of  the  wave-meter  itself. 
This  will  be  referred  to  again  later  in  the  discussion  of  wave-meter  decre- 
ment and  its  measurement. 

For  an  exciting  source,  the  oscillations  of  which  are  damped,  e.g.,  a 
spark  transmitter,  it  has  been  shown  l  that  a  derivation  such  as  that 
given  above  yields  an  expression  which  gives  the  sum  of  the  decrements 
of  the  impressed  voltage  and  of  the  wave-meter  itself;  that  is,  we  have 


where  di=the   decrement   of   the   circuit    under 

measurement; 
62  =  the  decrement  of  the  wave-meter  cir- 

cuit. 
This  formula  is  sufficiently  accurate  for  all  practical  purposes,  if 

1.  5i-f  52  is  small  compared  to  2?r. 

C  —C 

2.  —  ^  —  is  small  compared  to  unity. 

0 

3.  If  the  wave-meter  is  loosely  coupled  to  the  wave-meter  circuit. 
The  procedure  for  determining  5i,  assuming  62  known,  may  be  out- 

lined as  follows  : 

1  An  energy  distribution  curve  is  obtained  as  shown  in  Fig.  20. 
(Coupling  between  the  closed  circuit  and  the  antenna  circuit  of  the  trans- 
mitting set  assumed  to  be  loose.) 

2.  The  value  of  Cr  is  then  determined  from  this  curve.     The  value  of 

1  See  Chapter  IV,  page  272. 


804  WAVE-METERS  AND   THEIR  USE  [CHAP.  X 


C  is  preferably  obtained  for  that  point  of  the  curve  where  72>=-^-,  since 
then 


and  the  calculation  becomes  simpler. 

3.  Knowing  CT  and  Ci,  as  obtained  from  the  curve,  and  substituting 
in  the  equation 


(8a) 


the  value  of  61  +  62  is  readily  obtained,  from  which  the  known  decrement 
62  of  the  wave-meter  is  subtracted  to  determine  the  unknown  decrement. 

It  is  evident  that  two  values  of  capacity,  one  greater  and  one  less  than 

72 
the  resonant  value,  will  cause  I2  to  become  equal  to  — ,  as  indicated  in 

Fig.  20.     Therefore,  the  following  expression  may  also  be  used: 

r£j-2 (8*0 

Since  the  energy  distribution  curve  is  never  quite  symmetrical,  the 
value  of  61  as  determined  by  the  two  expressions  using  C\  or  €2,  will  be 
slightly  different.  It  is  therefore  desirable  to  average  the  results  directly, 
using  the  expression 

(9) 


This  expression  does  not  involve  a 
measurement  of  Cr,  which  is  usually 
more  difficult  to  determine  accurately, 
due  to  the  resonance  curve  being  flat  at 
that  point,  than  either  €2  or  Ci,  which 
are  read  at  a  point  where  I2  is  varying 
rapidly  with  capacity.  This  expression 
is  therefore  usually  employed  in  prefer- 
ence to  those  involving  Cr.  (Equations 
(8),  (8a),  and  (86).) 

io.  20.— In  getting  decrement  from  A»  an  illustration,  referring  to  Fig. 
the  energy  distribution  curve  the  20,  assume  that  the  coupling  between 
values  of  capacity  are  determined  the  wave-meter  and  the  search  coil  has 
for  those  two  points  (above  and  been  adjusted>  so  the  wave-meter  am- 
below  resonance)  which  reduce  the  ,  A  ~  ,  T  9,  r^i 

,   ,,  meter  reads  .40  (7r2)  at  resonance.     The 
wave-meter    (current)2  to  one-half 

its  maximum  value  as  well  as  the  capacity  is  then  decreased  until  the  am- 
capacity  required  for  resonance.  meter  reads  .20  (I2)  and  the  value  of  C\ 


DETERMINATION  OF  DECREMENT 


805 


noted  as  96.0.  It  is  immaterial  what  units  the  condenser  scale  reads  — 
whether  actual  capacity  or  simply  degrees  rotation,1  if  the  ordinary  semi- 
circular plate  condenser  is  used,  as  has  been  assumed  in  this  problem. 

The  condenser  value  is  then  increased  through  the  resonant  value 
to  Co,  at  which  point  the  ammeter  again  reads  I2  =  .20  and  €2  is  noted 
as  104. 

Substituting  in  Eq.  (9)  we  have, 

104-96.0    7rX8 

=         -=.  125 


Assuming  62  =  .040  (this  may  be  obtained  from  the   calibration   curves 
of  the  instrument  or  determined  as  described  below), 
we  obtain  5i  =  .085. 

If  the  scale  is  graduated  in  wave-lengths  and  wave-length  values  are 
ead,  the  following  expression  should  be  used, 


(10) 


since  \  =  K.Vc  and  \2=K'C. 


.20 


- 


-08 


.04 


500 


550 


C50 


700 


600 
Wave-Length  in  Meters 

FIG.  21. — If  the  coupling  of  the  oscillation  transformer  is  too  tight  a  double-humped 
resonance  curve  is  obtained  from  the  wave-meter  reading;  the  resonance  curve  for 
each  of  the  component  frequencies  of  the  curves  may  be  obtained  by  the  scheme 
shown  in  Fig.  22. 

If  the  coupling  of  the  set  is  increased  to  some  considerably  higher  value, 
a  double-peaked  energy  distribution  curve  is  obtained,  due  to  the  separate 
points  of  resonance  for  the  two  coupling  waves.  If  this  curve  has  well 

1  This  statement  assumes  that  the  condenser  capacity  is  zero  at  zero  scale  setting. 
In  case  the  amount  of  capacity  with  zero  setting  is  appreciable,  compared  to  the  actual 
capacity  used,  a  suitable  correction  must  be  made,  if  the  setting  of  the  condenser,  instead 
of  actual  capacity,  is  used  in  the  calculation. 


806 


WAVE-METERS  AND  THEIR  USE 


[CHAP.  X 


separated  peaks,  as  shown  in  Fig.  17,  curve  C,  the  decrement  of  each 
oscillation  may  be  determined  from  the  two  peaks  by  the  method  outlined 
above  for  the  one-peaked  curve.  The  curve  may,  however,  have  the 
appearance  illustrated  in  Fig.  21,  in  which  case  this  procedure  cannot  be 
followed,  since  both  oscillations  are  simultaneously  effective  in  the  wave- 
meter. 

The  decrement  of  each  oscillation  may  then  be  determined  by  coupling . 

the  wave-meter  to  the  primary 
and  secondary  circuits  of  the  set, 
as  shown  in  Fig.  22. 

The  higher-frequencycurrents 
in  the  primary  and  secondary 
circuits  are  out  of  phase  approxi- 
mately 180°  and  by  proper  ad- 
justments of  the  coupling  M  and 
M' ',  these  oscillations  may  be 
neutralized  in  the  wave-meter 
circuit.  The  decrement  of  the 
lower-frequency  oscillations  may 
then  be  determined  as  previously 
described,  after  which,  one  of  the 
coupling  coils  may  be  reversed, 

and  the  lower-frequency  oscilla- 
FIG.  22. — By  suitably  coupling  the  wave-meter     .  ,    .  .  .  ?      ,          . 

to  both  closed  circuit  and  antenna  of  the  tlons  (whlch  are  m  Phase  in  the 
transmitting  set,  a  resonance  curve  may  be  primary  and  secondary  circuits 
obtained  for  each  of  the  two  frequencies  of  the  set)  be  thus  neutralized 
generated  by  the  set.  and  the  decrement  of  the  high- 

frequency    oscillations    similarly 

determined.  The  energy  distribution  curves  determined  for  each  oscillation 
will  appear  somewhat  as  indicated  by  the  dotted  curves  in  Fig.  21. 

Determination  of  Wave-meter  Decrement  Using  an  Undamped 
Wave  Source. — It  has  already  been  indicated  how  the  decrement  62  of 
the  wave-meter  may  be  obtained  by  exciting  the  instrument  from  an 
undamped  wave-source.  In  this  case, 


T3T)  (W 

i— •HimiHir-1 


0) 


becomes, 


since, 


C2+Ci 


:  decrement  of  wave- meter 


5i=0. 


This  measurement   may  conveniently   be   made   by  any  one   of  the 
several  generators  of  high-frequency  continuous  oscillations  described  in 


DETERMINATION  OF  WAVE-METER  DECREMENT 


807 


Chapter  VII.  The  high-powered  tube  circuit  is  preferable  for  this  pur- 
pose, due  to  the  frequency  being  fixed,  and  the  exciting  circuit  being 
of  sufficient  power  to  be  unaffected  by  the  proximity  of  the  wave-meter 
circuit.  However,  in  case  the  tube  is  not  oscillating  powerfully,  the 
oscillations  may  be  affected  when  the  wave-meter  is  coupled  to -the  cir- 
cuit because  of  the  tighter  coupling  required.  To  prevent  this,  it 
is  desirable  to  use  very  weak  coupling  and  have  an  ammeter  in  the 
circuit  supplying  power  to  the  wave-meter  circuit.  The  indication 
of  this  meter  should  re- 
main constant  through- 
out the  decrement  de- 
termination showing 
that  the  power  gener- 
ated by  the  tube  was 
not  appreciably  affect- 
ed by  the  wave-meter 
tuning. 

The  wave  -  meter 
coupling,  if  made  too 
great,  may  also  affect 
the  frequency  of  the 
tube  oscillations  as  well 
as  their  amplitude.  The 
effect  of  this  frequency 
variation  on  the  de- 
crement determination 
may  be  analyzed  with 
the  help  of  Fig.  23. 

If  the  capacity  of 
the  wave-meter  con- 
denser is  less  than  that 


^20 


-18 


-.16 


-14 


-.10 


-08 


-06 


-.04 


-.02 


True  Energy 
Distribution 
Curve 


rgy  Distribution 
Curve  obtained 
w.ith  interfering 
conditions 


c; 


Wavemeter  Capacity 

required  for  resonance,  ^     00     T,  ,, 

'   FIG.  23.— If  the  wave-meter  is  coupled  too  tightly  (to  a 

then     a     current      will       low-powered  set)  the  energy  distribution  curve  will  be 
flow  in  the  wave-meter       unreliable  because  of  the  reactions  of  the  wave-meter 
circuit  which  is  leading      on  the  power  circuit, 
with    respect     to    the 

induced  e.m.f.  The  effect  of  this  leading  current  on  the  tube  cir- 
cuit is  to  increase  the  apparent  inductance,  causing  the  wave-meter 
indication  to  correspond  to  a  point  on  the  resonance  curve  of  a  circuit 
whose  resonant  frequency  is  below  that  given  by  CT.  Similarly,  a 
lagging  current  in  the  wave-meter  circuit  (wave-meter  capacity  greater 
than  resonance  value)  decreases  the  apparent  inductance,  the  wave- 
meter  indication  corresponding  to  a  point  on  a  resonance  curve,  the  reso- 


808  \Y.\VE-METERS  AND  THEIR  USE  [CHAP.  X 

nant  frequency  of  which  is  above  that  given  by  CT.  These  effects  have 
been  mathematically  derived  in  Chapter  I,  as  expressed  by  Eq.  (85),  p.  91. 

The  result  of  this  action,  as  indicated  in  Fig.  23,  is  to  squeeze  the 
apparent  energy  distribution  curve  together.  The  observed  decrement 
may  therefore  be  quite  inaccurate,  and  will  always  be  less  than  the  true 
value.  This  effect  should  be  guarded  against  by  decreasing  the  coupling 
to  as  small  a  value  as  possible. 

Determination  of  Wave-meter  Decrement  Using  Impulse  Excitation.— 
Although  the  above  method  represents  the  most  direct  and  simple  means 
for  determining  fc,  undamped  wave-generators  may  not  always  be  avail- 
able, in  which  case  impulse  excitation  may  be  employed.  In  its  ideal 
application,  the  condenser  of  the  instrument  would  first  be  charged  to 
a  given  potential,  and  allowed  to  discharge  through  the  circuit.  A  known 
resistance  is  then  inserted  in  the  wave-meter  circuit  and  the  condenser 
again  charged  to  the  same  potential  as  before  and  permitted  to  discharge. 
In  both  cases  the  energy  dissipated  in  the  circuit  is 


from  which 

•  (ii) 


where  R  is  the  resistance  of  the  wave-meter  circuit  and  A  R  the  inserted 
resistance.  /22  and  /i2  represent,  respectively,  the  reading  of  the  wave- 
meter  ammeter,  with  and  without  inserted  resistance,  these  readings  being 
proportional  to  the  square  of  the  wave-meter  current.  Knowing  the 
capacity  C  and  inductance  L  of  the  wave-meter,  the  decrement  is  readily 
obtained  from  the  relations: 

nn  & 

62  =7T/tC  W  =7T  j—  =  Tr 

Leo 
for  any  wave-length. 

The  above  ideal  case  is  approximated  closely  by  some  form  of  impact 
excitation,  for  which  a  spark  transmitting  set,  equipped  with  a  suitable 
quenched  gap  (such  as  is  used  in  spark  transmitters  operating  on  impact 
excitation)  and  with  the  antenna  circuit  open,  may  be  conveniently 
utilized  as  an  impulse  generator.  The  procedure  is  similar  to  that  de- 
scribed above,  but  the  energy  is  not  exactly  equal  for  the  two  conditions 
of  different  resistance,  and  a  constant  K  is  therefore  introduced  in  the 
energy  expression  as  follows: 

Ii2R=KI22(R+&R) 


DETERMINATION  OF  WAVE-METER  DECREMENT  809 


It  has  been  shown  1  that 


where  di  is  the  decrement  of  the  exciting  circuit; 

62  is  the  decrement  of  the  instrument  circuit ; 

A 5  is  the  additional  decrement  due  to  inserting  AR  in  the 

wave-meter  circuit. 

For  impulse  excitation  61  is  very  large  compared  to  62  and  K  is  essentially 
equal  to  unity;  therefore 

/22 


/!2-/22 


as  before. 


If  resistance  is  inserted  in  the  circuit  until  /22  =  i/i2,  then 

R  =A# 

and  is  thus  directly  and  conveniently  determined. 

The  Decremeter. — To  facilitate  the  rapid  and  accurate  measurement 
of  decrement,  without  necessitating  the  accurate  determination  of  an 
energy  distribution  curve,  an  instrument  called  a  decremeter  has  been 
developed  by  the  Bureau  of  Standards  2  which  directly  measures  the  decre- 


Secondary 
of  Oscillation 
Transformer 


Search 
Coil 


Buzzer 


FIG.  24. — Arrangement  of  circuits  in  the  decremeter. 

ment  of  radio  frequency  oscillations.  This  instrument  is  similar  to  the 
wave-meter,  but  is  equipped  with  a  variable  condenser  of  special  design, 
permitting  a  direct-reading  decrement  scale  to  be  attached  to  the  rotating 
element.  The  connections  of  the  instrument  are  shown  in  Fig.  24,  which 
illustrates  the  similarity  to  the  wave-meter,  differing  only  in  that  a  fixed 

1  Lehrbuch  der  Drahtlosen  Telegraphic,  Zenneck,  1913,  page  142. 

2  The  instrument  is  generally  called  a  Kolster  decremeter,  as  Dr.  F.  A.  Kolster  was 
responsible  for  its  development. 


810  WAVE-METERS  AND  THEIR   USE  [CHAT.  X 

capacity  is  shunted  across  the  special  variable  condenser.     The  function 
of  this  fixed  condenser  is  described  later. 
It  will  be  recalled  that 


The  fundamental  requirement  of  a  variable  condenser  which  is  to 
be  used  in  the  decremeter  is  that  .  the  fractional  change  in  its  capacity 
must  be  directly  proportional  to  the  angular  movement  of  the  rotating 
element  and  independent  of  the  final  value  of  capacity,  or, 

dC 


and 

C  =  em6+h=atme,       .......     (13) 

where 

a  =  e\ 

If  6=0, 

Co=ae°=a=initial  value  of  capacity.  This  is  the  fixed  condenser 
connected  across  the  variable  condenser  as  indicated  in  Fig.  24  and  pre- 
viously referred  to. 

The  maximum  capacity  is  also, 


and  the  ratio  of  maximum  to  minimum  capacity  is  therefore, 


The  capacity  of  the  fixed  condenser  Co  is  determined  experimentally, 
and  is  made  of  such  value  as  to  make  K  of  the  most  suitable  value  for 
the  particular  requirements  of  the  decremeter.  Since  K  is  thus  deter- 
mined, m  will  be  obtained  by  means  of  Eq.  (14)  given  above. 

A  rotary  condenser  constructed  in  accordance  with  the  above  require- 
ments, with  a  fixed  capacity  Co  connected  m  parallel,  so  chosen  as  to  give 
the  desired  ratio  between  the  maximum  (Ciso)  and  minimum  capacity 
(Co)  of  the  combined  condensers,  has  been  found  to  give  a  calibration 
curve  in  exact  agreement  with  the  theoretical  value. 

The  derivation  of  the  equation  for  the  boundary  curve  of  the  moving 
element  is  as  follows: 

From  Eq.  (13) 

C=aeme. 

Therefore 


THE   DECREMENTER 


811 


where 
and 
Also 

or, 


A  is  the  active  area  of  the  moving  plate, 

0  is  the  angular  displacement. 

dA 


But,  referring  to  Fig.  25, 


dA=bmemedd. 


Fixed  Plates 


where 
and 


FIG.  25. — Form  of  plates  used  in  the  decremeter  condenser. 

p  is  the  radius  vector  from  the  axis  to  the  enveloping 
curve, 


r  is  the  radius  of  the  circular  space  occupied  by  the 

separating  washers  between  the  plates. 
Equating  the  above  expressions  for  dA ,  we  have, 


or 


V2bmeme+r2, 


(15) 


where  b  and  m  are  design  constants,  which  determine  the  minimum  and 
maximum  values  of  the  capacity  to  be  used  (b  =K'a  while  m  is  the  same 


812 


WAVE-METERS  AND   THEIR  USE 


[CHAP.  X 


as  in  previous  expressions).  These  are  arbitrarily  chosen  to  suit  the 
particular  requirements  of  the  special  instrument. 

Fig.  25  illustrates  the  form  of  the  movable  plate  when  designed  in 
accordance  with  the  above  expression.  The  stationary  plate  is  made 
semicircular  for  convenience.  In  Fig.  26  is  shown  a  view  of  the  inside 
of  a  decremeter,  showing  the  peculiarly  shaped  plates  of  the  condenser. 
This  cut  is  taken  from  Circular  74  of  the  Bureau  of  Standards,  a  book 
every  student  of  radio  should  possess. 

The  Manipulation  of  the  Decremeter — Measurement  of  Decrement. — 
The  manipulation  of  the  decremeter  is  quite  similar  to  that  outlined  for 


FIG.  26. — Arrangement  of  the  different  parts  of  a  Kolster  decremeter. 

the  wave-meter.  The  instrument  is  loosely  coupled  to  the  exciting  cir- 
cuit as  shown  in  Fig.  24  and  tuned  to  resonance,  as  indicated  by  a  maximum 
reading  on  the  hot-wire  ammeter,  this  instrument  usually  being  gradu- 
ated to  read  I2.  The  condenser  value  is  then  decreased  to  Ci,  the  hot- 


/  2 

wire  ammeter  then  reading  ~. 


The  decrement  scale  is  then  set  to  zero 


and  clamped  to  the  condenser  shaft,  after  which  the  condenser  is  rotated 
until  the  value  €2  is  reached,  at  which  point  the  ammeter  indication  is 
again  one-half  of  that  obtained  at  resonance.  The  reading  of  the  decre- 
ment scale  then  gives  the  sum  of  the  two  circuit  decrements  5i  and  82 
directly.  It  has  been  found  that  the  angular  deflection  of  the  condenser 


WAVE-METER   USED   TO   MEASURE   RESISTANCE  813 

element  for  commercial  decrements  is  very  small,  and  the  decrement  scale, 
if  connected  directly  to  the  condenser  shaft,  would  be  crowded  and  difficult 
to  read  accurately.  Therefore  it  is  usual  to  gear  the  scale  to  the  con- 
denser shaft,  the  relative  angular  motion  of  the  decrement  scale  and 
capacity  element  being  about  6:1. 

The  decrement  of  the  meter  for  all  values  of  C  and  for  each  of  three 
fixed  inductance  coils  which  may  be  used  is  known  from  curves  supplied 
with  the  instruments.  These  decrements  vary  from  about  .07  to  .02,  the 
larger  value  corresponding  to  a  large  value  of  C  and  smallest  value  of  L. 
The  smaller  value  is  obtained  with  C  at  its  minimum  value  and  the  largest 
inductance  inserted  in  the  circuit. 

Measurement  of  Resistance.  —  Knowing  61,  the  decrement  of  the 
circuit,  the  resistance  is  at  once  known  at  the  frequency  of  oscillation  from 
the  following  relations,  which  have  previously  been  deduced  : 


The  capacity  C  and  inductance  L  of  the  circuit,  if  unknown,  are  simply 
determined  by  means  of  a  wave-meter  as  outlined  on  page  814.  The 
decremeter  is  thus  valuable  as  a  means  of  determining  high-frequency 
resistance. 

Measurements  of  Wave-length.  —  The  Kolster  decremeter  described 
above  is  evidently  also  applicable  to  the  measurement  of  wave-lengths, 
and  the  variable  condenser  is  therefore  equipped  with  a  scale  indicating 
directly  the  wave-lengths  in  meters  corresponding  to  the  condenser  adjust- 
ment. The  instrument  as  usually  furnished,  is  equipped  with  three 
inductances  to  cover  the  range  of  wave-lengths  required,  this  being  about 
300  to  2500  meters. 

Measurement  of  Phase  Difference  of  a  Condenser.1  —  The  decremeter 
may  also  be  used  to  measure  the  phase  difference  of  a  condenser,  since 

phase  difference  ^  =  R&C  =  —  (in  radians),     ....     (16) 

7T 

or, 

t  =  18.24  A6  (in  degrees),      ....     (160 

where  A  5  is  the  increase  in  total  decrement  due  to  inserting  the  condenser 
in  the  circuit. 

The  condenser  is  inserted  in  the  decremeter  circuit,  which  is  then 
tuned  to  an  undamped  wave-exciting  source.  The  decrement  measured 
under  these  conditions  is  the  sum  of  82  and  A57  where  62  may  be  obtained 
from  the  calibration  curves  furnished  with  the  instrument.  Substituting 
A  d  in  the  above  expressions,  the  phase  difference  \f/  is  readily  obtained, 
1  See  Chapter  II,  page  171. 


814 


WAVE-METERS  AND   THEIR  USE 


[CHAP.  X 


Use  of  Wave-meter  to  Measure  L  and  C. — A  wave-meter  may  be  used 
to  measure  an  unknown  inductance  or  capacity,  provided  a  known  capacity 
or  inductance  respectively  are  available.  The  procedure  then  is  simply 
to  connect  the  unknown  inductance  and  known  condenser  (or  known 
inductance  and  unknowrn  condenser),  into  an  oscillatory  circuit,  as  shown 
in  Fig.  27,  excited  by  means  of  a  buzzer.  Loosely  coupled  to  this  primary 
circuit  is  the  wave-meter,  by  means  of  which  the  wave-length  of  the  test 
circuit  oscillations  may  be  obtained. 

When  making  this  determination,  it  is  important  that  the  coupling 
between  the  two  circuits  be  very  loose,  if  accurate  results  are  to  be  obtained. 
Also  the  leads  used  in  making  up  the  test  circuit  should  be  as  short  as 
possible,  to  minimize  the  error  due  to  the  distributed  capacity  (shown  in 
figures  in  dotted  lines),  and  inductance  of  the  leads  which  would  tend 
to  increase  the  measured  wave-length.  It  may  be  found  impossible  to 


—  ^r•*t^ 

c  — 

1 

~ 

T 

AAA^A"! 

Test  Circuit  Wave-meter 

FIG  27. — Use  of  wave-meter  to  measure  L  or  C. 


tune  out  the  signal,  in  which  case  the  coupling  should  be  decreased,  and 
all  direct  induction  effects  from  the  buzzer  circuit  (to  which  this  con- 
tinuous note  is  due)  minimized  or  eliminated  by  making  the  buzzer  cir- 
cuit as  compact  as  possible.  If  no  point  of  maximum  note  occurs  as  the 
wave-meter  condenser  is  varied,  it  is  probable  that  the  wave-length  of 
the  test  circuit  is  beyond  the  range  of  the  instrument.  The  remedy  is 
evidently  to  change  the  known  value  of  inductance  (or  capacity)  in  the 
test  circuit,  or  to  try  others  of  the  various  coils  with  which  the  wave- 
meter  is  equipped. 

After  the  wave-length  has  been  determined,  the  unknown  value  of 
inductance  (or  capacity)  is  given  at  once  by  the  formula, 


L  and  C  being  measured  in  micro  units. 

Equivalent  results  are  obtained  if  the  wave-meter  is  employed  as  the 
exciting  circuit.  The  connections  are  then  as  shown  in  Fig.  28.  The 
wave-length  of  the  wave-meter  oscillations  is  varied  until  a  maximum 
note  is  heard  in  the  phones  across  the  test  circuit,  under  which  condition 
the  natural  frequency  of  both  circuits  is  in  agreement. 


WAVE-METER  USED   TO   MEASURE   L  AND   C 


815 


The  same  precautions  are  to  be  observed  in  this  case  as  for  the  preced- 
ing method,  with  especial  reference  to  the  phone  circuit  connected  across 


fTTl. 


Test  Circuit 


Wave-meter 


FIG.  28. — Another  method  of  measuring  L  or  C,  using  the  wave-meter  as  a  buzzer  excited 
wave  generator,  of  known  calibration.  Note  that  the  calibration  of  a  given 
wave-meter  will  generally  be  different  when  used  as  here  shown  than  when  used  as 
in  Fig.  27. 


the  test  circuit.  Long,  twisted  leads  must  especially  be  avoided  as  these 
will  cause  large  error,  due  to  their  distributed  capacity  (conventionally 
shown  in  dotted 
lines,  Fig.  28)  par- 
ticularly if  the  test 
circuit  capacity  is 
small.  It  is  to  be 
noted  that  a  wave- 
meter  will  have  a 
different  calibration 
when  used  with  a 
hot-wire  meter  for 
indicator,  and  when 
detector  and  phones, 
or  buzzer,  is  connect- 
ed in  parallel  with 
its  condenser.  The 
amount  of  correction 
required  is  greatest 
for  the  lowest  set- 
tings of  the  wave- 
meter  condenser. 

Use  of  Wave- 
meter  to  Measure 
the  Constants  of  an 


To  Vacuum  Tube 
Generator  of 
undamped 
Oscillations 


FIG.  29. — To  measure  the  natural  wave-length  of  an  antenna 
the  antenna  is  coupled  (by  a  small  search  coil)  to  a  source 
of  continuous  wave  power  of  variable  frequency.  When  the 
antenna  ammeter  reads  a  maximum,  the  wave-meter  is  used 
to  read  wave-length  of  power.  If  a  d.c.  generator  is  used  in 
the  plate  circuit  of  the  tube  generator  the  phones  and  detec- 
tor may  be  used  for  getting  resonance,  the  commutation 
ripples  being  audible;  otherwise  an  ammeter  will  be  used  in 
the  wave-meter  circuit. 


Antenna.  —  Another 

important  measurement  involving  the  use  of  the  wave-meter  is  that 
of  the  constants  of  an  antenna.  The  loading  coils,  short-wave  con- 
denser and  oscillation  transformer  are  first  removed  from  the  antenna 


816  WAVE-METERS  AND  THEIR  USE  [CHAP.  X 

circuit  and  a  search  coil  of  negligible  inductance  inserted  in  the  circuit 
as  shown  in  Fig.  29. 

The  antenna  is  then  excited  by  undamped  wave-oscillations,  using 
a  vacuum-tube  generator  of  sufficient  power  and  with  the  coupling  made 
loose  enough  to  prevent  any  appreciable  variation  of  plate  current  due 
to  reactive  effects  of  the  antenna  circuit.  The  generator  frequency  is 
varied  until  the  antenna  ammeter  A  indicates  a  maximum  and  the  wave- 
length of  the  tube  circuit  for  this  adjustment  is  then  determined  by  means 
of  the  wave-meter.  This  value  represents  the  natural  wave-length  of 
the  antenna,  and  is  expressed  by, 


when  LO  and  Co  are  the  effective  inductance  and  capacity  of  the  antenna 
for  the  quarter  wave-length  oscillation.  In  the  figure  the  antenna  ammeter 
represents  a  sensitive  current  meter,  involving  a  thermo-couple  and  gal- 
vanometer, or  similar  device. 

To  determine  LO,  an  additional  known  inductance  LI  is  inserted  in 
the  antenna  circuit  and  the  new  wave-length  Xi  determined  for  this  con- 
dition. Thus:  1 

Xi=1885V(L0+Li)C0. 
Therefore, 

)Co  — 


LoCo  -|-  LI  Co  —  LoCo 
LiCo 

Xi2-Xo2 
(1885)2L1 


Substituting  this  value  for  Co  in  the  above  expression  for  Xo,  LO  is 
obtained  as  follows: 

Xo2   _      L0(Xi2-Xo2) 
(1885)2~       (1885)2L!  ' 


The  following  alternative  method  may  also  be  employed.     The  known 
inductance  inserted  in  the  circuit  is  assumed  to  be  the  only  inductance 

1  In  the  equations  given,  the  wave-length  is  expressed  in  meters,  while  inductance 
and  capacity  are  expessed  in  microhenries  and  microfarads  respectively. 

2  This  deduction  is  a  very  simple  one  and  suffices  for  ordinary  purposes.     It  must 
be  noted,  however,  that  actually  Co,  the  same  as  L0,  is  not  a  constant,  but  varies  as  dif- 
ferent values  of  loading  are  used.     For  an  analysis  of  this  point  see  Morecroft,  "Some 
Experiments  with  Long  Electrical  Conductors,"  Proc.  I.  R.  E.,  Dec.,  1917,  and  Miller 
"Electrical  Oscillations  in  Antennae  and  Inductance  Coils,  Proc.  I.  R.  E.  (June,  1919), 
also  discussion  of  Miller's  paper  in  Proc.  I.  11.  E.,  Dec.,  1919. 


WAVE-METER   USED   TO    MEASURE   ANTENNA   CONSTANTS      817 

present,  i.e.,  LO  is  negligible  compared  to  LI.     This  requires  that  LI  be 
large  enough  to  give  the  antenna  a  wave-length  about  five  times  as  great 
as  its  natural  wave-length. 
Then  we  may  put 


and 


_ 

Xi=1885VLiC0, 


c  - 


1885%' 


The  known  inductance  is  now  removed  from  the  circuit  and  the 
natural  wave-length  of  the  antenna  is  accurately  measured. 
Then,  _ 

X2  =  1885  VLoCo, 
and 


1885' 


Li   18852' 


or 


If  the  value  of  LO  obtained 
from  this  equation  shows  it  to 
be  negligible  compared  to  LI,  as 
assumed,  then  the  determina- 
tions for  LO  and  Co  may  be 
accepted.  If  this  is  not  the 
case,  the  obtained  value  for  LO 
must  be  added  to  LI  and  the 
spark  Gan  calculation  for  Co  repeated. 


FIG.  30. — In  case  a  very  short  spark  gap,  a  low-powered  induction  coil,  and  very  weak 
coupling  are  used  the  phones  and  crystal  detector  may  be  used  for  getting  resonance 
in  the  wave-meter,  otherwise  the  ammeter  will  be  used  to  indicate  resonance. 

Where  undamped  oscillations  are  not  available  an  induction  coil  or 
low-powered  transformer  may  be  used  to  excite  the  circuit  as  shown  in 
Fig.  30. 

In  this  case  the  gap  resistance  has  been  inserted  in  the  circuit  and  the 
observed  wave-length  may  therefore  be  slightly  greater  than  with  the 


818 


WAVE-METERS  AND   THEIR  USE 


[CHAP.  X 


(High  voltage    -=- 
battery 


High 
resistance 


previous  method.     An  alternative  method  is  shown  in  Fig.  31,  with  which 
arrangement  the  antenna  is  charged  to  battery  voltage  when  the  buzzer 

contact  is  open  and  then  discharges 
through  the  buzzer  contact  when  this 
closes. 

The    methods   described    above  may 
also  be  used   for  determining  the  wave- 
length    of     the    antenna     circuit    with 
various   loading   coils,  oscillation   trans- 
former or   short 
wave  -  condenser 
connected     into 
the    circuit.     In 
all      cases     the 
FIG.  31. — Use  of  buzzer  for  determining  the  natural  wave-length  of   closed    circuit  of 

anantenna-  the        transmit- 

ting set  should   be   open   to   prevent   interference  effects. 

When  the  inductance  of  the  search  coil  required  for  coupling  to  the 
generator  circuit  (Fig.  28),  is  not  negligible,  the  natural  wave-length 
Xo  cannot  be  determined  directly,  but  is  determined  from  two  measure- 
ments as  follows: 

Xi  =  1885V(L0+Ls)Co,  (a) 

where  L,  =  inductance  of  search  coil, 

X2  =  1885V(L0+LJ+L'.)r0,  (&) 

where  L',  =  additional  known  inductance  inserted  which  is  made  equal 
to  L,. 

•'•    Q88rV)2  =  ^0^°  ~l~  2-k'tCo  —  LoCo  —  L',Co 


or 


2-2 


Substituting  in  (a), 


X22-Xi 
(1885)2LV 


(18) 


Xi 


or 


_ 
18852  18852L'S 

L',\i2  =  L0(X22  -  Xi2)  +  L'.(X22  -  Xi2) 


I/,(2Xi2-X32) 
X22-Xi2     ' 


(19) 


Knowing  Co  and  Lo,  the  natural  wave-length  Xo  is  obtained  from  the 
relation : 

X0  = 


WAVE-METER  USED   TO   MEASURE   COUPLING 


819 


In  the  above  it  has  been  assumed  that  L'S  =  LS.  This  is  a  purely 
arbitrary  relationship  and  it  is  usually  preferable  to  make  L's  larger  than 
this,  say  five  or  ten  times  Ls,  so  that  the  difference  between  \i  and  \2  is 
increased  and  the  experimental  errors  involved  in  the  measurement  thus 
decreased. 

Determination  of  Mutual  Inductance  and  Coefficient  of  Coupling. — The 
wave-meter  also  forms  a  convenient  instrument  for  readily  determining 
the  mutual  inductance  existing  between  the  closed  and  open  circuits  of 


500 


Wavelength  in  meters 


FIG.  32. — From  an  energy  distribution  curve,  obtained  with  non-quenching  gap,  the 
coefficient  of  coupling  may  be  obtained  from  the  spacing  of  the  two  resonance 
peaks. 


a  transmitting  set.  If  we  know  the  coefficient  of  coupling  K,  the  mutual 
inductance  M  (M^KVlLJ^,  where  LI  and  L2  are  the  total  inductance 
of  the  closed  and  open  circuits,  respectively)  is  readily  obtained,  LI  and 
L2  being  determined  as  described  on  page  814. 

The  following  two  methods  may  be  used : 

(a)  An  energy  distribution  curve  is  determined  for  the  set  as  shown 
in  Fig.  32,  from  which  \i  and  X2,  corresponding  to  the  peaks  in  the  curve, 
are  readily  determined. 


820 

Since 
and 
we  have, 


WAVE-METERS  AND   THEIR   USE 


[CHAP.  X 


X2  = 

Xi2  _l-K 
\22     1+K' 


Since 
and 

we  have, 
or 


~X22  +  X!2' 

Xr  is  approximately  equal  to 


(20) 


X2  -f-  Xi 


Xr2  is  approximately  equal  to 


?r_(X2-Xi)(X2H-X1)_(X2-X1)(2Xr) 
2Xr2  2Xr2 


x  =  X2^Xl=2X2- 


(21) 


The  latter  forms  are  somewhat  simpler  than  the  more  accurate  expres- 
sion, as  no  squared  terms  are  involved.  They  are,  however,  accurate 
enough  for  most  commercial  determinations.  The  last  form  is  perhaps 
the  most  desirable,  as  it  eliminates  all  measurement  of  Xr. 

(b)  The  second  method  is  as  follows:  The  oscillation  transformer  pri- 
mary and  secondary  are  connected  in  series  in  the  closed  circuit  as  shown 
in  Fig.  33. 

Step-up  power 
transformer 


FIG.  33. — Unless  a  very  short  spark  gap  (hence  low  power)  is  used  the  hot-wire  ammeter 
(or  similar  indicator)  would  be  used  in  place  of  the  phones  and  detector. 

To  get  greater  accuracy  the  loading  coils  should  be  disconnected  and 
removed  from  the  secondary  circuit,  so  that  only  those  inductances  are 
involved  which  are  coupled  during  the  operation  of  the  set,  i.e.,  the  pri- 
mary and  secondary  of  the  oscillation  transformer.  Damped  oscillations 


WAVE-METER  USED  TO   MEASURE  COUPLING  821 

are  then  set  up  in  this  circuit  as  in  the  normal  operation  of  the  transmitter 
and  the  wave-length  noted.  Calling  this  wave-length  Xi,  Lf,  the  total 
inductance  in  the  circuit,  is  obtained  from 


1885Ci 

The  connections  to  one  coil  are  then  reversed  and  the  readings  repeated. 
In  this  case, 


Therefore 

T  t       j  n 

M-±=±         (22) 

or 

L"-L' 

4      ' 

according  as  L'  is  greater  than  L"  or  vice  versa. 

Then  when  the  set  is  in  normal  operation,  using  loading  coils,  etc., 
we  find  the  coupling  coefficient  from  the  relation 


(23) 


where  LI  is  the  total  inductance  in  the  primary  circuit  under 

normal  operation; 

L/2t  is  the  total  inductance  in  the  secondary  circuit  under 
normal  operation,  i.e.,  the  inductance  of  the  oscil- 
lation transformer  secondary  +  the  effective  induc- 
tance of  the  antenna  -f-  the  inductance  of  the  loading 
coil  (if  inserted). 

The  above  methods  are  exactly  equivalent  in  result  and  may  be  used 
indiscriminately.  Method  (6)  is  perhaps  the  better,  since  the  consider- 
able amount  of  data  needed  to  plot  accurately  an  energy  distribution 
curve  is  not  required.  Sometimes,  however,  this  curve  is  required  as  illus- 
trating an  operating  characteristic  of  the  set,  and  the  coupling  is  then 
most  simply  determined  by  the  relationships  developed  in  Method  (a). 

How  to  Improvise  a  Wave-meter.  —  The  varied  and  important  uses 
of  the  wave-meter  as  described  on  the  preceding  pages  have  made  it  a 
fundamental  and  essential  part  of  any  radio  laboratory  or  station  equip- 
ment. Now  and  then  occasions  may  arise  where  this  instrument  may 
not  be  available,  through  loss,  damage,  etc.,  and  in  this  case,  a  "  home- 
made "  instrument  must  be  devised.  Also,  a  large  majority  of  amateur 
operators  prefer  to  construct  their  own  meters  for  the  enjoyment  and 


822 


WAVE-METERS  AND   THEIR  USE 


[CHAP.  X 


experience  which  such  constructive  work  brings  to  them.  For  these  rea- 
sons it  has  been  considered  desirable  to  give  a  brief  outline  of  the  pro- 
cedure to  be  followed. 

One  of  the  first  points  to  be  decided  is:  What  shall  be  the  maximum 
wave-length  which  the  wave-meter  to  be  designed  is  to  measure?  We 
will  assume  this  to  be  2000  meters.  A  suitable  variable  condenser  must 
next  be  chosen,  and  as  one  or  more  variable  condensers  are  normally 
available  in  even  the  simplest  installations  we  will  consider  that  such  con- 
densers are  available  in  this  case.  The  maximum  capacity  of  the  several 
condensers  should  be  measured,  either  electrically,  or  from  their  dimen- 
sions, by  means  of  the  expression  given  on  page  165,  Eq.  (30). 

The  wave-meter  condenser  should  have  about  .001  microfarad  capacity 
per  1000  meters  maximum  wave-length  to  be  measured.  Thus,  for  this 
problem,  the  capacity  should  be  .002  microfarad  and  that  condenser  should 
be  chosen  which  possesses  at  least  this  capacity. 

The  maximum  wave-length  and  capacity  thus  being  determined,  the 
required  inductance  is  readily  obtained  from 


or 


Ametere  —  Ioo5  v  xv^C^/ 

2000  = 


.  002 


L  =  563  microhenries. 

This  inductance  should  then  be  designed  (generally  in  the  form  of  a 
single  layer  solenoid)  in  accordance  with  the  formula  given  on  page  145, 
Eq.  (11).  The  coil  should  be  wound  with  finely  stranded  wire,  the  indi- 
vidual strands  being  insulated  to  minimize  the  resistance  of  the  wave- 
meter. 

A  small  hot-wire  ammeter  (0—100  milliamperes  preferable)  should 

then  be  obtained  and  as- 
sembled with  the  condenser 
and  coil,  the  connections 
being  made  as  shown  in 
Fig.  34. 

All  connections  should 
be  well  made  and  the  cir- 
cuit made  as  compactly  as 
possible  so  as  to  minimize 
the  resistance  of  the  wave- 
meter.  This  equipment  may 

then   be  enclosed  in  any  wooden  box  of  convenient  size,  with  only  the 
ammeter  and  condenser  index  and  associated  scale  visible.      Additional 


FIG.  34. — A  convenient  arrangement   of   terminals 
for  a  wave-meter. 


IMPROVISING  A  WAVE-METER  823 

binding  posts  may  be  added  for  phones,  detector,  arid  buzzer  circuit  as 
shown. 

The  wave-meter  is  then  ready  ror  calibration,  which  may  be  accom- 
plished by  coupling  the  instrument  to  a  transmitter  which  may  be  adjusted 
to  radiate  at  several  known  wave-lengths.  A  few  points  on  the  scale  may 
be  approximately  determined  by  using  the  wave-meter  (with  detector 
and  phones  as  indicating  devices),  as  the  closed  circuit  of  a  receiving  set, 
coupled  very  loosely  to  the  antenna.  A  few  stations  of  known  wave- 
length may  generally  be  heard  in  this  way,  and  so  a  few  points  of  calibra- 
tion obtained.  A  curve  should  then  be  plotted  between  the  known  wave- 
lengths and  corresponding  positions  of  the  condenser  index  (the  condenser 
scale  is  usually  graduated  in  degrees  or  in  100  divisions  to  the  semicircle) . 
This  curve  will  have  an  appearance  similar  to  the  wave-length  curve  in 
Fig.  11.  The  decrement  of  the  meter  may  also  be  measured  by  one  of  the 
methods  described  above,  and  should  not  exceed  .10  for  an  average  value 
of  the  condenser. 


CHAPTER  XI 
AMPLIFIERS 

Amplifiers  in  General. — An  amplifier  is,  as  the  name  implies,  an 
apparatus  for  increasing  the  strength  of  incoming  signals.  It  performs, 
in  modern  radio  communication,  and  also  in  ordinary  wire  communication, 
a  very  important  function,  in  so  far  as  it  makes  possible  the  detection  of 
very  feeble  signals  and  thus  increases  the  practical  range  of  transmission. 

The  reader  is  already  familiar  with  the  fact  that  the  signals  received 
in  radio  transmission  consist  of  very  high-frequency  currents  and  voltages, 
which  may  be  of  constant  or  varying  amplitude,  depending  upon  the  system 
used.  These  signals  are  generally  "  heard  "  in  telephone  receivers  by 
first  reducing  the  frequency  of  the  incoming  currents  and  voltages  from 
a  very  high  value  to  an  "  audible  value,"  and  thereafter  causing  the 
"  audio-frequency  "  currents  to  flow  through  the  receivers.  In  using  an 
amplifier  either  of  the  following  two  schemes  may  be  resorted  to: 

(a)  The    amplifier  may  be    so  connected  that    the  incoming  high- 
frequency  currents  and  voltages  are  first  strengthened  and  thereafter 
reduced  in  frequency. 

(b)  The  amplifier  may  be  so  connected  as  to  strengthen  the  currents 
and  voltages  after  they  have  been  reduced  in  frequency. 

The  above  forms  the  basis  of  the  division  of  amplifiers  into  two  general 
classes,  i.e.,  "  high-frequency  "  and  "  low-frequency." 

While  these  two  general  types  of  amplifiers  are  fundamentally  the 
same,  yet  the  constants  of  the  apparatus  used  in  their  construction  are 
often  so  different  that  the  two  types  cannot,  in  general,  be  used  inter- 
changeably. 

The  amplifiers  used  in  radio  communication  consist  invariably  of 
one  or  more  three-electrode  vacuum-tubes  with  other  suitable  apparatus. 
As  a  matter  of  fact,  it  was  not  until  the  advent  of  the  vacuum-tube  that 
suitable  amplifiers  could  be  constructed  and  operated.  The  character- 
istics of  a  good  amplifier  should  be  such  that  the  signal  currents  are 
strengthened  without  any  distortion;  the  vacuum-tube  can  be  made  to 
fulfill  these  two  conditions  admirably,  and  it  is  practically  the  only 
apparatus  which  can.  It  will  be  noted  from  this  brief  outline  that  an 
amplifier  must  be  a  kind  of  trigger  which,  actuated  by  the  very  weak 
voltages  impressed  by  the  antenna,  releases  from  a  local  energy  supply  an 

824 


TRIODE   SUITABLE   FOR  AMPLIFIER  825 

amount  of  energy  much  greater  than  that  actuating  the  antenna.  The 
suitability  of  the  three-electrode  tube  for  this  purpose  is  at  once  evident 
from  the  analysis  of  its  action  given  in  Character  VI. 

The  General  Characteristics  of  Triodes.  —  These  have  been  quite 
thoroughly  discussed  in  Chapter  VI;  on  pages  570  et  seq.  the  possibility 
of  using  a  tube  as  an  amplifier  was  pointed  out  and  an  elementary  analysis 
given. 

The  "  static  "  relation  between  the  plate  current  and  grid  and  plate 
potentials  was  shown  to  be  expressible  by 


(1) 


and  it  was  also  pointed  out  that,  for  small  variations  in  the  tube  poten- 
tials, the  exponent  might  be  treated  as  unity. 

It  was  further  shown  that,  if  a  sufficiently  small  sine  wave  e.m.f  was 
impressed  on  the  grid,  the  pulsations  in  the  plate  current  would  be  sinu- 
soidal in  form,  and  the  constant  (I/  A)  acquires  the  significance  of  "  alter- 
nating current  plate  circuit  resistance." 

We  then  have  the  equation  which  was  used  throughout  Chapter 
VI  in  analyzing  tube  action,  i.e.  : 


(2) 


where  Ip  =  effective  value  of  alternating  component  of  plate  cur- 

rent; 

RP  =  alternating  current  plate  circuit  resistance  ; 
E0=  effective    value    of    alternating    component    of    grid 

voltage  ; 
Ep  =  effective    value    of    alternating    component    of    plate 

voltage. 

We  must  point  out  again  the  limitations  of  the  applications  of  this 
relation.  The  steady  values  (c.c.  components)  of  grid  and  plate  poten- 
tials must  be  so  chosen  that,  for  the  value  of  Ea  impressed  the  linear 
relation  of  Eq.  (2)  holds  good.  This  requires  in  general  that  Ec  and  E* 
of  Eq.  (1)  above  be  properly  related. 

As  pointed  out  on  page  577  and  illustrated  by  the  curves  of  Fig.  184, 
page  576,  when  there  is  considerable  outside  impedance  in  the  plate  circuit 
the  plate  current  changes  linearly  with  respect  to  Ea  over  much  wider  ranges 
than  might  be  judged  from  the  static  characteristic.  This  is  conventionally 
illustrated  in  Fig.  1.  With  no  external  resistance  in  the  plate  circuit 
the  static  characteristic  of  a  tube  might  be  as  shown  by  curve  A,  whereas 
if  a  resistance  is  put  in  series  with  the  plate  (about  equal  to  Rp)  and  the 
plate  voltage  Eb  be  increased  sufficiently  to  make  /&  (for  Eg  =  0)  the  same 


826 


AMPLIFIERS 


[CHAP.  XI 


as  for  curve  A,  then  curve  B  will  be  obtained,  which  is  evidently  of  such 
a  shape  as  to  satisfy  Eq.  (2)  over  a  change  in  E8  f rom  perhaps— 4  volts 
to  zero. 

Hence  if  the  value  of  Ee  is  chosen  as  —2  volts  the  tube  having  char- 
acteristics shown  in  Fig.  1  would  operate  satisfactorily  with  an  impressed 
alternating  grid  signal  of  2  volts  maximum  value. 

It  will  be  noticed  that,  even  with  the  grid  potential  positive,  curve 
B  is  still  nearly  straight  so  that  it  might  seem  possible  to  operate  the  tube 


i          o          i 

Grid  Voltage 


FIG.  1. — Showing  the  effect  on  the  plate  current — grid  potential  curve  of  a  tube  of 
putting  external  resistance  in  the  plate  circuit;  a  tube  which  by  itself  gives  char- 
acteristic A,  will  give  characteristic  B  if  sufficient  external  resistance  is  put  in  the 
plate  circuit  and  the  voltage  in  this  circuit  suitably  increased, 


satisfactorily  with  signals  sufficiently  intense  to  make  the  grid  swing 
positive.  Such  is  not  the  case,  however;  if  the  grid  is  allowed  to  become 
positive  it  takes  current  (it  takes  negligible  current  as  long  as  it  is  neg- 
ative), and,  as  will  be  explained  later,  this  seriously  interferes  with  proper 
amplification. 

In  order  to  keep  the  grid  of  an  amplifier  suitably  negative  either  a 
small  dry  battery  may  be  inserted  in  the  grid  leak  resistance  circuit,  or 
the  leak  resistance  may  be  attached  to  a  point  in  the  filament  circuit 
which  is  sufficiently  negative  with  respect  to  the  filament.  These  two 
schemes  are  indicated  in  Fig.  2,  a  and  6;  in  scheme  b  an  extra  resist- 


GRID   MAINTAINED  AT  NEGATIVE   POTENTIAL 


827 


ance  R  is  put  in  series  with  the  filament  having  such  a  resistance  that 
when  normal  filament  flows  through  it  the  IR  drop  is  the  required  amount. 
In  some  multi-stage  amplifiers  (several  tubes  repeating  one  into  the  other) 
the  filaments  are  all  connected  in  series  to  the  A  battery,  the  filament 
of  the  preceding  tube  may  serve  as  the  resistance  R,  as  indicated  in  Fig. 
3.  In  the  operation  of 
tubes  as  amplifiers  the 
following  quantities  play 
a  very  important  part  : 

(a)  A.C.  resistance  of 
plate  to  filament  or  out- 
put circuit  of  tube. 

(6)  A.C.  resistance  of 
grid  to  filament  or  input 
circuit  of  tube. 


(a) 


or  a  resistance   inserted  in  the   negative  leg  of  the 
filament  may  be  employed  (6). 


FIG.  2. — To  keep  the  grid  of  an  amplifier  tube  negative 
(«)  Capacity  of  grid  to      either  a  gmall  battery  of  dry  ceUs  may  be  used  (fl) 

filament  under  static  con- 
ditions and  under  actual 
operating  conditions. 

All  of  the  above  quantities  have  been  fully  discussed  in  Chapter  VI,  and 
the  reader  will  do  well,  before  proceeding  with  the  study  of  this  chapter, 
to  go  over  the  fundamental  principles  of  three-electrode  tubes  as  outlined 
in  the  beginning  of  Chapter  VI.  The  fact  should  here  be  emphasized 
that  the  capacity  of  the  grid  to  filament,  while  small  under  static  con- 
ditions, may  attain  com- 
paratively large  values 
under  actual  operating 
conditions.  Again  the 
circuit  from  plate  to  fila- 
ment or  grid  to  filament 
is  made  up  of  a  resist- 


FIG.  3. — In  case  several  tubes  are  used  in  cascade  it  is 


ance  in  multiple  with  a 

possible  to  connect  all  filaments  in  series  and  connect  caPacity>  and>  wmle  ordl- 

the  leak  resistances  behind  the  filament  of  the  preced-  nanly  the   impedance   of 

ing  tube.     This  makes  the  grid  of  each  tube  negative  either   circuit    is    practi- 

with  respect  to  its  filament  by  an  amount  equal  to  the  cally  equal  to    its  resist- 

IR  drop  of  the  filaments.  anc6j     there     are      cageg 

when    the    frequency    is 

high  enough  to  make  the  impedance  much  less  than  the  resistance.  That  is, 
the  capacity  reactance  of  the  circuits,  shunting  the  resistance,  may  be 
low  enough  to  determine  the  impedance  of  the  path. 

Effect  of  External  Resistance  in  the  Plate  Circuit. — As  pointed  out 
in  Chapter  VI  the  function  of  a  triode  when  used  as  amplifier  is  to  make 


828  AMPLIFIERS  [CHAP.  XI 

available  in  the  external  plate  circuit  a  voltage  similar  to  that  impressed 
on  the  grid,  and  as  much  larger  as  feasible.  The  amount  of  increase 
depends  upon  the  MO  of  the  tube  used,  and  on  the  impedance  introduced 
in  the  plate  circuit. 

If  a  resistance  R  is  put  in  the  external  plate  circuit  the  total  impedance 
of  the  plate  circuit  is  RP-\-R.  The  magnitude  of  alternating  current  set 
up  in  the  plate  circuit  by  a  sine  voltage  Eg  acting  between  grid  and  fila- 
ment is  given  by 


and  this  alternating  current  flowing  through  the  resistance  R  gives  an 
available  voltage  in  the  plate  circuit  of 

r> 

(4) 


This  is  indicated  in  Fig.  4  and  experimental  curves  showing  how  the 
amplifying  power  of  a  tube  varies  with  the  value  of  R  used  are  given  in 
Fig.  181  of  Chapter  VI. 

It  is  evident  that  if  resistance  is  used  in  the  plate  circuit,  more  voltage 
must  be  supplied  by  the  B  battery  to  maintain  the  plate  voltage  at  its 

D 

proper  value.     Unless  this  is  done  the  expected  amplification  ^ 


does  not  increase  with  R  as  rapidly  as  might  be  expected  because  as  R 

is  increased  the  plate  voltage  (which 
is  equal  to  Eb—It>R)  decreases  and, 
as  pointed  out  on  page  425,  this  gives 
an  increase  in  Rp.  Hence  if  resist- 
ance  is  used  in  the  plate  circuit  of  an 
amplifying  tube  the  B  battery  e.m.f. 
must  be  considerabty  greater  than  rated 
plate  voltage  of  the  tube,  ordinarily 
two  or  three  times  as  much.  If  the 

FIG.  4.—  Amount  of  amplified  voltage  external  resistance  R  is  taken  equal 
with  resistance  in  plate  circuit.  ^  ^  tube  resistajlce  Rp  the  B  battery 

must    have    a    voltage    twice    as    great 
as  the  rated    plate   voltage   of  the   tube,  and   the    amount    of  voltage 

amplification  obtainable  is  ^. 

The  effect  on  the  amplifying  power  of  a  tube  of  having  the  grid  at 
different  potentials,  Ec,  is  well  brought  out  by  the  curves  of  Fig.  183, 
page  575.  It  is  there  seen  that  not  only  must  a  proper  plate  resistance 
be  used,  but  also  the  grid  must  be  at  a  proper  average  potential  if  the 
maximum  possible  amplification  is  to  be  obtained. 


USE  OF  REACTANCE   IN   PLATE   CIRCUIT 


829 


Effect  of  Reactance  in  the  Plate  Circuit. — If  we  use  in  the  plate  circuit, 
a  low-resistance  reactance,  instead  of  a  resistance,  the  amplifying  qualities 
of  the  tube  are  much  better.  Thus  if  we  put  in  series  with  the  plate, 
Z  =  R+juL,  we  shall  then  have  the  relation  shown  in  Fig.  5.  We  must 
have  from  Eq.  (2) 


and  hence  the  available  drop  in  the  external  circuit  is 

Z 


(5) 


It  is  to  be  pointed  out  here  that  R  and  L  are  the  alternating  current 

constants  of  coil  Z,  measured  under  the  conditions  which  obtain  in  the 

actual    use   of  the   coil;   i.e.,  R  and 

L    must    be    measured    in    an    a.c. 

bridge  (or  similar  scheme)  with  the 

frequency  and  magnitude  of  voltage 

to  which  the  coil  is   subjected  when 

used  in  the  tube  circuit.     Also  when 

these  measurements  are  made  there 

must    be    flowing    through    the    coil 

a  continuous  current    equal    to    the 

average    plate    current,    h.      These   FIG.  5.— Amount  of  amplified  voltage  with 

precautions    in    determining    Z    are  inductance  in  plate  circuit. 

not  necessary  if   an  air   core   coil  is 

used,  but  this  is  seldom  the  case;  generally  an  iron  core  coil  is  used. 

If  now  the  resistance  R  is  small  compared  to  Rp  and  coL  we  can  write 
the  voltage  amplification  of  the  tube  and  circuit  as 


The  voltage  amplification, 


EgHQ 

coL 


(6) 


may  be  made  nearly  equal  to  MO,  by  making  o>L  sufficiently  large  and  at 
the  same  time  the  B  battery  need  have  a  voltage  only  equal  to  the  actual 
voltage  of  the  tube  (on  the  assumption  that  the  resistance  of  the  coil  is 
negligible  compared  to  Rp). 

Classification  of  Amplifiers. — An  amplifier  generally  consists  of  two 
or  more  vacuum  tubes  so  arranged  that  the  varying  signal  voltage  is 
impressed  upon  the  grid  of  the  first  tube,  thus  producing  a  variation  of 
the  plate  current  in  this  tube;  this  varying  plate  current  is,  then,  made 


830 


AMPLIFIERS 


[CHAP.  XI 


to  produce  a  varying  voltage  between  the  grid  and  filament  of  the  second 
tube,  and,  similarly,  the  varying  voltage  is  relayed  from  the  second  to  the 
third  tube,  etc.,  until  the  plate  circuit  of  the  last  tube  is  reached,  wherein 
are  placed  the  telephone  receivers  or  any  other  device  used  for  making 
the  signals  readable.  From  this  brief  description  it  is  plain  that  the  signals 
must  be  "  repeated  "  from  one  tube  into  the  next.  Amplifiers,  either 
for  low-frequency  or  for  high-frequency,  are  divided  into  the  following 
classes,  according  to  the  arrangement  used  for  "  repeating." 

(1)  Transformer-repeating  amplifiers. 

(2)  Resistance-repeating  amplifiers. 

(3)  Inductance-repeating  amplifiers. 


Tube  1 


Tube  2 


Tube  3 


FIG.  6. — A  transformer  repeating  amplifier  for  audio-frequencies. 

A  tube,  together  with  all  co-acting  apparatus,  is  known  in  amplifier 
work  as  a  "stage  of  amplification  ";  and  an  amplifier  consisting  of  n 
tubes  is  known  as  an  ?i-stage  amplifier. 

The  two  terminals  of  the  amplifier  upon  which  the  incoming  signal 
voltages  are  impressed  are  known  as  the  "input  "  terminals,  while  the  two 
terminals  across  which  exist  the  amplified  signal  voltages  are  known  as 
the  "  output  "  terminals. 

Transformer-repeating  Amplifiers. — These  are  generally  used  for 
amplifying  audio-frequency  signals  and  we  will  discuss  their  principle  of 
operation  by  referring  to  Fig.  6,  which  is  intended  to  represent  an  audio- 
frequency transformer-repeating,  three-stage  amplifier. 

The  audio-frequency  varying  voltage  is  connected  at  D  and  stepped 
up  by  means  of  the  transformer  T,  after  which  it  is  applied  between  the 
grid  and  filament  of  the  first  tube;  this  produces  a  corresponding  vari- 
ation of  the  plate  current  of  Tube  1.  The  varying  current  flowing  through 
the  primary  PI  of  the  transformer  T\  induces  an  e.m.f.  in  the  secondary 


TRANSFORMER-REPEATING  AMPLIFIER  831 

Si.  This  e.m.f.  is  applied  to  the  grid  and  filament  of  the  second  tube, 
and  thus  the  varying  signal  voltage  is  "  repeated  "  from  the  first  into  the 
second" tube  and  finally  from  the  second  into  the  third  tube,  the  varying 
plate  current  of  which  is  caused  to  affect  the  telephone  receivers. 

It  will  be  at  once  apparent  that  in  an  arrangement  of  this  kind,  while 
each  tube  itself  is  always  amplifying,  the  advantage  of  this  may  be  lost 
by  a  poor  repeating  device.  The  object  to  be  gained  is,  of  course,  to  make 
the  varying  voltage  between  the  grid  and  filament  of  each  tube  greater 
than  for  the  preceding  tube.  This  requires  correct  proportioning  of  the 
primary  and  secondary  of  the  repeating  transformers  T\,  Tz\  otherwise 
the  grid-filament  voltage  of  the  second  tube  may  be  but  slightly  larger, 
or  even  smaller,  than  for  the  first  tube.  This  is  not  an  unusual  occurrence 
in  poorly  designed  "  amplifiers." 

We  will  study  the  repeating  action  from  the  first  into  the  second  tube. 
For  the  sake  of  simplicity  we  may  assume  that  the  repeating  transformer 
has  neither  leakage  inductance  nor  resistance  and  also  that  the  mag- 
netizing current  is  zero;  this  is  equivalent  to  saying  that  the  transformer 
is  ideal.  In  so  far  as  the  alternating  current  relations  of  the  circuit  are 
concerned,  such  a  transformer  may,  if  the  secondary  is  loaded  by  means 
of  a  non-inductive  resistance,  be  replaced  by  a  fictitious  resistance  placed 
in  the  primary  and  equal  to  the  secondary  circuit  resistance  divided  by 
the  square  of  the  ratio  of  transformation.  Let: 

Effi  =  effective  value   of  alternating  voltage  between  grid 

and  filament  of  Tube  1; 
E02  =  effective  value   of  alternating  voltage   between  grid 

and  filament  of  Tube  2; 
RPi  =  plate-filament  a.c.  resistance  of  Tube  1; 
Rg2  =  grid-filament  a.c.  resistance  of  Tube  2; 
MO  =  amplifying  constant  of  Tube  1; 
V=  effective  value  of  alternating  voltage  across  primary 

of  repeating  transformer,  T\  ; 

n=  repeating  transformer  ratio  expressed  as  the  ratio  of 
secondary  to  primary  voltage. 

The  above  quantities  are  illustrated  in  Fig.  7.  The  action  of  Eg\  upon 
the  plate  current  of  Tube  1  is  the  same  as  if  an  alternating  voltage  equal 
to  Mo#fi  had  been  impressed  upon  the  plate  circuit,  in  addition  to  the 
battery  e.m.f.  This  alternating  voltage  MO^I  is  impressed  upon  a  circuit 
which  may  be  simplified  as  shown  in  Fig.  8  and  consisting  of  the  plate 
resistance  of  the  first  tube  in  series  with  the  equivalent  resistance  of  the 
repeating  transformer  transferred  to  the  primary.  This  is  probably  the 
simplest  way  to  treat  the  problem  when  the  coupling  between  the  primary 
and  secondary  of  the  transformer  is  tight  and  the  load  circuit  of  the  trans- 


832 


AMPLIFIERS 


[CHAP.  XI 


former  is  resistive  only.  For  the  more  general  case,  i.e.,  leaky  trans- 
former and  reactive  secondary  load,  the  action  of  the  tube  is  best  analyzed 
by  using  for  the  external  impedance  in  the  plate  circuit  the  resistance  and 
reactance  of  the  primary  of  the  transformer  as  calculated  from  the  general 
equations  given  on  pages  86-87. 

From  Fig.  8  the  following  equation  is  easily  derived: 


ri2RPl+Rg, 


.     .     •     (7) 


•01 


FIG.  7. 


FIG.  8. 


FIG.  7. — Circuit  detail  of  the  amplifier  shown  in  Fig.  6. 

FIG.  8. — Under  ideal  conditions  (transformer  requiring  no  magnetizing  current,  having 
zero  internal  impedance,  and  secondary  load  resistive  only)  the  circuit  of  Fig.  7 
may  be  replaced  by  the  one  above. 

The  voltage  between  grid  and  filament  of  the  second  tube  is  equal  to  the 
voltage  across  the  transformer  primary  multiplied  by  the  ratio  of  trans- 
formation; thus: 

.._*,  E> 

5«        (8) 

(9) 


and 


ES 

En 


Eq.  (9)  may  be  written  as : 


where 


(10) 


It  will  be  noted  from  Eq.  (10)  that  the  ratio  -rr  varies  directly  with 

the  amplifying  constant  of  the  first  tube  and  it  also  varies  in  a  complex 

manner  with  RgjRp]  and  with  n.     It  will  further  be  noted  that: 

/-> 

1st.  If  HQ  and  n  are  kept  constant  and  the  ratio  -—-  increased  from 

/tn, 


TRANSFORMER-REPEATING  AMPLIFIER  833 


a  low  value,  then  -=p  will  constantly  increase  towards  the  limiting  value 
is* 

JT> 

fj^n  which  will  be  theoretically  reached  when  ~=~  =  oo  . 


2d.  If  no  and  -—^  are  kept  constant  and  the  value  of  n  changed  then 
Kpi 

ET 

^r1  may  be  shown  to  have  a  maximum  when: 


(11) 


It  follows  that  the  resistance  R02  should  be  made  as   high  as  possible, 
and  that,  once  this  has  been  done,  a  transformer  should  be  chosen  with 


a  transformation  ratio  about  equal  to  \-^-     It  is  not  always  possible 

\  tin 

adequately  to  satisfy  this  latter  condition,  as  will  be  more  fully  explained 
later.  The  resistance  Rgt  is  made  high  by  preventing  the  potential  of 
the  grid  of  Tube  2  from  ever  becoming  positive,  for,  in  this  case,  the  grid- 
filament  resistance  is  theoretically  infinite;  this  is  accomplished  by  keep- 
ing the  grid  at  a  negative  potential  by  a  suitably  connected  battery,  or 
by  any  of  the  circuit  arrangements  already  explained  on  page  827.  Prac- 
tically, on  account  of  gas  in  the  tube  and  the  leakage  from  grid  to  filament 
outside  of  the  tube,  the  grid-filament  resistance,  while  very  large,  is  at 
the  most  of  the  order  of  one  million  to  10  million  ohms,  and  may  in  some 
cases  be  as  low  as  a  few  hundred  thousand  ohms.  For  the  ideal  value 

ET 

of  n2  the  ratio  •=?  would  be  found  by  substituting  (11)  in  (10);  thus: 


If  the  tubes  used  for  the  various  stages  of  amplification  are  similar,  which 
is  almost  always  the  case,  the  transformers  may  have  the  same  ratio 
throughout. 

The  results  indicated  by  Eqs.  (11)  and  (12)  have  been  obtained  on  the 
basis  of  ideal  transformers  having  neither  leakage  inductance  nor  coil 
resistance  and  requiring  no  magnetizing  current.  The  effect  of  all  of 
these  in  an  actual  transformer  would  be  such  as  to  alter  the  best  value 
of  the  transformation  ratio,  and,  more  than  this,  to  diminish  the  ideal 
ratio  EgjE0l  as  given  by  Eq.  (12).  The  leakage  inductance  and  coil 
resistance  of  the  transformer  can  be  made  quite  small  and  negligible  as 
compared  with  the  resistance  Rfft  and  their  effect  will,  therefore,  be  but 
small.  On  the  other  hand,  it  is  very  important  to  make  the  magnetizing 
current  very  small,  or,  in  other  words,  to  make  the  no-load  reactance  of 


834  AMPLIFIERS  [CHAP.  XI 

the  transformer  primary  very  high.  This  will  be  made  clearer  by  a  study 
of  the  diagram  Fig.  9,  which  is  similar  to  Fig.  8,  with  the  exception  of  the 
introduction  of  XQ  in  multiple  with  Rgjn2,  where:  XQ  —  reactance  of 
transformer  primary  at  no  load. 

\       A  resistance  should,  in  the  above  diagram,  be  inserted  in  series  with 
XQ  to  represent  the  core  losses,  but  we  have  omitted  it  for  the  sake  of 
R  simplicity    and    also    because    in    such 

~^r  transformers  the  core  losses  are  made 

p__  /mvwwvWMA  negligibly  small. 


Ji-JWVWWWWVV — y        x          1^— 
iMaUMMMisJ 


•01 


The  diagram  shows  that  XQ  is  in 
multiple  with  Rgjn2  and  therefore 
diminishes  the  equivalent  impedance 
of  the  circuit  H-P]  if,  then,  XQ  were 
very  low  the  voltage  drop  across  H-P 

and,   therefore   the    secondary  voltage 
FIG.  9. — In  order  to  take  care  of  the    ,  ^  »  ,,  ,  ,,       T     .     . 

magnetizing  current  of  the  trans-  <f*>  would  be  small.  It  is  important, 
former  the  diagram  of  Fig.  8  must  be  then,  to  make  XQ  as  high  as  possible, 
changed  as  above,  the  value  of  X0  or,  in  other  words  the  primary  must 
being  equal  to  the  primary  reactance  have  a  very  large  number  of  turns, 
with  secondary  open,  There  is  a  point,  however,  beyond 

which  it   is   uneconomical    to    increase 

the  value  of  XQ,  since  the  gain  in  amplification  is  too  small  to  make  it 
worth  while.  To  show  this  we  have  worked  out  the  theoretical  curves 
of  Fig.  10,  after  having  assumed  the  following: 

MO  =6, 

#P  =  10,000. 

For  Rot  two  different  values  were  chosen,  i.e. : 

Rn  =  250,000  ohms  and  R02  =  1,000,000  ohms. 

For  RK  of  250,000  ohms  the  best  transformer  ratio  for  an  ideal  trans- 

/250  000 
former  is  found,  from  Formula  (11),  to  be:  A]  i n  QAQ  =^  anc*' 


I  000  000 
for  R02  of  1,000,000  the  best  transformer  ratio  would  be  \    inooo     =1Q' 

From  Formula  (12)  we  have: 

Maximum  possible  value  of  -^  for  Rg,  of  250,000  =6  Xf  =  15. 


Maximum  possible  value  of        for  /?,,  of  1,000,000  =6  X-1/  =30. 


TRANSFORMER-REPEATING   AMPLIFIER 


835 


The  points  on  the  curves  have  been  plotted  by  assuming  different 
values  of  XQ  and  then  obtaining  the  voltage  across  H-P  and  also  the 
secondary  voltage  Eff2,  after  which  E6JE0l  was  computed.  The  assump- 
tion was  made  that  the  transformer  had  no  leakage  inductance,  no  coil 
resistances,  and  no  core  losses.  Curves  were  drawn  for  two  different 


/(A)--Rj 


O-- 


(D) 


ti6 


trans 


/*o 


tance 


.C.  Resistar 


250,000  ohms 


=  1,000,000  dhms 


(D 


(C 


6          8         10        12        14        16         18        20        22        24        26        28 
No-load  reactance  of  repeating  transformer  primary  in  10*ohms 


30 


FIG.  10. — Calculated  values  of  voltage  amplification  using  transformers  of  different 
ratios  and  two  different  values  of  input  circuit  resistance  of  the  second  tube.  The 
curves  show  the  effect  of  varying  the  no-load  reactance  of  the  primary  of  the  trans- 
former abcissa?  being  no-load  reactance  in  thousand  ohms. 


ratios  of  transformation,  i.e.,  4  and  5  for  Rfft  of  250,000  and  3  and  4  for 
R0z  of  1,000,000  ohms.     They  show: 

1st.  That  for  low  values  of  XQ  the  ratio  Efft/Efl  may  be  very  small, 
even  smaller  than  the  amplifying  factor  of  the  tube,  which  is  in  this  case 
6.  Thus,  a  transformer  with  low  no-load  reactance  might  make  the  result 
of  two  tubes  no  better,  or  even  worse,  than  for  one  tube  alone. 


836  AMPLIFiEKS  [CHAP.  XI 

2d.  That  for  RC2  of  106  ohms  the  ratio  of  EgjESl  is  larger  than  for 
Rg2  of  250,000  ohms,  for  the  same  transformer  ratio,  even  though  the  value 
of  n  used  for  RS2  of  250,000  ohms  is  much  nearer  the  ideal  value  than  for 
R0z  of  106  ohms. 

jfr  3d.  Beyond  certain  values  of  XQ  the  ratio  EgJEgi  does  not  increase 
much  with  increase  of  XQ.  Not  only  is  it  of  no  advantage  to  increase 
the  reactance  XQ  above  a  certain  amount,  but  it  is  actually  disadvan- 
tageous. The  XQ  is,  of  course,  increased  by  increasing  the  cross-section 
of  the  core  or  the  number  of  turns  in  the  primary  winding.  The  former 
of  these  expedients  is  objectionable  because  it  increases  the  space  require- 
ments. As  regards  increasing  the  number  of  primary  turns,  it  must  be 
noted  that,  if  this  is  done,  the  secondary  -turns  must  be  proportionately 
increased  if  the  ratio  of  transformation,  n,  is  to  be  constant.  Now,  the 
higher  the  number  of  transformer  turns  the  higher  become  the  internal 
resistance  and  leakage  reactance  of  the  transformer,  which  have  so  far 
been  neglected  in  our  discussion. 

A  high  internal  transformer  impedance  may  produce  a  large  internal 
drop  due  to  the  "  load  "  attached  to  secondary,  i.e.,  the  grid-filament 
resistance  and  reactance  of  the  tube  into  which  the  transformer  is  repeat- 
ing, and  also  the  internal  distributed  capacity  of  the  secondary  winding 
itself;  the  final  result  would  be  that  the  voltage  applied  to  the  grid-filament 
might  be  far  less  than  that  calculated  on  the  basis  of  negligible  internal 
transformer  drop.  This  may  be  summed  up  by  stating  that,  for  a  given 
frequency,  the  higher  the  number  of  turns  used  the  more  does  the  ratio 
of  terminal  voltages  (secondary  to  primary)  depart  from  the  turn  ratio 
n,  being  only  a  fractional  part  of  n.  In  fact,  it  is  possible  to  increase  the 
transformer  turns  to  such  an  extent  (more  especially  if  the  ratio  be  high, 
say:  10  to  1),  that  the  terminal  voltage  of  the  secondary  (when  used  in 
the  tube  circuit)  is  less  than  the  voltage  impressed  upon  the  primary  winding. 
The  above  phenomenon  may  take  place  if  the  number  of  turns  is  kept 
constant  and  the  frequency  raised.  In  practice  the  value  of  XQ  for  an 
amplifier  to  be  used  at  constant  audio-frequency  is  made  equal  to  about 
once  or  twice  the  value  of  the  plate-filament  a.c.  resistance. 

4th.  The  higher  the  ratio  of  transformation  the  greater  the  ampli- 
fication. In  connection  with  this  it  will  be  noted,  however,  that  a  point 
may  be  reached  beyond  which  it  is  uneconomical  to  increase  the  ratio, 
since  the  gain  in  amplification  is  too  small,  as  for  example  in  the  case  of 
curves  A  and  B  for  transformer  ratios  of  4  and  5  respectively.  As  a  matter 
of  fact  if  we  consider  that,  for  a  constant  number  of  primary  turns,  the 
increase  in  ratio  is  obtained  by  increasing  the  number  of  secondary  turns 
and  that  simultaneously  the  internal  impedance  of  the  transformer  and 
effect  of  the  distributed  capacity  of  the  secondary  are  increased,  it  will  be 
apparent  that,  due  to  the  large  internal  drop,  the  voltage  across  the  sec- 


TRANSFORMER-REPEATING  AMPLIFIER 


837 


ondary  may  be  smaller  for  a  high  than  for  a  low  ratio  of  transformation. 
This  effect  has  already  been  pointed  out  in  connection  with  the  value 
of  Xo  and  plays  such  an  important  part  in  connection  with  the  trans- 


spuo  aAisssoong  OJA.&  JO  sit?i^aa^od: 


formation  ratio  that  it  has   been   found  advisable,  in  practice,  to  keep 
the  value  of  this  ratio  below  about  4  or  5. 

By  means  of  the  curves  of  Fig.  10  we  have  plotted  another  set  of  curves 
which  is  given  as  Fig.  11,  and  which  shows  how  the  frequency  affects  the 


838  AMPLIFIERS  [CnAP.  XI 

ratio  of  E02/Egi  for  different  values  of  no-load  inductance  of  the  primary 
of  the  repeating  transformer.  The  values  chosen  for  this  inductance  are 
2,  5,  10  henries.  The  curves  bring  out  the  following  very  important  facts: 

1st.  For  every  value  of  inductance  there  is  a  frequency,  below  which 
the  amplifying  action  of  the  tube  and  transformer  varies  very  widely, 
and  above  which  the  amplifying  action  varies  but  little. 

2d.  If  the  frequency  is  too  low  the  amplifying  action  may  be  very 
poor;  hence  an  amplifier  may  work  very  well  on  comparatively  high 
audio-frequency  and  fail  to  work  on  lower  frequencies. 

3d.  If  the  amplifier  is  to  be  used  over  a  wide  range  of  frequencies, 
as  in  the  case  of  amplification  of  telephone  or  radiophone  currents,  then 
it  is  extremely  important  to  choose  a  value  of  transformer  inductance 
such  that  the  amplifying  action  will  be  nearly  the  same  over  the  entire 
range  of  frequencies,  otherwise  the  low-frequency  components  would  suf- 
fer, and  speech  would  thereby  be  distorted.  Thus,  assuming,  as  is  gener- 
ally done,  that  the  speech  frequencies  vary  over  an  average  range  of  300 
to  2000  or  more  cycles  per  second,  an  inductance  of  10  henries  would, 
in  our  case,  be  sufficiently  high  to  amplify  all  frequencies  equally  well, 
provided  that  the  internal  leakage  reactance  and  capacity  do  not  come 
into  the  question;  any  higher  inductance  than  this  would  not  produce 
sufficient  gain  either  in  amplification  or  in  equality  of  amplification  for 
different  frequencies  to  warrant  its  use,  in  fact  due  to  its  high  internal  drop 
it  would  probably  make  the  amplification  of  the  higher  frequencies 
poorer. 

4th.  Much  greater  amplification  is  obtained  at  nearly  all  frequencies 
and  nearly  all  values  of  no-load  primary  inductance  for  R02  of  1,000,000 
ohms  than  for  R02  of  250,000  ohms. 

Our  analysis  shows  that,  while  theoretically,  the  ratio  of  transfor- 
mation should  be  equal  to  VRg2/R6l  and  the  value  of  Xo  should  be  very 
large,  yet,  practically,  the  transformation  ratio  should  not  be  made  much 
larger  than  4  or  5  and  XQ  should  not  be  much  larger  than  once  or  twice 
the  plate-filament  resistance.  Where  the  amplifier  is  to  be  used  for  tele- 
phone currents  it  is  important  that  the  primary  no-load  inductance  of 
the  repeating  transformer  be  chosen  high.  In  every  case  a  large  grid- 
filament  resistance  is  effective  in  producing  large  amplifications,  and 
this  condition  should  always  be  striven  for  by  preventing  the  grid  from 
assuming  a  positive  potential. 

In  the  case  of  the  first  transformer  T  (see  Fig.  6)  it  may  be  shown  by 
a  method  similar  to  that  used  for  the  other  transformers  that  the  ideal 
ratio  of  transformation  is  given  by: 


TRANSFORMERS   FOR  LOW-FREQUENCY  AMPLIFIER  830 

where  S  =  ratio  of  secondary  to  primary  voltage  for  transformer  7T; 

R  =  Resistance   connected  in  series  with  the  primary  of 
transformer  T. 

The  resistance  R  may  be  that  of  the  plate-filament  circuit  of  some  other 
tube  or  of  a  telephone  line  or  anything  else  which  may  be  in  series  with 
the  transformer  primary. 

Again,  as  in  the  case  of  the  other  transformers,  the  no-load  inductance 
of  the  primary  should  be  high,  and  the  ratio  S  should  not  be  made  so  high 
as  to  permit  the  internal  capacity  of  the  transformer  to  have  much 
effect. 

Construction  of  Transformers  for  Low-frequency  Amplifiers. — In 
order  to  make  the  no-load  reactance  of  the  primary  of  the  transformer 
high  it  should  be  constructed  with  a  good  quality  of  iron  suffering  but 
small  losses  and  having  high  permeability.  The  flux  leakage  of  the 
primary  and  secondary  coils  should  be  very  low. 

The  main  difficulty  in  connection  with  a  transformer  of  this  type 
is  to  so  arrange  the  windings  that  they  will  have  as  little  distributed 
capacity  as  possible.  In  view  of  the  necessity  of  saving  space  the  large 
reactances  of  the  coils  are  obtained  by  the  use  of  a  very  large  number  of 
layers  of  fine  wire  placed  on  a  comparatively  small  core;  hence  the  dif- 
ficulty of  making  the  capacity  between  layers  small.  Ordinarily  sheets 
of  insulation  are  placed  between  adjacent  layers  so  as  to  make  the  distance 
larger  than  would  otherwise  be  the  case,  and  thus  diminishing  the 
capacity.1 

It  will  be  readily  understood  that  a  large  capacity  connected  either 
across  the  secondary  or  across  the  primary  or  both  lowers  the  no-load 
impedance  of  the  transformer  and  reduces  amplification.  As  long  as  the 
internal  capacity  of  the  transformer  is  small  compared  to  the  capacity  of 
the  input  circuit  to  which  the  secondary  is  connected,  it  will  be  of  little 
importance  in  determining  the  behavoir  of  the  amplifier. 

Impedance  of  Telephone  Receivers. — The  receivers  used  in  the  plate 
circuit  of  the  last  tube  of  the  amplifier  should  be  suitably  chosen.  The 
impedance  of  a  telephone  receiver  is  made  up  of  the  following  four  com- 
ponents : 

1st.  The  static  reactance. 
2d.    The  static  effective  resistance. 
3d.    The  motional  reactance. 
4th.  The  motional  resistance. 

The  first  two  components  are  due  to  the  constants  of  the  electric  and 
magnetic  circuits  of  the  receiver  and  the  losses  taking  place  therein  and 

1  In  case  the  secondary  coil  is  wound  in  layers,  the  end  of  the  outside  layer  should 
connect  to  the  grid  of  the  next  tube,  not  the  end  of  the  inside  layer. 


840 


AMPLIFIERS 


[CHAP.  XI 


are  the  effective  reactance  and  resistance  measured  with  the  diaphragm 
"  locked." 

The  motional  reactance  and  resistance  are  produced  by  the  motion 
of  the  diaphragm  and  are  to  be  added  to  the  static  reactance  and  resist- 
ance respectively.  It  is  plain  that  the  motional  resistance  is  the  resist- 


8000 


5200 
4800 
4400 

14000 

I 

I  3600 


|  3200 


_Cha 


actei 


istic 


^T—f-Resistance 


ics  of  telephone  receiver 
Diaphragtn  free;  to  movie 


Diaphragm  clamped  fast 


Reac 


700 


900  1000  1100 

Cycles  per  second 


1200 


1300 


1400 


FIG.  12. — Resistance  and  reactance  of  such  a  receiver  as  is  used  in  radio  work  as  a 
function  of  the  frequency;  one  set  of  curves  gives  the  characteristics  with  dia- 
phragm free  to  move  and  the  other  with  it  clamped  tight. 


ance  equivalent  of  the  power  expended  in  moving  the  diaphragm  to  and 
fro,  part  of  which  is  useful  in  producing  sound;  in  other  words,  for  a  cer- 
tain receiver,  the  greater  the  motional  resistance  the  greater  will  be  the 
receiver  response  to  a  certain  value  of  incoming  alternating  current.  The 
value  of  this  resistance  varies  with  the  frequency  and  is  a  maximum  at 
about  900  to  1000  cycles  per  second.  Curves  are  given  in  Fig.  12,  showing 
the  relation  between  frequency  and  resistance  and  reactance  of  a  receiver 
with  the  diaphragm  locked  and  with  the  diaphragm  vibrating.1  In  view 

1  It  must  be  pointed   out  that  where  the  motional  resistance  is  negative,  the  dia- 
phragm is  not  acting  like  a  generator,  giving  off  electric  power  due  to  its  motion;   the 


IMPEDANCE   OF   TELEPHONE   RECEIVER  841 

of  the  many  components  of  the  impedance  of  a  receiver  and  their  variation 
with  the  frequency  it  is  difficult  to  lay  down  any  set  rules  for  the  choice 
of  a  receiver.  We  may,  however,  simplify  matters  by  first  assuming  that 
we  are  dealing  with  a  receiver  having  nothing  but  motional  resistance. 

Let  Rm  =  motional  resistance  of  receiver; 

Rp  =  plate-filament  a.c.  resistance  of  last  tube; 
HoEg=  effective  value  of  alternating  voltage  impressed  upon 

the  plate  circuit  of  the  last  tube; 
Ip=  effective  value  of  the  alternating  current  component 

in  the  plate  circuit  of  the  last  tube; 
Pm=  power  expended  in  Rm. 
Then 


Rm+Rp 

and 


o 


For  maximum  response  in  the  receivers  the  power  (Pm)  expended  in  the 
motional  resistance  should  be  a  maximum,  and  since  the  expression  of 
Eq.  (14)  is  a  maximum  when  Rm  =  Rp,  we  conclude  that  if  the  receiver 
had  nothing  but  motional  resistance  then  maximum  response  would  be 
obtained  by  making  the  motional  resistance  equal  to  the  plate-filament 
a.c.  resistance  of  the  last  tube. 

In  the  case  of  a  practical  receiver  containing  motional  and  static  resist- 
ance and  reactance  it  is  apparent  that  the  larger  we  make  the  number 
of  turns  of  copper  wire  the  more  we  increase  all  the  components  of  the 
impedance,  including  the  motional  resistance,  and  the  greater  is  likely 
to  be  the  receiver  response.  It  is,  however,  difficult  to  determine  theo- 
retically how  far  we  should  go  on  increasing  the  number  of  turns  and  the 
total  impedance.  In  practice,  a  receiver  is  generally  chosen  whose 
total  impedance  is  about  equal  to  the  a.c.  resistance  from  plate  to 
filament. 

Connections  of  Transformer-repeating  Low-frequency  Amplifiers 
for  the  Reception  of  Damped  and  of  Undamped  Waves.  —  The  diagram 
of  Fig.  6,  page  830,  shows  in  a  schematic  manner  a  low  frequency  trans- 
former repeating  amplifier  without  any  connections  to  any  receiving 
apparatus.  Fig.  13  shows  how  such  an  amplifier  would  be  connected 
to  another  tube  for  the  reception  of  damped  waves  or  of  radiophone 

negative  motional  resistance  merely  signifies  that  the  diaphragm  in  motion  (in  the  right 
motional  phase)  absorbs  less  power  as  eddy  currents  and  hysteresis  than  if  it  is  locked 
and  so  unable  to  move. 


842 


AMPLIFIERS 


ICHAP.    XI 


messages.     Fig.  14  shows  a  crystal  detector  receiver  for  damped  waves 
and  the  manner  in  which  it  would  be  attached  to  the  amplifier,  while 


Fig.  15  shows  an  autodyne  tube  receiver  for  undamped  waves  and  the 
manner  in  which  it  would  be  connected  to  the  amplifier.     Considering 


CONNECTION   OF  AMPLIFIER  TO   RECEIVER 


843 


Fig.  13  it  will  be  noted  that  the  rectifying  tube  is  connoc'ed  in  the  standard 
manner  already  discussed  in  Chapter  VI,  page  451,  with  a  grid  condenser 
and  leak  resistance,  and  that, 
in  this  case,  the  telephone  re- 
ceivers, which  would  ordinarily 
be  connected  to  the  points  Q 
and  S,  have  been  replaced  by 
the  amplifier.  The  condenser 
C  is  of  a  fairly  large  capacity 
(5000  fjLfjf  or  more)  and  is  used 
for  the  purpose  of  carrying 
whatever  high-frequency  cur- 
"rents  flow  in  the  plate  circuit 
of  the  rectifying  tube;  these 
high-frequency  currents  flow 
readily  through  the  low  im- 
pedance which  the  condenser  jrIG.  14.— How  a  crystal  detector  set  would  be 
C  has  at  high-frequency,  while,  connected  to  the  amplifier, 

on  the  other  hand,  the  audio- 
frequency currents  which  are  to  be  amplified  take  the  path  of  the  primary 
of  the  transformer  T.     As  a  matter  of  fact  the  repeating  transformers 
such  as  T,  T\,  T2,  have  such  a  high  distributed  capacity,  on  account  of 


To  Points  Q  &  S 
of  Amplifier 


To  Points  Q  &  S 
of  Amplifier 


FIG.  15. — How  an  autodyne  tube  receiving  continuous  wave  signals  would  be  connected 

to    the   amplifier. 

the  very  large  number  of  layers  of  wire  enclosed  in  a  small  space,  that 
the  by-pass  capacity  C  may  often  be  dispensed  with,  in  which  case  the 
distributed  capacity  of  transformer  T  carries  the  high-frequency  currents. 


844  AMPLIFIERS  [CHAP.  XI 

The  amplifier  shown  in  Fig.  13  has  batteries  KI,  K^  K%  in  series  with 
the  grids  for  the  purpose  of  keeping  them  at  an  average  negative  poten- 
tial; it  will  also  be  noted  that  a  single  battery  (A?)  is  being  used  for  the 
filaments  of  all  the  amplifying  tubes,  and  that  the  battery  #2  feeds  the 
plates  of  all  the  amplifying  tubes.  Instead  of  using  the  grid  batteries 
KI,  fa,  KZ  the  lower  ends  of  the  secondaries  of  the  repeating  trans- 
formers may  be  connected  to  the  filament  battery  circuit  at  a  point  of 
suitable  negative  potential.  This  has  been  discussed  on  page  827  and 
is  exemplified  in  the  amplifier  circuit  of  Fig.  16,  page  845.  Figs.  14  and  15 
hardly  need  any  explanation  and  show  in  every  case  that  the  amplifier 
is  connected  in  place  of  the  telephone  receivers. 

Transformer-repeating  Amplifiers  for  High  Frequencies. — These  are 
similar  to  the  amplifiers  for  audio  frequency  with  the  exception  of  different 
electrical  constants  for  the  transformers,  made  necessary  by  the  use  of 
radio  frequencies.  A  diagram  is  given  in  Fig.  16  showing  a  three-stage 
high-frequency  transformer-amplifier  connected  for  the  reception  of 
undamped  waves.  It  will  be  noted  that  the  grid  of  the  first  amplifying 
tube  is  connected  directly  across  the  receiving  tuning  condenser.  Q  and 
S  are  the  input  terminals  of  the  amplifier  while  Qi  and  Si  are  the  output 
terminals;  the  latter  are  shown  connected  to  an  autodyne  rectifying  tube, 
and  the  telephone  receivers  are  placed  in  the  plate  circuit  of  the  rectify- 
ing tube.  The  grids  are  maintained  at  an  average  negative  potential 
by  making  use  of  proper  resistances  in  series  with  the  negative  sides 
of  the  filaments.  If  grid  batteries  should  be  used  instead  they  should 
be  connected  on  the  lower  side  of  the  secondaries  of  the  repeating  trans- 
formers; if  connected  next  to  the  grid  they  will  increase  the  free  capacity 
of  the  grid  connection  and  thus  reduce  to  some  extent  the  voltage  impressed 
on  the  grid  itself. 

This  type  of  amplifier  is  not  a  very  efficient  one,  and,  in  fact,  we  might 
say  that  it  is  almost  impossible  to  construct  an  efficient  amplifier  for  very 
high  frequencies.  We  will  discuss  the  main  features  and  difficulties 
encountered  in  this  amplifier,  and  will  find  later  that  these  difficulties 
exist  in  all  types  of  high-frequency  amplifiers. 

The  repeating  transformers  Tit  T^  T-3  are  generally  constructed  with- 
out any  iron,  in  order  to  prevent  the  excessive  eddy  current  and  hysteresis 
losses  which  would  take  place  at  radio  frequencies. 

The  optimum  electrical  constants  of  the  transformers  cannot  be  derived 
on  the  same  basis  as  for  the  repeating  transformers  of  the  low-frequency 
amplifiers  for  the  reason  that  the  high-frequency  transformers  do  not 
approach,  even  to  a  small  extent,  the  ideal  transformer  without  leakage. 
Consider  the  plate. and  grid  circuits  of  two  adjacent  amplifying  tubes  as 
represented  in  Fig.  17.  Assume,  for  the  sake  of  simplicity,  that  the  grid 
takes  no  current,  or,  in  other  words  that  its  resistance  is  infinite.  We  will 


TRANSFORMER  AMPLIFIERS   FOR  HIGH   FREQUENCY 


845 


first  discuss  the  action  of  the  transformer  without  considering  either  the  dis- 
tributed capacity  of  the  coils  LI  and  Lo  or  the  capacity  of  the  grid-filament 


1 — ^mm^ 


circuit  of  the  second  tube;  all  these  capacities  play  a  very  important  part 
in  the  operation  of  the  amplifier  and  will  be  taken  into  consideration  later. 


846 
Let 


AMPLIFIERS 


[CHAP.  XI 


/io  =  amplifying  constant  of  first  tube ; 
En  =  alternating  grid  voltage  of  1st  tube ; 
Egt  =  alternating  grid  voltage  of  2d  tube; 

Ip=  alternating  component  of  plate  current  of  1st  tube; 
co  =  angular  velocity  of  radio  frequency  currents ; 

M  =  mutual  inductance  between  LI  and  L2; 

k  =  coefficient  of  coupling  between  LI  and  L2 


FIG.  17. — Circuit  detail  of  the  high-frequency  transformer. 

Since  the  circuit  of  L2  is  assumed  of  infinite  impedance  it  follows  that 
E^  is  equal  to  the  e.m.f.  induced  in  L2;  or 


but 
therefore 


gJc  V  Z/lZ/2 


and 


(15) 


The  ratio  E02/Egi  varies  directly  with  k  and  A/L2  but  it  varies  in  a  com- 
plex manner  with  LI.  If  all  other  quantities  are  kept  constant  and  LI 
only  varied,  it  may  be  shown  that  EgjE^  is  a  maximum  when 

«Li=#p (16) 

If 

RP  =  10,000  ohms  (previously  assumed  value) 
and 

co  =3X106  (about  600  meters  wave-length) 

then,  for  maximum  value  of  Eg2/Egi, 
10,000  X106 


3X106 


=  3300  microhenries, 


TRANSFORMER  AMPLIFIERS  FOR  HIGH   FREQUENCY 


847 


Tube  1 


Tube  2 


An  inductance  of  3300  microhenries  cannot  be  constructed  to  have  an 
internal  capacity  which  is  negligible  at  a  frequency  of  500,000  cycles  per 
second,  especially  if  the  space  requirements  prohibit  much  space  between 
layers.  Even  if  such  internal  capacity  is  very  small,  say,  20  ///*/,  the 
natural  wave-length  of  the  coil  would  be  given  by: 

natural  wave-length  of  coil  LI  =  1. 885  X  V3300  X  20  =485  meters. 

In  other  words,  the  coil  whose  inductance  is  LI  may  have  a  natural  wave- 
length within  the  range  of  wave-lengths  of  the  signals  received  by  the 
amplifier.  It  follows  that  when 
the  wave-length  of  the  incoming 
signal  is  equal  to  the  natural  wave- 
length of  the  coil  LI,  then  the  coil 
will  act  like  a  high  resistance :  this 
equivalent  high  resistance  of  the 
coil,  connected  in  series  with  the 
smaller  plate  resistance,  Rp,  will 
cause  the  changing  iJLoEgi  to  be 
impressed  practically  wholly  upon 
the  coil  LI,  and  hence  the  repeat- 
ing action  from  LI  into  L%  will 
be  very  good  at  the  wave-length 
under  consideration.  For  other 
wave-lengths  than  that  equal  to 


FIG.  18. — When  receiving  fixed  wave-lengths 
the  use  of  a  condenser  C\  in  parallel  with 
a  low-inductance  primary,  is  preferable 
to  a  primary  which  by  itself  has  suitably 
high  reactance. 


the  natural  wave-length  of  L\  the 
repeating  action  will  not  be  so 
good  and  may  be  very  poor.  This  is,  of  course,  objectionable. 

The  remedy  to  the  above  may  be  found  in  making  LI  small  and  placing 
a  tuning  condenser  in  multiple  with  it,  as  shown  in  Fig.  18.  The  tuning 
condenser  Ci  would  be  adjusted  so  that  L\-C\  are  tuned  to  the  incoming 
frequency.  When  this  is  done  the  resistance  between  the  points  H  and 
J  would  be  so  large  that  the  resistance  of  the  plate  to  filament  of  the  first 
tube  may  be  neglected.  The  results  will  be  the  same  as  if  the  voltage 
jjLoEQl  were  applied  directly  across  H-J  without  any  drop  in  the  plate  circuit. 
Assume  this  to  be  the  case  and  let : 

/i  =  alternating  component  of  current  in  LI  ; 


E  = 


848  AMPLIFIERS  [CHAP.  XI 

and 

Til         ,,^A/TT 

--. (17) 

This  last  equation  shows  that  when  L\-C\  is  tuned  to  the  incoming 
frequency  the  ratio  EgjEVl  varies  inversely  as  VZ7;  hence  it  is  advisable 
to  make  LI  very  small,  a  condition  which  is  very  desirable,  since  then 
the  distributed  capacity  is  negligible.  There  is,  however,  a  limit  to  decreas- 
ing LI,  in  view  of  the  fact  that  the  resistance  of  a  multiple  resonating 
circuit  such  as  L\-C\  will,  after  decreasing  LI  below  a  certain  value, 
decrease  and  will  thus  cause  a  much  lower  voltage  to  be  applied  across 
the  points  H-J  of  Fig.  18.  This  effect  can  be  calculated  from  Eq.  (50), 
page  72,  from  which  it  may  be  seen  that  the  effective  resistance  of  the 
parallel  circuit,  at  resonance,  depends  upon  the  ratio  of  L  to  R;  the 
smaller  L  is  made  the  lower  in  the  ratio  L/R  unless  large  well-stranded 
conductors  are  used.  * 

As  regards  L2,  it  should  be  made  large,  yet  if  it  be  so  made  its  dis- 
tributed capacity  may  be  such  as  to  practically  short-circuit  the  grid- 
filament  of  tlie  second  tube  and  make  the  ratio  EgJE0l  practically  zero. 
Hence,  it  is  advisable  to  keep  L>2  as  small  as  is  consistent  with  reasonable 
amplification.  We  will  illustrate  by  means  of  the  following  example: 

Take  MO  =6; 

k  =0.3; 

-r  OKA       TT 

Li2  =*OU  jJiti. 

Then 

ffg,^6X0.3X  V256 
EOI  V36 

which  is  a  small  value  as  compared  with  8.5  to  9.5  for  audio-frequency 
amplifier. 

Of  course  we  could  increase  L2  above  256,  but,  in  so  doing,  its  distrib- 
uted capacity  would  begin  to  affect  the  grid  voltage  adversely  and  nothing 
would  be  gained  by  the  increase  in  L2. 

The  effect  of  the  grid-filament  capacity  must  now  be  considered. 
This  capacity  is  comparatively  small  under  static  conditions  but,  as  shown 
on  page  432,  Chapter  VI,  it  increases  very  much  under  the  conditions 
present  in  amplifiers;  of  course  the  reactance  of  this  capacity  is  in  parallel 
with  the  grid-filament  circuit  and  causes  the  voltage  across  the  grid  to 
fall  to  a  small  value,  in  spite  of  all  the  precautions  which  we  may  have 
been  taken  in  designing  the  repeating  transformer.  As  a  matter  of  fact 
it  is  shown  in  Chapter  VI  that  the  higher  the  alternating  voltage  produced 


RESISTANCE   REPEATING  AMPLIFIER  849 

at  the  output  terminals  of  the  tube  the  lower  becomes  the  capacity  react- 
ance of  the  input  circuit,  or,  in  other  words,  the  better  the  repeating 
transformer  the  poorer  may  the  amplification  be.  Thus  the  capacity 
of  the  input  circuit  of  an  amplifying  tube,  may  be  50  to  75  wf>  Assuming 
a  value  of  50  MM/  the  reactance  of  this  capacity  at  600  meters  would  be 
only  6400  ohms! 

This  is  the  most  important  difficulty  encountered  in  the  design  and 
construction  of  all  high-frequency  amplifiers,  a  difficulty  which  makes 
such  amplifiers,  especially  for  short  wave-lengths,  very  difficult  to  con- 
struct. The  only  remedy  is  to  reduce  the  capacity  of  the  input  circuit 
or,  in  other  words,  to  make  the  area  of  the  grid  as  small  as  feasible,  and 
keep  the  wires  connecting  to  the  grid  as  far  from  the  other  wires  of  the 
tube  as  possible  and  use  a  tube  having  a  low  ^Q.  Some  very  small  tubes 
have  been  built  for  high-frequency  amplifiers  with  these  ideas  incorpo- 
rated.1 The  no  of  such  tubes  is  generally  low,  probably  not  more 
than  3. 

In  case  tuned  plate  circuits  are  used  for  a  high-frequency  amplifier 
it  is  evident  that  unless  all  the  tuning  condensers  are  controlled  by  one 
handle  the  adjustment  of  the  amplifier  for  signals  of  various  frequencies 
would  be  tedious  and  difficult. 

Resistance-repeating  Amplifiers. — We  will  first  discuss  this  type  of 
amplifier  relative  to  audio-frequency  amplification.  The  diagram  of  Fig. 
19  shows  such  an  amplifier  for  three  stages,  The  incoming  signal  voltage 
is  applied  to  the  points  QS  and  is  caused  to  affect  the  grid  of  Tube  1 
through  the  means  of  the  high  resistance  R.  The  grid  and  filament  of 
Tube  1  are  connected  across  the  resistance  R  through  the  comparatively 
large  condenser  Ci;  a  leak  resistance  r\  is  connected  from  the  grid  to  the 
filament.  The  purpose  of  the  leak  resistance  and  of  the  condenser  C\ 
will  be  explained  later,  but  it  will  be  presently  understood  that  any  vari- 
ations of  potential  difference  across  R  will  be  impressed  upon  the  input 
circuit  of  Tube  1  with  the  exception  of  any  drop  of  potential  which  may 
take  place  in  the  condenser  C\. 

The  variations  of  the  grid  potential  of  Tube  1  will  cause  a  correspond- 
ing variation  of  the  plate  current  in  this  tube,  and  hence  a  varying  differ- 
ence of  potential  will  exist  across  the  high  resistance  M.  Since  the  point 
o  is  at  constant  potential  it  is  plain  that  the  potential  difference  between 
the  points  k  and  o  will  be  varied  and,  as  the  battery  resistance  is  com- 
paratively low,  the  variation  of  this  potential  difference  must  necessarily 
be  very  nearly  the  same  as  that  across  R\. 

The  grid  and  filament  of  Tube  2  are  connected  across  k  and  o  through 
the  comparatively  large  condenser  €2,  and,  therefore,  any  variation  in 
the  potential  difference  across  k  and  o  will  be  impressed  upon  the  grid 
1  Such  a  tube  is  shown  at  0  in  Fig.  21  of  Chapter  VI,  page  389. 


850 


AMPLIFIERS 


[CHAP.  XI 


of  Tube  2,  or,  in  other  words  the  signal  will  be  repeated  into  the  second 
tube  by  means  of  the  repeating  resistance  RI. 

In  a  similar  manner  the  signal  will  be  repeated  from  Tube  2  to  3, 
where  it  will  be  picked  up  on  the  receivers.     The  purpose  of  the  grid 

condensers  €2  and  €3 
is  to  insulate  the  grids 
of  Tubes  2  and  3  re- 
spectively from  the 
batteries  B\  and  82. 
Thus,  if  condenser  €2 
were  removed  it  is 
plain  that  the  grid  of 
Tube  2  would  then  be 
connected  to  battery 
BI  through  the  resist- 
ance Ri,  and  the 
battery  would  impress 
such  a  high  positive 
potential  upon  the 
grid  as  to  probably 
spoil  the  tube.  A 
similar  reasoning  ap- 
plies to  the  case  of 
grid  condenser  C\  in 
so  far  as  it  insulates 
the  grid  of  tube  1  from 
any  high  direct  electro- 
motive force  wrhich 
may  be  to  the  left  of 
the  points  QS;  some- 
times, as  will  be  shown 
later,  it  is  possible  to 
dispense  with  the  grid 
condenser  C\  and  the 
resistances  r\  and  R 
for  the  first  tube. 

As  regards  the  leak 
resistances  n,  r2,  rs 
they  are  made  neces- 
sary by  the  use  of  the  insulating  grid  condensers  C\,  €2,  and  €3-  It  has 
already  been  found  in  Chapter  VI,  page  410,  that,  when  a  condenser  is 
connected  in  series  with  the  grid,  if  the  grid  is  very  highly  insulated,  the 
operation  of  the  tube  is  very  uncertain.  The  accumulation  of  electrons 


RESISTANCE-REPEATING  AMPLIFIER  851 

in  the  grid  generally  forces  it  to  assume  a  negative  potential  of  one  or  two 
volts,  this  amount  depending  upon  filament  current,  etc.  If  a  sudden  pulse 
of  e.m.f.  (such  as  given  by  a  "stray")  is  impressed  on  the  grid  it  probably 
will  accumulate  sufficient  electrons  to  force  the  plate  current  to  zero  and 
this  accumulated  charge  of  electrons  in  the  grid  has  no  way  of  escaping. 

Of  course  as  long  as  the  plate  current  of  one  tube  is  zero  the  amplifier 
is  "dead";  it  is  said  to  be  "  paralyzed,"  or  "blocked."  The  grid  of 
a  triode  should  never  be  left  "  free  "  or  "  floating,"  as  the  behavior  of 
the  tube  will  then  always  be  erratic.  As  to  just  how  much  leak  resistance 
is  required  from  grid  to  ground  to  make  the  tube  stable  depends  upon  the 
size  of  the  tube  and  degree  to  which  it  has  been  pumped;  it  may  be  any- 
thing between  105  and  107  ohms  for  the  small  tubes  used  for  amplifiers. 

Suitable  Values  of  Repeating  Resistances.  —  Confining  our  attention 
to  the  repeating  resistance  from  tube  1  to  tube  2,  i.e.  Ri  (Fig.  19)  let: 

E0l—  effective  value  of  alternating  voltage  impressed  upon 

the  grid  of  first  tube; 
Eff2=  effective  Value  of  alternating  voltage  impressed  upon 

the  grid  of  second  tube; 
Ip=  effective    value    of    alternating    component    of    plate 

current  of  Tube  1  ; 
fjLQ  —  amplifying  constant  of  Tube  1  ; 
RP=SL.C.  resistance  of  plate-filament  for  first  tube. 

If  we  assume  that  the  impedance  of  the  circuit  k-Cz-h-y-o  is  very 
high  as  compared  with  the  resistance  Ri,  then  the  impedance  between 
the  points  k  and  o  will  be  made  up  practically  entirely  of  the  resistance 
Ri,  hence  we  may  write: 


, 

•L     — 


Again,  assuming  that  the  reactance  €2  is  very  low  as  compared  with  that 
of  the  grid-filament  of  tube  2,  there  will  be  a  negligible  drop  of  potential 
over  €2  and  the  voltage  of  the  grid  to  filament  for  Tube  2  will  be  given  by: 


and 

7?          ,,^P, 

(20) 


Eq.  (19)  shows  that  the  ratio  EeJEai  increases  continously  with  increase 
of  #1  and  it  approaches  a  maximum  which  will  be  reached  when  RI  is  so 
large  that  Rp  may  be  neglected;  this  maximum  will  be  given  by: 

ET 

Maximum  possible  value  of  TT=  MO (21) 


852 


AMPLIFIERS 


[CHAP.  XI 


This  result  is  to  be  compared  with  that  given  by  Eq.  (12)  and  applying 
to  the  case  of  a  repeating  transformer  amplifier,  for  which: 


Maximum  possible  i=r  =MO~. 
&  2 


(21o) 


repeating  Amplifier 


Curve  shoeing  theoretical  relati 
ratio  of  the  potential  of  two 
grids  and  the  repeating  resistanc  : 


n  between 
uccessi 


Plate  -  filament  A.  C.  resistance  - 


Inpedance  of  grid 


-filament  circuit  was 
large  as  compared  with 
esistance 


assumed 
repeating 


10  20  30  40 

Repeating  resistance  in  Thousand  Ohms 

FIG.  20. — Variation  in  the  amplifying  power  of  a  resistance-repeating  tube  as  the  value 
of  the  external  resistance  used  in  the  plate  circuit  is  varied. 

In  order  to  study  more  fully  the  relation  expressed  by  Eq.  (20)  we  have 
plotted  curve,  Fig.  20,  for  which: 

Mo  =6 
Rp  =  10,000. 

The  curve  shows  that  it  is  hardly  worth  while  to  increase  Ri  beyond 
about  30,000  ohms  for  this  particular  tube,  for   the  gain  in    EvJ'E0i  is 


RESISTANCE^REPEATING  AMPLIFIER  853 

thereafter  too  small  for  even  very  large  increases  of  Ri.  Futhermore, 
it  must  not  be  forgotten  that  the  insertion  of  a  resistance  in  series  with 
the  plate  requires  a  corresponding  increase  in  the  voltage  of  the  B  battery 
as  previously  pointed  out.  As  a  matter  of  fact  such  a  tube  would  prob- 
ably not  be  used  with  more  than  20,000  ohms  in  the  plate  circuit.  This 
would  require  a  B  battery  of  twice  the  voltage  required  if  there  was  no 
IR  drop  in  the  external  plate  circuit  and  will  give  a  voltage  amplification 
of  2/3  of  MO  (in  the  above  case,  4). 

As  regards  the  first  repeating  resistance  R  it  may  be  shown  that  it 
should  be  very  high  as  compared  with  the  resistance  in  series  with  it;  the 
latter  may  be  the  plate-filament  resistance  of  another  tube  or  the  resist- 
ance of  a  telephone  line,  etc. 

The  repeating  resistances  used  are  made  up  in  units  of  small  dimen- 
sions, approximately  \  inch  in  diameter  and  2  to  3  inches  in  length.  There 
are  three  general  types  in  use:  Type  1  consists  of  a  tube  of  insulating 
material  wound  with  high  resistance  wire  and  coated  with  enamel;  it 
is  made  up  in  units  up  to  about  5000  ohms.  Type  2  consists  of  a  tube 
of  insulating  material  wound  with  a  few  turns  of  carbon  filament  contain- 
ing a  large  percentage  of  clay  and  thus  having  a  very  high  resistance;  it 
is  made  up  in  units  up  to  50,000  ohms.  Type  3  consists  of  an  evacuated 
glass  tube  upon  the  inside  walls  of  which  there  is  "  sputtered  "  a  film  of 
tungsten  which  is  very  thin  and  therefore  of  very  high  resistance;  it  is 
made  up  in  units  up  to  2,000,000  ohms. 

In  every  case  it  must  be  kept  in  mind  that  no  matter  what  type  of 
resistance  is  used  for  repeating  purposes  it  must  have  a  current-carrying 
capacity  such  as  will  enable  it  to  carry  the  average  current  flowing  in  the 
plate  circuit  of  the  tube  wherein  it  is  to  be  connected  without  overheating. 
Thus,  in  the  case  of  a  tube  whose  average  plate  current  is  4  milliamperes 
a  repeating  resistance  of  50,000  ohms  should  be  able  to  dissipate  0.8  watt 
without  overheating. 

The  repeating  resistance  should  have  negligible  distributed  capacity, 
for,  this  would  lower  the  value  of  its  impedance  and  cause  a  reduction 
in  the  amplification. 

Another  important  point  regarding  the  resistances  used  for  repeating 
comes  up  in  connection  with  internal  noises  in  an  amplifier.  It  seems 
that  some  of  the  high  resistance  units  are  "  microphonic,"  that  is,  their 
resistance  continually  varies  by  a  very  small  amount.  It  will  be  at  once 
evident  that  such  a  resistance  will  give  rise  to  noises  in  the  amplifier, 
especially  if  the  microphonic  resistance  is  in  one  of  the  first  stages  of  the 
amplifier.  In  general  the  higher  the  resistance  the  more  likely  is  it  to 
be  microphonic. 

Suitable  Value  of  Grid  Condenser. — The  grid  condenser  must  have  a 
small  reactance  as  compared  with  the  circuit  from  grid  to  filament,  which 


854  AMPLIFIERS  [CHAP.  XI 

circuit  consists  of  the  leak  resistance  and  the  capacity  and  resistance  of 
grid  to  filament;  the  point  to  keep  in  mind  is  that  the  variation  of  poten- 
tial difference  existing  between  the  points  k  and  o  (see  Fig.  19)  should 
be  made  to  suffer'  but  a  negligible  drop  over  the  reactance  of  the  grid 
condenser,  so  that  it  may  be  applied  very  nearly  in  its  entirety  to  the 
grid-filament  circuit.  For  audio-frequencies  the  reactance  of  the  capacity 
of  the  grid  to  filament  is  very  high,  i.e.^  one  to  two  million  ohms  and  does 
not  appreciably  affect  the  impedance  between  the  grid  and  filament, 
which  is  almost  entirely  made  up  of  the  leak  resistance  and  the  internal 
grid  to  filament  resistance  in  multiple,  which  make  up  a  resistance  of  the 
order  of  200,000  ohms.  In  this  case  the  grid  condenser  may  be  allowed 
to  have  a  reactance  of  50,000  ohms  without  seriously  affecting  the  grid 
voltage,  or,  in  other  words,  for,  say,  1000  cycles  per  sec.  the  capacity 

of  the  grid  condenser  may  be  about  X6280  or,  roughly,  3000  wf. 

ou,OUU 

If,  however,  the  amplifier  is  used  for  high  frequencies,1  say  X=600 
meters,  then  the  impedance  of  grid  to  filament  is  made  up  almost  wholly 
of  the  grid-filament  capacity  reactance,  which,  for  the  amplifying  tubes 
generally  used,  is  of  the  order  of  about  6000  ohms,  hence  the  grid  condenser 
reactance  should  be  of  the  order  of  about  1500  ohms  or  less;  its  capacity 
may  then  be  as  low  as  200  /*///  without  decreasing  the  value  of  Eat  more 
than  20  per  cent.  It  is  then  apparent  that  smaller  values  of  grid  condenser 
capacity  may  be  used  at  high  than  at  low  frequencies.  In  any  case  it 
is  not  advisable  to  use  any  larger  capacity  than  just  necessary,  for  in 
doing  so,  the  amplifier  is  too  likely  to  block  for  longer  periods  of  time  than 
necessary.  If  a  pulse  of  e.m.f.  is  impressed  on  the  amplifier  all  of  these 
repeating  condensers  will  become  charged  and  so  cut  the  various  plate 
currents  to  probably  zero.  Before  the  amplifier  can  function  the  plate 
currents  must  come  back  to  normal  value  and  this  requires  that  all  these 
condensers  (Ci,  €2,  Ca,  etc.)  discharge  themselves.  The  time  required  for 
discharge  is  fixed  by  the  time  constants,  RC,  of  these  condensers.  More- 
over if  Cs  and  €2  discharge  themselves  before  C\  does  they  will  charge  up 
again  when  Ci  discharges,  due  to  this  discharge  sending  another  pulse  of 
e.m.f.  through  the  amplifier.  It  is  then  evident  that  the  time  constant 
RC  should  be  only  a  small  fraction  of  the  time  between  two  "  dots  "  of  a 
signal,  for  example,  if  the  blocking  is  not  to  interfere  with  reading  the  signal. 
Hence  RC  must  be  made  small  and  this  must  be  accomplished  by  making 
C  as  small  as  permissible  because  if  the  leak  resistance  R  is  made  small  it 
would  decrease  the  impedance  of  the  grid-filament  circuit  so  much  that 
too  large  a  proportion  of  the  voltage  IVR\  would  be  used  up  across  the  grid 

1  It  must  be  pointed  out  that  the  amplifier  as  arranged  in  Fig.  19  will  not  amplify 
high-frequency  spark  signals ;  the  condensers  in  series  with  the  grids  rectify  the  wave- 
trains  so  that  in  the  later  stages  of  the  amplifier,  only  low-frequency  signals  occur. 


RESISTANCE   AMPLIFIER  FOR  HIGH   FREQUENCY  855 

condenser,  thus  cutting  down  the  voltage  impressed  on  the  grid.  The 
proper  relative  values  of  R  and  C  to  keep  RC  small  must  therefore  be  a 
compromise. 

Suitable  Value  of  Leak  Resistance. — The  leak  resistance  should  be 
as  high  as  possible  without  causing  any  of  the  tubes  to  "  block."  The 
blocking  would  occur  in  case  the  grid  became  so  negative  as  to  make  the 
plate  current  zero;  the  signal  would,  then,  not  go  through  until  some  of 
the  electrons  had  escaped  off  the  grid. 

It  is  very  difficult  to  lay  down  any  exact  rules  or  formulae  as  to  the 
best  value  of  the  leak  resistance  since  some  of  the  quantities  which  affect 
it,  such  as  the  number  of  electrons  collected  on  the  grid  are  somewhat 
indeterminate.  It  should  be  kept  in  mind,  however,  that  a  low  leak 
resistance  reduces  the  total  impedance  between  points  k  and  o  on  Fig. 
19  and  hence  makes  the  drop  over  the  repeating  resistance  very  small, 
thus  diminishing  the  amplification,  and  that  a  high  leak  resistance  may 
cause  the  tube  to  "  block."  In  most  amplifiers  the  leak  resistance  is  in 
the  neighborhood  of  1  to  5  million  ohms. 

The  resistances  commonly  used  for  "  leaks  "  are  made  up  of  a  thin 
strip  of  carboard,  clamped  between  two  terminals,  over  which  there  is 
a  coating  of  dried  ink  extending  between  the  two  terminals.  The  whole 
is  enclosed  in  a  glass  tube.  India  ink  is  a  poor  conductor,  and  such  a 
type  of  resistance  as  here  described  may  be  made  up  in  units  ranging 
from  J  to  5  million  ohms,  depending  upon  the  thickness  and  length  of 
the  ink  line.  Of  course  the  power  capacity  of  such  resistances  is  extremely 
limited,  and  care  should  be  taken  not  to  overload  them;  they  are  meant 
to  be  used  on  low-voltage  tubes  only. 

Another  type  of  resistance  used  for  "  leaks  "  is  the  glass  tube  with 
the  tungsten  film  deposited  thereon  already  described  on  page  853. 

As  regards  the  connections  of  the  low-frequency  resistance-repeating 
amplifier  to  the  rectifying  devices  for  damped  or  undamped  waves  they 
are  exactly  similar  to  the  connections  for  the  low-frequency  transformer- 
repeating  amplifier  shown  in  Figs  13,  14,  15. 

In  every  case  the  rectifying  device,  be  it  for  damped  or  undamped 
waves,  is  to  be  connected  to  the  input  points  Q  and  S  (Fig.  19)  of  the 
resistance-repeating  amplifier. 

Resistance-repeating  Amplifier  for  High  Frequency. — The  connec- 
tions of  this  type  of  amplifier  for  the  purpose  of  receiving .  undamped 
waves  are  shown  in  Fig.  21,  where  the  last  tube  is  an  autodyne  rectifying 
tube.  The  input  terminals  of  the  amplifier  are  shown  at  QS  and  the  out- 
put terminals  at  QiSi.  The  varying  signal  voltage  existing  across  the 
terminals  of  the  receiving  condenser  C  is  applied  to  the  grid  of  the  first 
tube  and  repeated  from  tube  to  tube,  and  it  is  finally  made  to  affect  the 
grid  of  the  rectifying  or  autodyne  tube  after  several  stages  of  amplifica- 


856 


AMPLIFIERS 


[CHAP.   XT 


tion.     It  will  be  noted  that  the  grid-filament  of  the  autodyne  tube  is  con- 
nected not  only  across  the  output  terminals  of  the  amplifier  but  also  across 


the  condenser  Ci  of  the  local  oscillating  circuit;  hence  it  will  have  impressed 
upon  it  both  the  local  oscillations  and  the  incoming  antenna  oscillations. 


INDUCTANCE-REPEATING   AMPLIFIER 


857 


In  the  case  of  the  incoming  waves  being  damped  the  same  arrange- 
ment may  be  used  as  shown  in  Fig.  21,  after  reducing  the  coupling  between 
the  grid  and  plate  coils  of  the  rectifying  tube  to  the  point  where  no  oscillations 
are  generated  by  it.  The  rectifying  tube  may,  in  the  case  of  damped 
waves,  be  connected  in  the  simpler  manner  shown  by  Fig.  22.  The  high 
frequency  resistance-repeating  amplifier  is  in  no  way  different  from  the 
low-frequency  amplifier  of  the  same  type  and  the  two  may  be  used  inter- 
changeably. The  only  point  thai;  must  be  noted  in  this  respect  is  that 
the  grid  condenser  may  be  made  much  smaller  for  the  high-frequency 
than  for  the  low-frequency  amplifier,  as  already  discussed  on  page  854, 
and,  furthermore,  it  is  very  important 
that  in  the  high-frequency  amplifier 
the  repeating-resistances  be  made 
with  the  least  amount  of  distributed 
capacity,  otherwise  their  impedance 
will  be  lowered  and  the  amplification 
diminished. 

As  in  the  case  of  the  transformer- 
repeating  high-frequency  amplifier 
the  resistance-repeating  amplifier  suf-  FJQ 
fers  from  the  fact  that  at  high  radio 
frequencies  the  condensive  reactance 
of  the  grid-filament  circuit  becomes 
so  low  as  practically  to  short-circuit 
the  repeating  resistance,  and  con- 
sequently reduces  the  amplifying 
action.  Thus  a  resistance-repeating 
amplifier  which  operates  very  successfully  at  audio-frequency  may  fail 
to  amplify  at  all  at  radio  frequency,  not  because  of  any  fault  of  the 
amplifier,  but  because  of  the  capacity  of  the  grid  to  filament  of  each 
tube. 

Inductance-repeating  Amplifiers. — This  type  is  similar  to  the  resist- 
ance-repeating amplifier,  except  that  instead  of  a  resistance  in  the  plate 
circuit  of  each  amplifying  tube  an  inductance  is  used  whose  reactance  at 
the  frequency  for  which  the  amplifier  is  designed,  is  high.  The  theory 
upon  which  the  repeating  action  from  tube  to  tube  is  based  is  exactly 
the  same  as  for  the  resistance-repeating  amplifier  and  will  not  be  gone 
into  here  again.  This  method  of  repeating  has  an  advantage  over  resist- 
ance repeating  in  so  far  as  the  repeating  inductance  offers  but  little 
opposition  to  the  flow  of  the  direct  current  through  the  plate  circuit  and 
hence  the  B  battery  may  be  of  lower  voltage  than  if  resistance  repeating 
is  used.  For  this  reason  the  inductance-repeating  amplifier  is  to  be  pre- 
ferred to  the  resistance  repeater  for  low  frequencies;  but  for  high  f re- 


-In case  the  resistance-repeating 
amplifier  is  used  to  amplify  spark  signals 
it  will  be  found  unnecessary  to  use  a 
rectifying  tube  with  condenser  in  series 
with  grid  for  detector;  the  high-frequen^ 
cy  signal  will  be  changed  to  radio-fre- 
quency  before  going  through  the  ampli- 
fier very  far. 


858  AMPLIFIERS  [CHAP.  XI 

quencies  the  distributed  capacity  of  the  inductance  introduces  difficulties 
which  make  it  less  desirable  than  the  resistance  repeater. 

Suitable  Value  of  Repeating  Inductance. — Let  X\  =  reactance  of  the 
repeating  inductance  at  the  given  frequency.  Then,  using  the  same 
symbols  and  making  the  same  assumptions  as  in  the  similar  discussion 
on  the  repeating  resistance  given  on  page  851,  we  have: 


(22) 


The  value  of  the  ratio  E02/E0l  increases  continuously  with  increase  of 
Xi  and  has  a  maximum  of  juo  which  will  take  place  when  X\  =  oo  .  The 
relation  between  E0t/E0l  and  Xi  for  a  typical  case  is  shown  by  the  curve 
of  Fig.  23,  for  which  juo=6  and  ^  =  10,000  ohms.  Comparing  this  curve 
with  the  similar  one  for  the  resistance  repeater  (Fig.  20),  it  will  be  noted 
that  the  value  of  EgJE0l  rises  much  more  sharply  for  the  inductance 
repeater  than  for  the  other,  and,  as  a  matter  of  fact,  for  the  same  value 
of  repeating  impedance  the  resistance  amplifier  gives  a  smaller  ratio 
Eff,/Efi  than  the  inductance  amplifier. 

The  curve  shows  that  there  is  very  little  to  be  gained  by  using  a  repeat- 
ing reactance  larger  than  about  20,000  ohms,  or  twice  the  resistance  of 
the  plate  to  filament.  On  the  basis  of  20,000  ohms  for  the  repeating 
reactance  the  inductance  would  need  be  about  3  henries  for  1000  cycles 
per  second  and  0.006  henry  for  600  meters. 

Of  course  the  repeating  inductance  for  audio-frequency  is  built  on  an 
iron  core  in  view  of  its  very  large  value.  The  construction  of  this  induc- 
tance is  regulated  by  the  same  principles  as  the  construction  of  the  repeat- 
ing transformers  for  audio-frequency  amplifiers,  i.e.,  low  iron  losses  and 
small  distributed  capacity  together  with  small  dimensions. 

In  the  case  of  the  inductance  for  600  meters,  as  given  above,  it  will 
be  noted  that  it  is  almost  impossible  to  build  an  ironless  inductance  of 
0.006  henry  to  fit  in  a  comparatively  small  space  and  with  little  distributed 
capacity.  The  effect  of  the  distributed  capacity  is  to  cause  best  repeating 
action  to  take  place  at  a  wave-length  equal  to  the  natural  wave-length 
of  the  repeating  coil;  for  other  wave-lengths  the  repeating  action  will 
not  be  so  good  and  may  be  very  poor.  A  similar  difficulty  was  noted  in 
connection  with  the  radio-frequency  repeating-transformer  amplifier,  as 
discussed  on  page  848.  A  straight  inductance-repeating  amplifier  is 
very  poor  for  short  wave-amplification.  It  may  be  improved,  however, 
by  connecting  a  variable  condenser  across  the  repeating  inductance  and 
adjusting  it  so  that  the  condenser  and  inductance  are  tuned  to  the  incoming 
frequency;  the  equivalent  impedance  of  the  combination  will  then  be 
very  high,  while  the  value  of  the  inductance  may  be  made  quite  low 
and  the  condenser  may  be  relied  upon  to  tune  up  to  the  required  frequency. 


INDUCTANCE-REPEATING  AMPLIFIER 


859 


A  similar  tuned  plate-circuit  impedance  has  already  been  discussed  for 
the  case  of  transformer  amplifiers. 

Fields  of  Use  of  Radio-frequency  and  Audio-frequency  Amplifiers.— 
For  amplifying  wire  telephone  or  wire  telegraph  currents  the  audio- 
frequency amplifier  is,  of  course,  to  be  used.  For  receiving  radio-tele- 


Inductance 


3 


•epeating  Amplifier 


Cui-ve  shoeing  theoretical  relation  between 
the|  ratio  of  the  potentials]  of  two  |succ< 
grids  and  the  repeating  reactance 


inent  A.C. 


Plate -filament  A.C.  resistance  =10,000  ohms 


Inpedance  jof  grid  -[filament  circuit  was 
assumed  very  large  as  compared  yt-  ith 
repeating  reactance 


10  20  30 

Repeating  reactance  in  Thousand  Ohms 


40 


FIG.  23. — Amplifying  characteristics  of  a  tube  using  an  inductance  in  the  plate  circuit; 
the  amplification  obtainable  is  much  greater  than  with  the  same  number  of  ohms  of 
resistance. 

graph  or  radio-telephone  currents  it  is  a  question  as  to  whether  to  amplify 
the  received  high-frequency  currents  first  and  then  rectify  them  or  to 
rectify  them  first  and  then  amplify  them.  The  former  of  these  two 
methods  requires  the  use  of  a  radio-frequency  amplifier  and  the  latter 
of  an  audio-frequency  amplifier.  The  advantage  of  using  a  radio-fre- 
quency amplifier  lies  in  the  fact  that  atmospheric  disturbances  and 


860  AMPLIFIERS  [CHAP.  XI 

other  so-called  "  static  interferences/'  which  are  always  more  or  less 
seriously  affecting  the  reception  of  signals,  produce  audio-frequency  currents, 
which  are  amplified  but  little,  or  not  at  all  by  the  radio-frequency  ampli- 
fier; therefore,  in  this  case,  the  final  effect  upon  the  telephone  receivers, 
or  any  other  device  used  for  detecting  the  signals,  is  due  more  to  the  ampli- 
fied radio-frequency  signal  currents  than  to  the  unamplified  low-frequency 
interfering  currents.  On  the  other  hand,  in  the  case  of  the  audio-fre- 
quency amplifier,  this  will  amplify  not  only  the  rectified  radio-frequency 
signal  currents,  but  the  atmospheric  disturbances  as  well,  so  that  the 
telephone  receivers  will  be  subjected  to  both  the  signal  and  the  inter- 
fering currents  which  have  been  equally  well  amplified.  It  would  seem, 
then,  as  if  the  radio-frequency  amplifier  would  have  the  field  entirely  to 
itself,  but,  unfortunately,  the  radio-frequency  amplifier  is,  as  has  already 
been  pointed  out,  very  difficult  of  construction  for  low,  or  even  moderate, 
wave-lengths,  on  account  of  the  effect  of  the  grid-filament  capacity  of 
the  tubes  upon  amplification.  Tubes  have  been  built  where  the  grid- 
filament  capacity  has  been  reduced  to  a  very  low  value  and  they  have 
been  employed  with  some  success  in  the  construction  of  high-frequency 
amplifiers,  but  they  are  still  in  the  experimental  stage.  An  amplifier 
quite  extensively  used  during  the  war  had  three  high-frequency  air  core, 
transformer-repeating  stages  feeding  into  a  detecting  tube  which  in  turn 
fed  into  a  three-stage  low-frequency  amplifier.  (The  advantage  of 
amplifying  the  high-frequency  signal  as  much  as  possible  before  putting 
it  into  the  detector  tube  will  be  realized  at  once  when  it  is  remembered 
that  the  detecting  efficiency  of  a  three-electrode  tube  increases  with  the 
square  of  the  signal  voltage.)  The  overall  voltage  amplification  of  this 
set  was  probably  of  the  order  of  10,000. 

With  the  tubes  at  present  available  a  good  amplifier  may  be  con- 
structed for  frequencies  of  the  order  of  50,000  cycles  per  second,  and  since 
this  frequency  is  very  much  higher  than  that  of  most  atmospheric  dis- 
turbances, the  latter  will  not  be  amplified,  as  much  as  the  signal  currents 
of  50,000  cycles  will  be.  In  an  amplifier  originated  by  E.  H.  Armstrong 
the  difficulty  of  amplifying  a  high-frequency  signal  has  been  ingeniously 
overcome;  in  it  the  incoming  high-frequency  currents  are  first  reduced 
by  the  heterodyne  or  autodyne  method  to  about  50,000  cycles  per  second, 
then  amplified  through  a  number  of  stages  and  finally  reduced  again  by 
another  and  last  autodyne  process  to  audio-frequency  and  transferred  to 
the  receivers.  The  arrangement  is  shown  in  a  simple  form  in  the  schematic 
diagram  of  Fig.  24.  It  might  seem  that  such  an  arrangement  is  very 
complicated  to  handle,  but,  as  a  matter  of  fact,  it  is  no  more  so  than  the 
ordinary  single  tube  autodyne  set  for  receiving  undamped  waves.  For, 
it  will  be  noted  that  the  inductances  and  capacities  in  the  second  autodyne 
tube  are  fixed,  and  their  values  are  originally  adjusted  so  that,  when 


ARMSTRONG   SHORT- WAVE   AMPLIFIER 


861 


862  AMPLIFIERS  [CHAP.  XI 


electromotive  forces  of  50,000  cycles  are  induced  in  the  circuit  of 
by  the  amplifier,  the  telephone  receivers  will  be  subjected  to  a  rectified 
current  of  1000  cycles;  in  other  words,  the  last  autodyne  tube  is  definitely 
adjusted  to  oscillate  at  a  frequency  of  either  49,000  or  51,000  cycles  per 
second.  The  only  operation  that  the  operator  needs  to  perform,  then, 
is  to  adjust  the  receiving  inductance  LI  and  receiving  capacity  Ci  so  that 
the  signal  may  be  heard  in  the  phones;  when  this  is  the  case  the  frequency 
of  the  currents  passing  through  the  amplifier  is  either  50,000  or  48,000 
cycles  (assuming  that  the  last  autodyne  tube  is  adjusted  to  oscillate  at 
49,000  cycles  per  second). 

As  already  pointed  out  in  the  discussion  of  the  transformer-repeating 
amplifier  for  radio-frequencies  given  on  page  845,  the  plate  circuits  of 
the  various  amplifier  tubes  may  be  tuned  to  the  frequency  to  be  amplified, 
by  means  of  condensers  placed  across  the  primaries  of  the  repeating  trans- 
formers. This  may  be  very  easily  done  in  the  case  of  the  Armstrong 
amplifier  without  subtracting  from  the  flexibility  of  the  apparatus,  since 
the  condensers  C,  C,  C  shown  in  Fig.  24  need  not  be  variable,  but  adjusted 
once  for  all  to  resonate,  together  with  the  primaries  of  the  transformers, 
to  50,000  cycles. 

Instead  of  a  transformer-repeating  amplifier  one  may  use  a  resistance- 
repeating  or  else  an  inductance-repeating  amplifier  whose  plate  circuits 
have  preferably  been  tuned  to  50,000  cycles  by  means  of  fixed  condensers 
connected  across  the  repeating  inductances. 

If  the  amplifier  be  either  a  transformer-repeating  or  an  inductance- 
repeating  one  the  transformers  or  the  inductances  may,  for  this  com- 
paratively low  radio  frequency,  be  constructed  with  iron  cores  provided 
the  laminations  be  made  very  thin  (laminations  of  the  thickness  of  1.5 
mils  have  been  used)  or  still  better,  iron  dust;  1  in  this  case  the  number 
of  turns  necessary  to  give  the  required  reactance  at  50,000  cycles  for  a 
tube  of  Rp  =  10,000  ohms  need  be  comparatively  small  and  they  can  easily 
be  constructed.  If  transformers  or  inductances  with  iron  are  used  it  is 
not  necessary  to  tune  the  plate  circuits  by  means  of  condensers,  for  the 
required  reactance  may  be  obtained  without  them.  But  if  no  iron  is 
used  the  number  of  turns  of  the  repeating  transformers  or  inductances 
would  have  to  be  made  so  large  as  to  require  the  use  of  shunting  condensers 
around  the  coils  to  bring  the  impedance  up  to  the  required  value. 

The  effect  of  the  grid-filament  capacity  in  a  50,000-cycle  amplifier  is, 
of  course,  not  negligible,  as  in  the  audio-frequency  amplifier,  but  it  is  not 
such  as  to  affect  seriously  the  amplifying  action.  Thus,  assuming,  as 
we  did  previously,  the  grid-filament  capacity  to  be  50  /*///,  we  have: 

Reactance  of  grid-filament  capacity  at  50,000  cycles  per  sec.  =64,000 
ohms,  which  reactance,  while  not  as  high  as  might  be  desired,  is  yet  suf- 

1  See  page  138. 


POSSIBLE  AMPLIFICATION  863 

ficiently  high  to  prevent  serious  interference  with  the  action  of  the 
repeating  devices,  provided  the  tube  itself  has  a  sufficiently  low  plate 
resistance,  say  Rp  =  10,000  ohms. 

Desirability  of  Different  Characteristics  for  Various  Stages  of  Ampli- 
fication.— It  has  already  been  shown  that  the  manner  in  which  an  amplifier 
operates  is  to  cause  an  increase  of  voltage  to  be  applied  across  the  grid 
and  the  filament  of  any  one  tube  over  that  for  the  preceding  tube,  so  that 
finally  the  variations  of  the  grid  potential  of  the  very  last  tube  are  many 
times  larger  than  for  the  first  tube.  Thus,  assuming  a  low-frequency 
transformer  amplifier  in  which  the  ratio  of  grid  voltages  of  two  succeeding 
tubes  is,  say,  7  and,  assuming,  in  addition,  that  the  same  ratio  is  main- 
tained from  the  first  to  the  last  tube,  then,  we  have: 

Ratio  of  grid  voltage  of  last  tube  of  an  n  tube  amplifier  to  grid 

voltage  of  first  tube=7ra"1. 
We  give  below  the  values  of  ln~ l  for  various  values  of  n. 

Number  of  tubes  77*"1 

3 49 

5 2,400 

7 118,000 

It  is  apparent,  therefore,  that,  as  the  number  of  tubes  increases,  the  grid 
voltage  applied  to  the  end  tubes  increases  enormously.  It  might  seem, 
therefore,  that  different  types  of  tubes  should  be  used  for  succeeding  stages, 
but  such  is  not  the  case  unless  some  loud-speaking  apparatus  is  to  be 
operated  from  the  amplifier.  In  that  case  it  is  quite  likely  that  the  last 
tube  of  the  amplifier  will  feed  into  a  group  of  low-resistance  tubes  con- 
nected in  parallel. 

In  one  successful  amplifier  there  were  two  tubes  in  cascade,  each  giving 
with  its  associated  circuit  a  voltage  amplification  of  32,  the  two  thus 
amplifying  the  impressed  voltage  about  1000  times.  This  amplified 
signal  was  supplied  to  the  grids  of  three  other  tubes  all  connected  in  par- 
allel. The  //o  of  these  tubes  was  about  4  and  their  a.c.  plate  resistance 
1500  ohms.  Thus  the  three  plate  circuits  in  parallel  had  a  resistance 
of  only  500  ohms.  In  the  common  plate  circuit  was  the  primary  of  a 
step-up  transformer  having  a  ratio  of  30  to  1,  this  voltage  being  supplied 
to  a  very  high  impedance  load.  The  overall  voltage  amplification  of  this 
outfit  was  about  30,000. 

For  ordinary  amplifiers  of  radio  signals,  however,  it  is  not  necessary 
to  change  the  type  of  tube  used  in  the  various  stages  because,  for  the 
loudest  signal  an  operator  could  stand  the  grid  of  the  last  tube  of  the 
amplifier  need  have  an  impressed  e.m.f.  of  perhaps  1  volt;  a  comfortably 
loud  signal  is  obtained  with  a  fraction  of  this  value.  As  practically  any 
but  the  very  highest  impedance  tubes  operate  very  satisfactorily  with 


804 


AMPLIFIERS 


[CHAP.  XI 


an  impressed  grid  voltage  even  greater  than  this  it  is  evident  that  it  is 
entirely  needless  to  change  the  type  of  tube. 

Filters.1 — By  the  term  "  filter  "  is  understood  a  network,  or  combi- 
nation of  resistances,  inductances,  and  condensers  (or  merely  two  of  these 
kinds  of  circuits)  which  "  passes  through  "  signals  of  one  frequency  better 
than  it  does  others;  in  other  words  it  is  a  selective  conductor  of  some 
sort.  If  filters  have  resistances  and  inductances,  or  resistances  and  con- 
densers, they  are  aperiodic,  having  no  natural  period  of  their  own.  If 
they  contain  inductances  and  condensers  they  may  be  periodic  (i.e., 


Frequency  Frequency 

FIG.  25. — Characteristics  of  different  types  of  filters  a  and  b  having  either  resistance 
and  capacity  or  resistance  and  inductance  while  c  and  d  must  have  resistance, 
inductance,  and  capacity  properly  combined.  Filters  made  up  of  combinations 
of  condensers  and  coils  may  be  so  proportioned  that  they  let  through  a  certain 
range  of  frequencies  with  but  little  attenuation;  such  are  called  band  filters. 

having  one  or  more  natural  periods  of  oscillation)  depending  upon  how 
much  resistance  is  associated  with  the  network. 

The  characteristic  of  a  filter  is  generally  given  by  supposing  a  signal 
of  fixed  amplitude  and  variable  frequency  to  be  impressed  on  the  input 
terminals  and  plotting  against  frequency,  the  voltage  at  the  output 
terminals.  For  different  types  of  filters  we  may  get  characteristics  such 
as  indicated  in  Fig.  25,  (a),  (b),  (c),  and  (d).  The  first  two  (a  and  b)  have 

1  For  an  excellent  mathematical  discussion  of  the  properties  of  various  types  of 
filters  the  reader  is  referred  to  Chapter  XVI  of  Pierce's  "  Electric  Oscillations  and  Elec- 
tric Waves." 


FILTERS  865 

only  resistance  and  inductance  or  resistance  and  capacity  used  in  their 
structure,  while  the  other  two  have  inductance,  resistance  and  capacity. 

A  filter  is  generally  applied  to  high-frequency  amplifiers  and  may  be 
constructed  to  serve  either  one  or  both  of  two  different  purposes,  i.e. : 

(1)  To  prevent  signals  from  all  transmitting  stations,   except  one, 
from  being  amplified,  and  hence  to  keep  interfering  signals  from  reaching 
the  operator's  ear. 

(2)  To  prevent  currents  due  to  "  strays,"  "  static,"  etc.,  from  being 
amplified  as  much  as  they  would  otherwise  be  and  hence  to  keep  static 
interference  from  reaching  the  operator's  ear. 

These  two  purposes  of  the  filter  might  be  carried  out  as  shown  in 
Fig.  26.  This  figure  represents  a  high-frequency  resistance-repeating 
amplifier.  It  will  be  noted  that  all  incoming  currents  which  go  past  the 
tuned  receiving  circuit  (a),  will  produce  varying  voltages  across  the  grid- 
filament  of  the  first  tube  and  be  thereby  amplified  into  the  plate  circuit 
of  this  tube.  Across  the  points  Y  and  0  there  is  connected  the  circuit 
Cz-Hi-Ki-0;  the  circuit  from  HI  to  K\  consists  of  L\-Ci  in  multiple 
with  the  grid  condenser  C±,  the  leak  resistance  r\  and  the  grid-filament 
of  the  second  tube.  For  the  sake  of  convenience  this  part  of  the  amplifier 
circuit  is  reproduced  in  Fig.  27.  The  condenser  €3  serves  the  purpose 
of  keeping  the  battery  B\  from  sending  any  direct  current  into  the  circuit 
from  HI  to  0,  and  may  be  made  quite  large,  so  as  to  have  a  low  reactance 
at  as  low  a  frequency  as  1000  cycles  per  second  or  less.  The  circuit  L\-C\ 
is  one  that  is  tuned  to  the  frequency  which  it  is  desired  to  amplify,  and, 
of  course,  at  this  frequency  it  has  a  very  high  impedance,  while  at  all 
other  frequencies,  higher  or  lower,  it  offers  a  lower  impedance. 

The  characteristic  of  this  filter  is  given  by  curve  (c)  of  Fig.  25.  The 
result  is  that  the  circuit  of  €3,  HI,  Li-Ci,  K\  will  practically  short-circuit 
the  resistance  from  Y  to  0  at  all  frequencies  except  the  one  to  which  L\ 
and  Ci  are  tuned,  and,  therefore,  the  repeating  resistance  R\  will  repeat 
but  poorly  all  frequencies  except  the  desired  one.  Of  course  the  fre- 
quencies nearest  the  desired  one  will  be  repeated,  though  not  strongly, 
into  the  second  tube  and  these  frequencies  are  still  further  weakened 
in  the  process  of  repeating  from  the  second  into  the  third  tube,  so  that, 
finally,  the  output  currents  will  contain  the  component  of  the  original 
input  currents  of  the  desired  frequency  strongly  amplified  and  components 
of  other  frequencies  very  much  weakened  or  totally  suppressed. 

It  will  be  noted  that  this  type  of  filter  acts  as  a  barrier  not  only  to  high- 
frequency  interfering  currents,  but  also  to  low-frequency  static  inter- 
ference. It  has  the  objection  of  requiring  the  filtering  circuits-  Li-Ci, 
L,2~C2,  etc.,  to  be  tuned  to  the  incoming  signal  frequency,  and,  if  this  is 
a  variable  one,  the  tuning  complicates  the  operation  of  receiving.  The 
steady  state  impedance  from  H\  to  K\  of  the  parallel  circuit  L\~C\y  is 


AMPLIFIERS 


[CHAP.  XI 


about  as  shown  in  curve  c  of  Fig.  28,  where  /o  is  the  frequency  of  the  signal 
which  it  is  desired  to  amplify.  The  exact  expression  from  which  the 
curve  can  be  plotted  is  given  on  the  bottom  of  p.  71.  It  must  be  noted 

li 
II 

5  3 

3 


Cf 


*r 
— ^vwvwvwwv— J 


. 


S 


that  this  impedance  curve  holds  only  for  the  steady  state,  and  hence 
gives  no  idea  as  to  how  the  circuit  will  react  to  pulses  or  highly  damped 
signals.  In  fact  just  because  of  the  behavior  of  this  circuit  to  pulses  it 
is  really  a  very  poor  filter  to  use  with  an  amplifier  for  reasons  now  to 
be  given. 


FILTERS 


867 


Tube  2 


It  was  shown  on  pages  268  et  seq.  that  when  a  damped  wave  of  e.m.f. 
is  used  for  exciting  a  tuned  circuit  two  distinct  effects  are  produced.  A 
forced  current,  of  the  same  fre- 

Tube  1 

quency  as  the  impressed  e.m.f.,  A  c« 

flows  in  the  circuit,  and  another 
current  of  the  same  frequency 
as  the  natural  frequency  of  the 
circuit  is  also  set  up.  The  rela- 
tive amplitudes  of  these  two 
currents  are  discussed  in  Chap- 
ter IV,  page  270.  It  is  there- 
fore evident  that  any  impulsive 
e.m.f.  will  start  the  circuit  L\-C\ 
oscillating  at  its  natural  fre- 
quency which  is  practically  the 
same  frequency  as  that  for 
which  the  amplifier  is  best 
adjusted;  this  pulse  of  e.m.f. 
(atmospheric  disturbance)  will 
therefore  be  sent  through  tube 
1  of  the  amplifier  as  a  pulse 

but  after  passing  the  filter  L\-C\  it  will  be  propagated  through  the  rest 
of  the  amplifier  as  a  damped  wave-signal  of  practically  the  same  fre- 
quency as  that  for  which 
•the  amplifier  is  adjusted, 
the  damping  of  this  spuri- 
ous signal  being  fixed  by 
the  damping  constant  of 
circuit  Li-Ci. 

This  is  an  effect  which 
must  be  carefully  guarded 
against  in    the  design  of 
amplifiers.     With  suitable 
filtering  circuits  the  pulse 
—     A,    Fig.    29,    can    be   so 
affected     that    it     comes 
FIG.  28.-The  impedance  between  H,  and  A,  varies  with   through  the  amplifier  with 
impressed   frequency  as  shown  here;    the  lower  the 
resistance   in   the   Li~C\  circuit  the  sharper  is  this 
resonance  curve. 


FIG.  27. — Circuit  detail  to  show  action  of  filter; 
the  circuit  between  HI  and  A'i  practically  short 
circuits  any  frequency  except  that  for  which  it 
is  tuned. 


Frequency 


much  less  amplification 
than  the  signal  B.  But 
if  tuned  filter  circuits  are 

used  it  may  be  that  the  pulse  will  be  changed  to  a  damped  signal  and  be 
amplified  to  practically  the  same  extent  as  the  signal  B. 

This  tuned  type  of  filter  is  excellent  for  differentiating  between  two 


868  AMPLIFIERS  [CHAP.  XI 

continuous  wave-signals  of  nearly  the  same  frequency.  For  a  continuous 
wave-signal  (the  "  dot  "  of  which  lasts  for  several  hundred  cycles  of  the 
signaling  frequency)  curves  like  those  of  Fig.  25  give  a  correct  idea  of  the 
relative  selectivity  of  the  filter,  and,  as  the  selection  takes  place  pro- 
gressively as  it  goes  from  one  section  of  the  filter  (Z/i-Ci)  to  the  others 
(Z>2-C2,  etc.),  the  disturbing  signal  is  completely  nullified.  If  for  example 
the  desired  signal  is  /o  and  the  interfering  signal  is  /',  it  may  be  that 

one  section  of  the  filter  will 
cut  down  the  interference  to 
.2  of  its  initial  value  and  the 
desired  signal  to  .98  of  its 
impressed  value.  After  going 

Time  through  three  sections  of  such 

a  filter  the  signal  will  be  cut 
down  to  .983  or  about  .94  of 
its  impressed  value,  whereas 
the  interfering  signal  will  be 
reduced  to  .23=.008  of  its 
impressed  value.  If  the  am- 
plifying power  of  the  tubes 
A  A  A  A (apart  from  the  filtering  ar- 


Time  rangement)    is     100    times    in 

voltage,  the   signal  will    come 
through   the    amplifier  with   a 
voltage  amplitude  94  times  as 
FIG.  29.— In  a  well-designed  amplifier  the  pulse  great  as  its    input   amplitude, 
A  will  come  through  much  less  amplified  than   whereas  the  interference  would 
the  signal  B  for  which  the  amplifier  is  designed;    ,  0      ,.    ., 

when  filters  using  inductance  and  capacity  are  haVe  but  '8  °f  ltS  lnPUt  am' 
used,  however,  tuned  to  the  signal  B,  it  is  likely  plltude. 

that  the  pulse  A  will  be  changed  into  a  damped  For  differentiating  between 
wave  signal,  of  same  frequency  as  B,  and  will  spark  stations  the  relative 
be  amplified  as  much.  selectivity  is  not  as  good,  be- 

cause of  the  natural  oscillations 

set  up  in  the  filter  sections  by  the  interfering  signal;    in  fact  for  sepa- 
rating highly  damped  spark  signals  this  filter  is  of  practically  no  value. 

Non-resonant  Filters. — A  simpler  filter  which  acts  to  weed  out  low- 
frequency  interference  much  more  than  it  does  high-frequency  signals 
is  the  one  shown  in  Fig.  30. 

This  diagram  is  similar  to  the  one  of  Fig.  26  except  that  the  resistance 
R'I  is  here  substituted  for  the  tuned  circuit  ~L\-C\  of  Fig.  26.  The  general 
characteristic  of  this  type  of  filter  is  shown  in  Fig.  25,  curve  (a).  If  a 
given  amplitude  of  voltage  of  variable  frequency,  is  impressed  across 
the  points  QS  (of  Fig.  30)  and  the  resultant  voltage  across  M-N  be 


FILTERS 


869 


measured  it  will  be  found  to  have  somewhat  the  form  of  the  curve  (a) 
of  Fig.  26. 

While  no  definite  design  of  such  a  filter  can  be  given  here  (it  depend- 


ing  upon  the  tubes  used,  etc.)  it  has  proved  satisfactory  to  make  the  react- 
ance of  Ca  and  €4  for  the  signal  frequency  about  one-fifth  of  the  resist- 
ance R'I.  In  addition  to  this  consideration  the  reactance  of  Ca  and  C*  in 


870 


AMPLIFIERS 


[CHAP.  XI 


series  must  be  small  compared  to  the  impedance  between  points  M-N,  and, 
furthermore,  the  impedance  of  the  network  Cy-Itfr-Cf-ri,  etc.,  as  measured 
between  the  points  Y-0  must  be  high  compared  to  the  resistance  /fa; 
and  this  resistance  R\  should  be  about  equal  to  the  resistance  of  the  plate 
circuit  of  the  tube.  With  this  design  of  filter  and  amplifier  circuit  the 
voltage  amplification  per  stage  is  about  Mo/3. 

As  an  example  of  how  a  filter  of  this  kind  differentiates  between  signals 
of  different  frequencies  a  case  has  been  worked  out  in  Fig.  31.  Points 
0-Y  on  the  figure  would  normally  connect  across  the  plate  cirpuit  resist- 

ance of  one  tube,  and  points  M-N 
would  connect  to  the  input  circuit 
of  the  next  tube  of  the  amplifier. 

Power  from  Generators  for 
Amplifiers.  —  By  using  a  suitable 
filter  it  is  possible  to  use  a  small 
generator  for  lighting  the  fila- 
ments or  for  furnishing  the  plate 
current  of  an  amplifier.  Such  an 
arrangement  is  indicated  in  Fig. 
32.  The  amount  of  filter  required 

will  depend    upon  the  quality  of 

,.          /.  ,-,  •,  •  » 

commutation  of  the  machine.     As 

the     ordinary     commutation   fre- 


H 

C  =-500  MM/. 
R  =50,000  ohms. 

II             ,             " 

c 

nr 

c 

nr 

c 

£ 

h 

• 

••         \ 

ThIn-UafireacrOSS°Y  =  1 

Voltaic  across  WIN  at  50,000  Cycles/Sec.  =0.83 

«        "     *    5,000       "          »    =0.11 


FIG.  31.  —  A  section  of  a  resistance  capacity 

v,-  u  Cnnnn 
filter,  through  which  50,000  cycles  is  propa- 

gated with  but  little  attenuation,  whereas 
5000  cycles  is  cut  down  to  one-tenth  of  its  quency  is  about  1000  per  second 
incoming  amplitude.  the  reactance    of   each  condenser 

used  in   shunting  the  line  should 

be  small,  at  this  frequency,  compared  to  the  inductive  reactance  of  the 
coils  (perhaps  one-tenth  as  much).  Iron  core  coils  may  be  used,  the 
dimensions  of  LI,  LI,  etc.,  being  necessarily  much  larger  than  Lz,  L^ 
etc.,  because  of  the  greater  current  they  have  to  carry. 

Stability  of  Amplifiers  —  "  Squealing."  —  An  amplifier,  especially  if  of 
the  inductance  or  transformer-repeating  type,  is  very  likely  to  produce 
in  the  telephone  receivers  audio-frequency  sustained  notes  which  are 
entirely  independent  of  the  incoming  signals;  this  action  is  known  as 
"  squealing,"  and  is  extremely  objectionable  and  very  difficult  to  over- 
come. The  squealing  of  an  amplifier  is  generally  due  to  the  fact  that 
the  circuits  of  the  various  tubes  are  capable  of  oscillating,  and  may  oscil- 
late if  the  conditions  are  favorable;  this  applies  to  both  high-frequency 
and  low-frequency  amplifiers.  Thus  assume,  for  the  sake  of  clearness, 
that  a  single  tube  is  connected  by  itself  as  it  would  be  connected  were 
it  used  in  the  low-frequency  transformer-repeating  amplifier  of  Fig.  13, 
page  842,  and  let  Fig.  33  represent  it.  The  coils  of  the  repeating  trans- 
formers TI  and  T2  have  a  large  amount  of  distributed  capacity,  and  hence 


STABILITY  OF  AMPLIFIERS 


871 


the  circuit  may  be  roughly  represented  by  its  equivalent  of  Fig.  34.  It 
will  be  noted  that  L\C\  is  an  oscillating  circuit  and  the  grid  is  connected 
across  it;  furthermore  the  circuit  Lz-Cz  may  have  a  high  impedance 
to  currents  of  the  natural  frequency  of  the  circuit  L\-C\.  Any  oscillations 
started  in  L\-C\  will  produce  a  change  in  grid  potential  which  will  pro- 


duce a  change  in  plate  current;  the  latter  will  cause  a  variation  of  plate 
potential  to  take  place,  in  view  of  the  impedance  of  L^-Ci  being  connected 
in  series  with  the  plate  battery,  and  finally  the  variation  of  plate  poten- 
tial may,  through  the  capacity  of  plate  to  filament  and  grid  to  filament, 
react  back  upon  the  grid,  and  may  impress  a  higher  voltage  across  the 
circuit  Li-G  than  at  first  existed.  Such  a  condition  would,  of  course, 


872 


AMPLIFIERS 


[CHAP.  XI 


be  favorable  to  the  maintenance  of  currents  of  the  natural  frequency  of 


Secondary 
of  repeating 
Transformer 


Primary 
of  repeating 
Transformer 


The  tube  may  also  oscillate  at  the  natural  frequency  of  L^-Ci ',  whether 
it  oscillates  at  the  frequency  of  I/i-Ci  or  of  L^-C^  depends  entirely  upon 
which  of  these  frequencies  gives  correct  phases  of  e.m.f.'s  and  the  smaller 

losses  in  the  entire   circuit. 
If  the    frequency   at    which 
the  tube  oscillates  is  audible, 
the  currents  produced  there- 
by will  be  heard  in  the  tele- 
phones connected  in  the  plate 
circuit   of    the   last   tube  of 
the  amplifier,  and  will   thus 
produce   squealing.      If    the 
FIG.  33.— Circuit  detail  of  a  transformer  repeating  frequency    is    inaudible   the 
amplifier;    it  may  well  be  that,  due  to  internal   telephone  win    give   no   indi- 
capacities  of  the  coils  (giving  the  circuit  a  natural        , .          ,.  , ,  <•         i 

period)  and  the  coupling  between   plate  and  grid    CatlOn  °f  the  Presence  of  such 
circuit  inside  the  tube,   self-sustained  oscillations   currents,  but   they   will   sen- 
are  set  up  in  the  circuit.  ously  interfere  with  the  am- 
plifying action  of  the  tubes. 

[n  the  case  of  a  high-frequency  transformer-repeating  amplifier  the  tube 
circuits  may  also  oscillate,  but  they  will  do  so  at  radio  frequencies  and  will 
not  be  heard,  but  the  efficiency  of  the  amplifier  as  a  whole  may  be  seriously 
impaired  by  the  presence  of  these  interfering  currents. 

On  the  other  hand  inductance  repeating  high-frequency  amplifiers, 
oscillating  at  radio  frequency,  sometimes  produce  an  audible  tone  in  the 
telephones  due  to  the  fact  that  the 
grid  condensers  may,  as  a  result  of 
the  oscillations,  become  so  highly  nega- 
tive as  to  cause  the  plate  current  to 
become  zero  and  thus  stop  the  oscil- 
lations; after  a  time  the  electrons 
collected  on  the  grid  will  leak  off  and 
the  plate  current  will  start  flowing; 
but  the  oscillations  will  again  start 
in  and  again  make  the  plate  current 
zero,  etc.  This  starting  and  stopping 
of  the  oscillations,  with  consequent 

pulsations  in  plate  current,  may  take  place  at  audio-frequency,  in  which 
case  the  amplifier  will  "  squeal."  This  phenomenon  is  similar  to  the 
one  fully  discussed  on  page  523  in  connection  with  oscillating  receiving 
tubes  equipped  with  grid  condensers. 

In  the  discussion  given  above  we  have,  for  the  sake  of  simplicity, 


FIG.  34. — The  transformer  coils  of  Fig. 
33,  with  their  internal  capacities  give 
a  circuit  as  shown  here. 


STABILITY    OF  AMPLIFIERS  873 

considered  the  action  taking  place  in  each  individual  tube,  which  may 
be  caused  to  oscillate  due  to  the  varying  currents  in  the  plate  circuit  of 
that  one  tube  reacting  back  upon  the  oscillating  circuit  to  which  the  grid 
and  filament  of  the  same  tube  are  connected.  Of  course  each  tube  may 
be  caused  to  oscillate  in  the  same  manner  at  the  same  or  a  slightly  different 
frequency  from  every  other.  What  does  happen,  however,  is  that  all 
tubes  are  subjected  to  one  single  frequency  and  the  value  of  this  frequency 
is  the  one  at  which  it  is  "  easiest  "  for  the  entire  amplifier  to  oscillate, 
that  is,  the  one  frequency  at  which  the  losses  in  the  whole  amplifier  (for 
a  given  strength  of  oscillation)  are  a  minimum;  of  course  if  these  losses 
are  greater  than  can  be  supplied  by  the  plate  battery  through  the  reactions 
of  each  plate  upon  each  grid  circuit  the  amplifier  will  fail  to  oscillate  at 
that  frequency  or  at  any  other  frequency  for  which  this  condition  prevails. 

It  may  happen,  however,  that  the  output  circuit  of  the  amplifier  is 
coupled,  either  magnetically  or  electrostatically,  or  both,  to  the  input 
circuit,  in  which  case  the  amplifier  may  oscillate,  even  if  it  would  not 
otherwise  do  so.  Thus,  consider  the  three-stage  transformer-repeating 
amplifier  of  Fig.  6,  which  is  similar  to  that  of  Fig.  13.  Assume  that  oscil- 
latory currents  start  in  the  secondary  of  transformer  T]  these  currents 
will  be  repeated  and  amplified  from  tube  to  tube;  if  now  the  plate  circuit 
of  the  last  tube  is  so  related  to  the  grid  circuit  of  the  first  that  the  varying 
currents  in  the  former  can  produce  varying  voltages  in  the  latter,  which 
are  sufficiently  large  and  in  the  right  phase  to  increase  and  sustain  the 
currents  started  in  the  secondary  of  transformer  T,  then  the  amplifier 
will  oscillate.  It  will  be  easily  understood  that  if  there  is  coupling  between 
the  output  and  input  circuit  it  is  not  a  necessary  condition,  in  order  for 
the  amplifier  to  oscillate,  that  the  oscillations  shall  start  in  the  grid  cir- 
cuit of  the  first  tube,  for,  they  may  start  in  the  grid  circuit  or  even  the 
plate  circuit  of  any  one  of  the  tubes,  including  the  last,  and,  in  every  case, 
the  amplifying  action  of  the  apparatus  may  make  it  likely  that  oscillations 
be  sustained,  even  if  the  coupling  between  the  output  and  input  circuits 
is  feeble. 

Again,  while  in  the  preceding  paragraphs  we  have  assumed  that  the 
plate  circuit  of  the  last  tube  is  coupled  to  the  grid  circuit  of  the  first  tube 
the  amplifier  may  oscillate  even  if  the  plate  circuit  of  an  intermediate 
tube  is  coupled  to  the  grid  circuit  of  the  first  tube  or,  in  general,  it  may 
oscillate  if  the  plate  circuit  of  any  one  tube  is  coupled  to  the  grid  circuit 
of  any  of  the  preceding  tubes.  For,  as  long  as  any  currents  started  in 
the  oscillatory  circuit  of  any  one  tube  are  sustained  by  the  reactions  of 
the  other  tubes  the  amplifier  as  a  whole  may  oscillate. 

Remedies  for  Amplifier  Squealing. — It  must  be  stated  at  the  outset 
that  the  more  an  amplifier  amplifies  the  more  likely  it  is  to  squeal;  in 
9ther  words,  a  silent  amplifier  is  not  necessarily  better  than  one  which 


874  AMPLIFIERS  [CHAP.  XI 

shows  tendency  to  self  oscillation;  in  fact  if  a  series  of  tubes  connected 
in  cascade  show  no  tendency  to  squeal  it  is  likely  that  the  combination 
is  so  adjusted  that  the  overall  amplification  is  much  lower  than  it  should 
be.  Even  when  all  precautions  against  squealing  have  been  taken  it 
may  be  found  upon  testing  the  amplifier  that  it  squeals  most  objection- 
ably. In  general  the  following  points  should  be  observed: 

(a)  An  amplifier  without  any  oscillatory  circuits  is  not  very  apt  to 
squeal.  A  resistance-repeating  amplifier  may  be  constructed  practically 
without  any  oscillatory  circuits,  although  it  must  be  understood  that 
even  a  short  pair  of  wires  from  an  oscillatory  circuit,  with  a  very  high 
natural  frequency  to  be  sure,  but  nevertheless  an  oscillatory  circuit. 
Hence  even  a  resistance  amplifier  may  oscillate  at  very  high  frequency 
and  yet  be  "  heard  "  if  the  grid  condensers  intermittently  "  block  "  the 
plate  current.  Resistance-repeating  amplifiers  (with  an  overall  voltage 
amplification  of  about  25,000)  have  been  constructed  which  do  not  squeal. 

(6)  Under  no  circumstances  should  the  output  and  input  circuits  of 
an  amplifier  be  coupled  together  even  in  the  feeblest  manner.  It  is  best 
to  use  for  both  of  these  circuits  short  twisted  leads  and  the  output  and 
input  circuits  should  be  kept  as  far  apart  as  possible.  The  twisted  leads 
should  be  "  shielded  "  by  enclosing  them  in  a  grounded  flexible  metallic 
casing.  As  a  matter  of  fact  it  is  advisable  that  all  plate  circuit  leads  be 
kept  from  being  coupled  to  grid  circuit  leads  of  previous  tubes;  hence 
the  leads  inside  of  the  amplifier  box  should  be  run  with  this  very  important 
point  in  view. 

(c)  Each  tube  and  its  holder  should  be  placed  in  a  shielded  chamber, 
the  surfaces  of  which  are  covered  with  copper  connected  to  ground;   this 
prevents  any  electrostatic  or  magnetic  field  from  one  tube  from  appre- 
ciably affecting  the  adjacent  tubes,  or,  in  other  words,  it  prevents  coupling 
between  adjacent  tubes,  since  the  energy  contained  in  any  varying  fields 
produced  by  one  tube  is  absorbed  by  the  currents  created  in  the  surround- 
ing   copper.       This  precaution  should  always  be  taken  in  the  case  of 
high-frequency  amplifiers  especially. 

(d)  Wherever  possible,  separate  plate  batteries  and  filament  batteries 
should  be  used  for  each  tube,  for  in   this  manner  a   means  of  coupling 
between  the  tubes  is  done  away  with.     Unfortunately,  separate  batteries 
for  all  tubes  add  so  much  to  the  weight,  size,  and  cost  of  an  amplifier  as 
to  make  the  arrangement  impossible  for  any  but  special  laboratory  work. 
In  any  case  both  of  these  batteries  should  be  of  as  low  a  resistance  as 
feasible. 

(e)  All  leads  should  be  rigidly  held  in  their  proper  places  and  all  con- 
nections be  well  soldered. 

Even  when  all  these  precautions  have  been  taken  it  may  be  that  an 
amplifier  known  to  be  correctly  built,  and  of  previous  good  behavior 


TUBE   NOISES   IN  AMPLIFIERS  875 

gives  loud  "  sputtering  "  noises  in  the  telephones,  even  when  the  input 
circuit  is  short-circuited.  This  may  be  due  to  a  "  bad  "  tube  somewhere 
in  the  amplifier  (to  be  discussed  in  the  next  section)  or  it  may  be  due 
to  either  the  A  or  B  batteries.  A  storage  battery  is  practically  always 
used  for  filament  heating,  so  it  is  evident  that  this  battery  has  a  low 
resistance,  but  it  will  be  found  that  if  a  good  amplifier  (high  amplification) 
is  used  with  an  A  battery  nearly  discharged  (say  lower  than  1.8  volts 
for  a  lead  cell)  all  sorts  of  odd  noises  may  be  heard  in  the  amplifier, 
whereas  if  a  normally  charged  A  battery  is  substituted  the  amplifier  is 
quiet. 

The  same  remark  holds  true  regarding  the  B  battery  to  an  even 
greater  degree;  the  small  dry  cells  generally  used  for  the  plate  battery 
develop  a  very  high  variable  resistance  towards  the  end  of  their  life,  and 
if  there  is  one  such  "  worn-out  "  cell  in  the  battery  it  will  result  in  very 
bad  noises  in  the  amplifier.  A  test  of  the  cells  with  a  low  resistance  volt- 
meter will  at  once  show  of  the  defective  cell. 

Tube  Noises. — Another  feature  which  causes  considerable  difficulty 
in  the  operation  of  an  amplifier  is  the  "  noise  "  produced  by  the  tubes. 
The  reader  will  realize  that  any  slight  change  in  the  currents  flowing  in 
the  plate  or  filament  circuit  of  an  amplifier  tube,  especially  if  it  be  one 
of  the  first  tubes,  may  be  so  amplified  as  to  finally  produce  a  very  large 
change  in  the  plate  current  of  the  last  tube,  and  hence  a  loud  click  in  the 
phones.  Sometimes  these  clicks  are  frequent  and  almost  deafening  as 
compared  with  the  signals,  hence  very  objectionable.  As  a  matter  of 
fact  these  noises  form  one  of  the  limitations  of  amplifiers  in  so  far  as  the 
number  of  stages  is  concerned,  since  it  is  almost  impossible  to  prevent 
minute  changes  of  currents  in  the  first  tubes,  which,  if  repeated  and 
amplified  through  a  large  number  of  stages,  may  finally  "  swamp  "  the 
legitimate  signals.  These  minute  changes  of  current  in  the  tube  circuits 
may  take  place  due  to  several  causes,  the  most  common  of  which  are: 

(1)  Sudden  slight  changes  in  the  electromotive  forces  of  the  vari- 
ous batteries  (discussed  in  previous  section). 

(2)  Mechanical  vibration  of  the  elements  of  the  tubes. 

(3)  A  slight  amount  of  gas  causing  ionization,  or,  what  is  more 
difficult  to  overcome,  actual  irregularities  in  the  rate  of  emis- 
sion of  electrons  from  the  filaments.     This  is  probably  due 
to  surface  impurities  of  the  hot  filament. 

It  is  evident  that  mechanical  vibrations  of  the  tube  elements  will 
vary  the  distance  between  the  grid  and  filament  and,  of  course,  the  plate 
current  will  change  accordingly;  the  same  is  true  of  any  changes  in  the 
distance  between  plate  and  filament  and  plate  and  grid.  Hence  the 
elements  should  be  firmly  supported.  Of  course,  no  matter  how  firmly 


876  AMPLIFIERS  [CHAP.  XI 

supported,  they  may  always  be  made  to  vibrate,  though  imperceptibly, 
and  yet  enough  to  be  detected  by  the  amplifier;  hence  the  care  must 
be  exercised  in  supporting  the  elements.  The  importance  of  this  point 
was  not  at  first  fully  realized,  and  tubes  were  used  for  aeroplane  work 
the  elements  of  which  were  not  sufficiently  well  supported,  with  the  result 
that  an  amplifier  consisting  of  these  tubes  became  practically  useless. 
The  matter  of  supporting  the  tubes  themselves  is  extremely  important 
in  this  connection  and  should  be  given  the  greatest  attention.  Amplifier 
tubes  are  generally  supported  on  thick  pieces  of  soft  spongy  rubber  or 
else  on  light  springs;  the  point  to  strive  after  is  to  obtain  a  support  such 
that  if  the  tube  as  a  whole  is  caused  to  vibrate  it  will  do  so  at  a  very  low, 
inaudible,  frequency,  and,  furthermore,  it  will  not  be  able  to  communicate 
the  vibrations  to  the  elements  of  the  tubes,  the  natural  frequency  of  which 
is  very  high  in  view  of  the  rigid  suspension  of  the  elements. 

It  will  be  realized  that  the  behavior  of  the  first  tube  of  a  multi-stage 
amplifier  must  be  extremely  regular  if  it  is  to  produce  inappreciable  noises 
in  the  telephones  at  the  output  end.  Assuming  an  amplifier  which  multi- 
plies the  input  voltage  by  104  having  a  resistance  (or  reactance)  in  the 
first  plate  circuit  of  50,000  ohms  and  assuming  that  a  voltage  of  .02  on 
the  grid  of  the  last  tube  will  give  an  audible  signal  in  the  telephones,  it 
may  be  seen  that  a  change  in  current  in  the  plate  circuit  of  the  first  tube 
of  only  10~10  ampere  will  produce  an  audible  noise.  This  might  be  a 
variation  in  the  plate  current  of  the  first  tube  of  only  one  part  in  ten 
million!  But  if  we  try  to  conceive  of  the  surface  conditions  of  the  hot 
metal  from  which  the  electrons  are  being  boiled  out,  it  seems  impossible 
that  the  emission  of  electrons  should  be  steady  enough  to  eliminate  such 
a  slight  irregularity.  In  fact  it  seems  that  with  present  tubes  a  much 
larger  variation  of  the  plate  current  is  continually  occurring. 

Again  any  outside  disturbances  impressed  on  the  input  terminals 
even  as  small  as  10~6  volt  will  produce  an  audible  noise  in  the  telephone. 

We  may  therefore  conclude  that  if  the  input  circuit  of  an  amplifier 
is  not  subject  to  interfering  signals  as  great  as  10 ~6  volt  an  amplifier  may 
usefully  be  employed  with  a  voltage  amplification  of  between  104  and 
105,  if  quiet  tubes  are  used  in  the  first  stages;  with  present  tubes  more 
than  this  (or  as  much  as  this  in  most  cases)  is  not  worth  while;  the  signal 
may  be  made  louder  by  using  perhaps  one  or  two  more  tubes,  but  in 
general  it  is  no  more  readable. 

Arrangement  of  Apparatus  in  Amplifiers. — In  Fig.  35  is  shown  a  three- 
stage  audio-frequency  amplifier  using  transformer  repeating.  The  tubes 
used  have  /-to  =7  and  the  transformer  ratio  is  about  3.5;  in  series  with 
the  negative  lead  from  each  filament  is  a  small  piece  of  resistance  wire, 
so  that  the  grids  are  held  at  a  negative  potential,  with  respect  to  each 
filament.  The  filaments  are  in  parallel  the  currents  being  controlled  by 


CONSTRUCTION   OF  AMPLIFIERS 


877 


a  common  rheostat;  the  battery  used  in  the  plate  circuit  (the  same  battery 
serves  all  tubes)  should  be  about  40  volts.  An  over-all  voltage  ampli- 
fication of  about  3000  is  obtained,  but  there  is  generally  an  audible  tube 
noise  present,  making  it  useless  for  reading  very  weak  signals. 

In  Figs.  36  and  37  is  shown  a  very  carefully  designed  amplifier  having 
its  best  performance  for  a  signal  of  6000  meters  wave-length.  Induc- 
tance repeating  is  used,  the  coils  being  toroids  with  iron-dust  cores;  they 
have  a  reactance  of  about  50,000  ohms.  The  tubes  used  have  MO  equal 
to  35  and  use  a  plate  potential  of  130  volts.  The  total  voltage  ampli- 


FIG.  35. — A  compact  transformer-repeating  audio-frequency  amplifier;  the  tubes  are  in 
spring  suspensions,  each  in  its  separate  metallic  compartment.  It  has  a  voltage 
amplification  of  about  3000. 

fication  possible,  without  squealing,  is  about  50,000,  but  its  useful  ampli- 
fication for  very  weak  signals,  is  only  about  5000. 

This  question  of  useful  amplification  is  seldom  mentioned  in  texts, 
but  is  really  very  important.  It  may  be  that  two  amplifiers  are  com- 
pared in  the  laboratory  and  it  is  found  that  one  gives  a  voltage  ampli- 
fication ten  times  as  much  as  the  other.  It  may  be  that  this  comparative 
figure  checks  when  different  tests  are  made  so  that  there  is  no  doubt 
regarding  its  accuracy.  It  might  be  then  assumed  that  if  a  signal  giving 
a  certain  current  in  the  antenna  is  just  readable  with  amplifier  A  (the 


878 


AMPLIFIERS 


[CHAP.  XI 


FIG.  36. — External  appearance  of  a  very  well-designed  amplifier  for  a  frequency  of 
50,000  cycles;  the  input  circuit  can  be  connected  to  various  stages  by  means  of  the 
plug  and  flexible  cord.  The  total  amplification  of  this  instrument  is  about  50,000 
but  it  can  seldom  be  used  efficiently  with  an  amplification  greater  than  about 
5000  because  of  tube  noises. 


FIG.  37. — Airangement  of  the  apparatus  of  the  amplifier  shown  in  Fig.  36, 


CONSTRUCTION   OF   AMPLIFIERS  879 

poorer  one)  that  when  amplifier  B  is  used  the  signal  would  be  readable 
if  the  antenna  current  were  decreased  to  one-tenth  its  former  value.  It 
will  probably  be  found,  however,  that  when  amplifier  B  is  used  an  antenna 
current  about  one-half  that  used  with  amplifier  A  is  the  least  audible 
signal,  instead  of  one-tenth,  as  is  naturally  assumed.  The  reason  for  this 
is  the  "  background  "  of  noise  (from  tubes  and  other  sources)  present 
to  a  greater  extent  with  B  than  with  A.  And  the  presence  of  the  noisy 
background  requires  a  much  stronger  signal  in  the  phones  when  using 
amplifier  B  than  is  required  when  A  is  used. 


CHAPTER  XII 
EXPERIMENTS  WITH  RADIO  CIRCUITS 

IN  this  chapter  is  indicated  a  brief  course  of  selected  experiments  to  be 
performed  in  the  radio  laboratory.  As  in  any  branch  of  engineering,  a 
laboratory  course,  to  parallel  the  theoretical  studies,  is  essential  if  the 
principles  and  actions  of  the  apparatus  investigated  are  to  be  fully  under- 
stood and  the  greatest  good  obtained. 

The  experiments  have  been  selected  primarily  to  give  the  student 
training  in  the  manipulation  and  operation  of  vacuum  tubes  in  their 
several  applications  of  detection,  amplification,  generation,  and  modu- 
lation; the  first  few  experiments,  however,  are  designed  to  investigate 
the  action  of  coupled  circuits,  receiving  circuits  and  spark  transmitters. 
The  apparatus  requirements  have  been  made  as  simple  as  possible  con- 
sistent with  satisfactory  results,  and  most  of  the  equipment  specified 
should  be  found  readily  available  in  any  laboratory  intended  for  investi- 
gation of  radio  engineering  problems. 

EXPERIMENT  NO.  1 

Object 

To  investigate  the  phenomena  of  resonance  in  a  simple  series  circuit 
and  in  two  circuits  coupled  together  by  mutual  inductance.  To  find  the 
effect  of  coupling  upon  the  form  of  the  resonance  curve  and  to  study 
the  effect  of  mis  tuning  the  secondary  circuit. 

Apparatus1 

Two  fixed  condensers  Ci  and  €2.  (These  should  be  of  suitable  value 
and  may  be  equal  in  value,  although  not  necessarily  so.) 

Two  fixed  inductances  LI  and  Z/2.  (These  inductances  should  have 
such  value  that,  when  combined  with  C\  and  €2  respectively,  the  oscil- 
lation frequencies  are  at  the  middle  of  the  range  of  frequencies  obtain- 
able with  the  alternator  available.) 

1  In  this  experiment,  as  well  as  those  which  follow,  suitable  values  of  apparatus 
constants  have  been  suggested  wherever  considered  desirable,  and  in  the  specific  direc- 
tions for  each  test,  such  suggested  apparatus  has  been  considered  as  available. 

i880 


RESONANCE  CURVES 


881 


Alternator.  (The  speed  should  be  widely  variable  so  that  a  wide 
range  of  frequencies  may  be  covered.) 

One  alternating  current  voltmeter. 

Two  alternating  current  ammeters  (to  measure  primary  and  secondary 
current). 

Frequency  indicator.  (Tachometer  or  speed  counter  will  probably 
be  found  convenient  as  the  voltage  may  be  too  low  for  the  commercial 
frequency  meter.) 

One  variable  non-inductive  resistance. 

Operation 

NOTE:  In  each  test  the  terminal  voltage  of  the  alternator  should  be 
held  constant  throughout.  A  preliminary  run  should  be  made  to  insure 
all  meters  reading  on  scale  at  the  resonant  frequency  and  to  prevent 
damage  to  meters  and  apparatus. 

Test  No.  1. — (a)  Obtain  the  resonance  curve  for  the  circuit  connected 
as  shown  in  Fig.  1,  using  as  low  resistance  in  the  circuit  as  possible. 

(6)  Repeat  test  1  (a)  with  same  alternator  voltage,  using  a  high  resist- 
ance in  the  circuit. 


Fir,.  1. 


FIG.  2. 


Readings  of  current  and  frequency  should  be  taken,  about  ten  or 
twelve  readings  at  least  being  taken  over  the  range  of  available  frequencies. 
The  readings  may  be  spread  out  where  the  current  changes  but  little 
with  frequency  and  should  be  concentrated  on  the  more  rapidly  curving 
portions  of  the  resonance  curve. 

Test  No.  2.  —  (a)  Determine  the  resonance  curves  for  coupled  circuits 
connected  as  shown  in  Fig.  2,  the  primary  and  secondary  circuits  being 
tuned.  A  suitable  alternator  voltage  will  be  about  twice  the  value  used 
in  test  1.  Use  a  coefficient  of  coupling  K  of  approximately  0.05.  If 

necessary,  measure  M,  LI  and  L2,  in  order  to  determine  K(K=  }. 

\       vLiL2/ 


Read  the  current  in  each  circuit  and  frequency,  as  the  frequency  is  varied, 
following  the  procedure  indicated  for  Test  No.  1. 


882  EXPERIMENTS   WITH   RADIO  CIRCUITS  [CHAP.  XII 

(6)  Repeat  Test  No.  2  (a),  using  a  coefficient  of  coupling  of  approxi- 
mately 0.15. 

(c)  Repeat  Test  No.  2  (a),  using  a  coefficient  of  coupling  of  approxi- 
mately 0.40. 

Test  No.  3.  —  Using  a  high  value  of  coupling  (say  0.40),  determine 
the  resonance  curves  for  coupled  circuits,  with  the  secondary  circuit 
mistuned  about  50  per  cent.  (Increase  or  decrease  €2  so  that 


=  1.5\/LiCi  or  .SVLiCi,  choosing  that  variation  which  may  be  most 
convenient  to  make  with  the  apparatus  at  hand.) 

Curves 

Plot  resonance  curves  for  each  of  the  six  runs  specified  above.  Illustra- 
tive curves  are  shown  in  Chapter  I,  Figs.  53,  54  and  95.  For  tests  Nos. 
2  and  3,  calculate  «'  and  co",  using  formulae  (97),  (98),  (103)  and  (104), 
Chapter  I.  It  is  suggested  that  the  student  review  that  part  of  Chapter 
I  dealing  with  coupled  circuits  before  attempting  to  carry  out  the  fore- 
going tests. 

EXPERIMENT  NO.  2 

Object 

Use  of  a  buzzer-wave  generator;  setting  up  and  adjusting  a  receiving 
circuit  using  a  crystal  detector;  characteristic  curves  of  a  crystal  rectifier 
by  continuous  current  test;  operation  of  a  crystal  rectifier  on  alternating 
current. 

Apparatus 

Two  dry  cells. 

Fixed  inductance  L'  (about  150  microhenries). 

Fixed  capacity  C'  (about  .005  microfarad). 

Buzzer  rheostat. 

Buzzer. 

Variable  inductance  L  (0-5000  microhenries). 

Variable  capacity  C  (0-.0010  microfarad). 

Phones. 

Crystal  rectifier. 

Micro-ammeter  (0-1000  micro-amperes). 

Potentiometer. 

Low-reading  d.c.  voltmeter. 

Source  of  low  potential  alternating  current.     (May  be  conveniently 
obtained  from  an  alternator  operated  with  its  field  circuit  open.) 
»      Low-reading  a.c.  voltmeter. 


CHARACTERISTICS  OF  CRYSTAL  RECTIFIERS  883 

Operation 

Test  1. — Connect  the  buzzer  wave-generator  in  accordance  with 
Fig.  3.  Vary  the  buzzer  adjustment  and  series  resistance  until  a  pure 
musical  note  is  obtained. 

Test  2. — Connect  the  receiver  circuit  in  accordance  with  Fig.  4. 
Couple  this  circuit  closely  to  the  buzzer  generator,  and  adjust  the  recti- 
fying crystal  until  a  loud  signal  is  heard  in  the  phones.  Jar  the  crystal 
and  note  how  easily  its  adjustment  is  spoiled.  Note  how  easy  or  difficult 
it  is  to  find  another  good  rectifying  point  on  the  crystal.  £, 

Test  3. — With  tight  coupling,  and  holding  the  inductance  constant, 
vary  the  capacity  until  resonance  is  obtained  (maximum  signal  in  phones). 
Note  the  range  of  condenser  adjustment  over  which  the  signal  is  heard. 
This  is  a  measure  of  the  selectivity.  (See  Note.)  Repeat  this  test  with 
various  values  of  coupling,  and  note  the  relation  between  selectivity  and 
coupling. 


c' 


\     mh      i 


FIG.  3.  FIG.  4. 

NOTE:  A  circuit  is  said  to  be  selective  when  it  is  necessary  (in  order 
to  get  a  maximum  strength  of  signal)  to  adjust  closely  the  value  of  induc- 
tance or  capacity  being  used  for  tuning  the  circuit.  If  the  signal  is  of 
about  the  same  strength  for  widely  different  values  of  the  tuning  con- 
denser or  inductance,  the  circuit  is  said  to  be  non-selective;  or  it  may 
be  said  that  the  tuning  is  broad  for  such  a  circuit,  while  a  selective  circuit 
is  said  to  have  sharp  tuning.  A  circuit  which  has  no  natural  period  is 
said  to  be  "  aperiodic." 

Test  4. — With  loose  coupling  make  the  inductance  as  low  as  possible, 
obtain  resonance  by  varying  the  condenser,  and  note  the  strength  of 
signals  and  selectivity.  Repeat,  using  a  very  high  inductance.  Com- 
pare the  strength  of  signals  and  selectivity  in  the  two  cases. 

Test  5. — Obtain  the  continuous  current  characteristic  of  the  rectifier 
(in  this  case  a  crystal),  making  the  connections  as  indicated  in  Fig.  5. 
Vary  the  voltage  impressed  on  the  crystal  from  plus  one  volt  to  minus 
one  volt.  Get  a  reading  of  the  current  for  each  0.1  volt  between  the 
limits  named.  The  above  test  should  be  made  for  a  point  on  the  crystal 
which  shows  good  rectification  in  the  receiving  circuit  of  Fig.  4.  Obtain 
another  curve  for  a  second  point  on  the  crystal  which  shows  poor  detection 


jVWWWVVVAAA/VWv'VWV 


884  EXPERIMENTS   WITH   RADIO   CIRCUITS  [CHAP.  XII 

when  tried  with  the  buzzer.     Make  a  note  of  which  side  of  the  detector 

is  positive  when  the  larger  current  flows. 

Test  6. — Replace  the  battery  shown  in  Fig.  5  by  a  low  potential  alter- 
nating current  source  and  connect  the  a.c.  volt- 
meter directly  across  this  source.  Starting  with  a 
potentiometer  setting  which  gives  the  lowest  volt- 

j\^^WWWVAAA^AA\\VV  .  ,. 

\      /~\     fi  age,  get  a  series  of  readings  of  the  micro-ammeter 

\  and  of  the  impressed  voltage,    and   note  how  the 

__//\\_^j /  rectification    varies    with    the    impressed   voltage. 

The    voltage    impressed    across    the    crystal    and 
FlG-  5-  galvanometer  is  to  be   calculated   from  the   meas- 

ured voltage  of  the  a.c.  generator  and  the  position 

of  the  potentiometer  contact;   the  resistance  used  in  the  potentiometer 
must,  of  course,  be  low  compared  to  that  of  the  crystal. 

QUESTIONS 

1.  If  in  a  buzzer  circuit  L  =  100  microhenries  and  C  =  .0004  micro- 
farad, what  is  the  wave-length?     If  C  =  .0002  microfarad,  what  value 
must  L  have  to  generate  a  wave-length  of  600  meters? 

2.  Judging  from  your  experimental  results  is  tight  coupling  or  loose 
coupling  generally  desirable   under    actual  field  conditions  where  much 
interference  is  likely  to  occur? 

3.  A  circuit  is  tuned  for  an  incoming  signal  with  certain  values  of 
L  and  C.     If  L  is  increased  four  times  what  change  must  be  made  in  C 
to  maintain  the  tuning? 

4.  What  three  characteristics  should  a  good  crystal  rectifier  possess? 

EXPERIMENT  NO.  3 

Object 

Study  of  the  wave-meter;  use  of  the  meter  for  measuring  the  wave- 
length of  low-  and  high-powered  circuits,  i.e.,  receiving  and  transmitting 
circuits;  measurement  of  inductance  and  capacity  by  means  of  the  wave- 
meter,  using  the  meter  as  a  detecting  circuit  or  as  a  calibrated  wave- 
generator. 

Apparatus 

Two  dry  cells. 

Coil  A — standard  fixed  inductance  (about  50  microhenries). 

Coil  B — unknown  fixed  inductance  (one  designed  for  low  voltage 
service). 

Coil  C — unknown  fixed  inductance  (antenna  loading  coil  or  one  coil 
of  an  oscillation  transformer). 


CONSTRUCTION   AND   USE  OF  WAVE-METER  885 

Condenser  D — unknown  fixed  condenser.  (Small  capacity  intended 
for  low  voltage  service.) 

Condenser  E — unknown  fixed  condenser.  (Condenser  used  for  high 
voltage  service,  e.g.,  in  the  closed  circuit  of  a  spark  transmitter,  2  or  3 
Ley  den  jars  in  parallel  would  be  suitable.) 

Condenser  F — unknown  variable  condenser  (such  as  used  in  receiving 
circuit — is  to  be  adjusted  only  for  maximum  capacity). 

Wave-meter  (range  to  at  least  1000  meters). 

Buzzer. 

Buzzer  rheostat. 

Crystal  rectifier. 

Source  of  power  for  high  power  test  (Test  No.  7).  This  is  most  con- 
venientty  obtained  by  disconnecting  the  normal  closed  circuit  capacity 
and  inductance  from  an  ordinary  spark  transmitter,  no  change  being 
made  in  the  low-tension  circuit,  step-up  transformer  or  spark  gap  con- 
nections. (See  Fig.  7.) 

Operation 

Test  1.  Inspection  of  Wave-meter. — Open  and  inspect  in  detail 
whatever  wave-meter  may  be  available.  Draw  a  diagram  of  the  con- 
nections, and  study  carefully  the  various  parts.  Note  how  the  unilateral 
connection  of  the  detector  and  phones  may  be  obtained. 

Test  2.    Measurement  of  Capacity. — Set  up  a  buzzer-excited  circuit 
as  indicated  in  Fig.  6  and  consisting  of  A  and  D.     (See  Note.)     Measure 
by  means  of  the   wave-meter,    the   wave- 
length of  the  oscillations  generated,  using 
no  tighter  coupling   than   necessary  (weak 
coupling     is     necessary     if    an     accurate 
setting     of     the     wave-meter    is     to     be 

obtained).      From     the    measured    wave-  CCD/^1  ' T 

length     and    the     known     value     of    the 

inductance    calculate    the  capacity  of  the  FlG-  6- 

condenser. 

NOTE:  In  this  and  in  subsequent  tests  make  connections  with  short 
leads.  Use  particularly  short  leads  in  the  oscillating  circuits.  The 
capacity  of  the  leads  connecting  the  condenser  to  the  inductance  or  to 
the  detector  circuit  or  to  the  buzzer  acts  as  part  of  the  capacity  of  the 
oscillating  circuit,  thus  making  the  capacity  of  the  circuit  greater  than 
that  of  the  condenser  and  giving  an  error  proportional  to  the  capacity 
of  the  leads.  The  error  depends  upon  the  value  of  the  capacity  of  the 
condenser;  for  large  condensers  the  effect  is  small,  but  for  condensers 
of  100  micro-microfarads  or  less  an  error  of  25  per  cent  may  easily  be  made. 


886 


EXPERIMENTS   WITH   RADIO   CIRCUITS 


[CHAP.  XII 


A  similar  error  occurs  due  to  the  inductance  of  the  leads  in  the  oscillating 
circuit. 

Test  3.  Measurement  of  Capacity. — Repeat  Test  2,  substituting 
condenser  E  for  condenser  D. 

Test  4.  Measurement  of  Capacity;  Computation  of  Capacity  from 
Dimensions. — Repeat  Test  2,  substituting  condenser  F  (set  for  maximum 
capacity)  for  condenser  D.  Before  performing  this  test  take  apart  con- 
denser F,  obtain  the  dimensions  and  number  of  plates,  and  compute 
capacity.  Compare  the  computed  with  the  measured  capacity. 

Test  5.  Measurement  of  Inductance;  Computation  of  Inductance 
from  Dimensions. — Calculate  the  value  of  inductance  of  Coil  B  from 
its  dimensions,  and  then  measure  it,  using  for  a  standard  capacity  such 
a  combination  of  condensers  D,  E,  and  F  as  will  produce  a  wave-length 
within  the  range  of  the  wave-meter.  This  value  of  wave-length  is  to  be 
calculated  from  the  known  values  of  the  capacities  and  the  computed 
value  of  the  inductance. 

Test  6.  Wave-length  of  an  Oscillating  Circuit  Excited  by  a  Buzzer. — 
Measure  the  wave-length  produced  by  the  combination  of  Coil  C  and 

condenser  E,  using  a  buzzer  circuit 
as  in  previous  tests. 

Test  7.  Wave-length  of  an  Os- 
cillating Circuit  Excited  by  a  Power 
Set.— Transfer  C  and  E  to  the  high- 
power  circuit  shown  in  Fig.  7,  and 
again  measure  the  wave-length.  It 
should  be  found  that  the  wave-length 
for  tests  6  and  7  is  the  same. 

Test  8.  The  Wave-meter  as  a  Wave-generator. — Connect  the  wave- 
meter  as  a  wave-generator  as  indicated  in  Fig.  8  and  couple  to  it  the  oscil- 
lating circuit  consisting  of  coil  A  and  condenser  D,  with  detector  and 
phones  as  shown  in  the  fig- 
ure. Vary  the  wave-length 
generated  by  the  wave-meter 
until  the  test  circuit  indi- 
cates resonance;  the  wave- 
length of  the  test  circuit  is 
then  read  from  the  wave- 
meter.  From  this  and  the 

known  inductance  compute  the  capacity.  It  should  be  found  that  the 
capacity  thus  obtained  agrees  with  that  found  in  Test  2,  when  the  wave- 
meter  was  used  as  the  detecting  circuit.  What  small  difference  occurs 
is  due  to  the  capacity  and  inductance  of  leads,  personal  error,  etc. 


FIG.  7. 


FIG.  8- 


ADJUSTMENT  OF  TRANSMITTING   SET  887 

QUESTIONS 

1.  If  the  wave-length  of  a  circuit  is  to  be  increased  from  600  meters 
to  2500  meters  how  much  must  the  L  of  the  circuit  be  increased,  the  C 
of  the  circuit  remaining  the  same? 

2.  The  maximum  capacity  of  the  condenser  of  a  certain  wave-meter 
is  5500  micro-micro-farads.     Its  maximum  wave-length  is  6200  meters. 
What  is  the  inductance  of  the  coil  used?     If  the  range  of  the  meter  is 
to  be  increased  to  12,000  meters  how  much  inductance  must  be  added 
to  that  of  the  meter? 

3.  A  solenoiclal  coil  has  a  winding  5  inches  long,  25  turns  to  the  inch, 
and  is  4  inches  in  diameter.     What  is  L  in  cm.  and  in  microhenries  and 
in  millihenries? 

4.  A  sliding  plate  condenser  has  eleven  fixed  plates  and  ten  movable 
plates.     The  plates  are  3  inches  by  4J  inches  and  the  separation  of  adjacent 
plates  is  -£%  inch.     What  is  the  capacity  in  cm.  and  in  microfarads? 

EXPERIMENT  NO.  4 

Object 

To  set  up  and  adjust  a  transmitting  set,  using  inductive  coupling; 
to  investigate  the  effect  on  antenna  current  of  tuning  the  antenna  circuit 
to  the  closed  circuit;  effect  of  coupling  on  the  amount  of  antenna  current 
and  wave-lengths  radiated;  energy  distribution  curve;  determination 
of  the  decrement  of  the  set ;  conductive  coupling. 

Apparatus 

Source  of  alternating  current  supply  (500~  or  60^)  and  step-up 
power  transformer  designed  for  radio  service  (about  1  kw.  rating).  Spark 
gap  (plain  open  gap).  Oscillation  transformer  (the  inductances  used 
may  be  of  the  flat  spiral  type,  should  be  insulated  for  high  voltages,  and 
have  a  maximum  inductance  of  about  40-50  microhenries) . 

High-voltage  condensers  for  primary  and  secondary  circuits.  (These 
may  conveniently  consist  of  Leyden  jars,  properly  connected.  The 
amount  of  capacity  will  depend  on  the  wave-length  for  which  it  is  decided 
to  adjust  the  set,  but  will  probably  not  exceed  -.005  to  .010  microfarad 
for  either  circuit.) 

Hot-wire  ammeter  for  antenna  circuit. 

Wave-meter. 

Loading  inductance  (may  or  may  not  be  needed,  depending  on  relative 
values  of  closed  and  open  circuit  inductance  and  capacity)- 


888 


EXPERIMENTS  WITH   RADIO  CIRCUITS 


[CHAP.  XII 


Loading  resistance  (may  be  found  necessary  to  limit  current  in  antenna 
circuit  to  a  safe  value  and  will  probably  not  be  more  than  5  or  10  ohms). 

Switch  for  controlling  the  low-voltage  supply  to  the  step-up  trans- 
former (usually  a  S.  P.  S.  T.  switch). 

Operation.    Inductively  Coupled  Transmitter 

Test  1.  Connections. — Make  connections  as  shown  in  Fig.  9  with 
the  exception  of  the  antenna  circuit,  which  is  to  be  left  open;  use  short 
wires  arranged  in  direct  and  orderly  fashion.  The  high-voltage  wiring 
between  the  power  transformer  and  the  primary  winding  of  the  oscillation 
transformer  is  dangerous,  and  must  be  so  arranged  that  accidental  contact 
with  it  is  not  likely.  Before  turning  power  on  the  set  ask  the  instructor 
to  look  over  the  connections  and  to  set  the  spark  gap  to  a  suitable  length. 

1C, 


Note:  L'and 
R  may  not 
be  required 


Low  Frequency 


and  Low  Tension 
Not  Dangerous 


High  and  Low 
Frequency     -  High 


Tension 
Dangerous 


-High 


uency. 


and  High  Tension 
Burn  only 


FIG.  9. 


Test  2.  Adjustment  of  Closed  Circuit. — When  the  gap  is  sparking 
properly,  place  the  wave-meter  in  proximity  to  the  primary  of  the  oscil- 
lation transformer  and  read  the  wave-length  which  is  being  generated. 
Change  the  amount  of  inductance  used  until  the  set  is  generating  the 
wave-length  for  which  the  set  is  to  be  adjusted.  Keep  the  antenna  cir- 
cuit open. 

Test  3.  Tuning  of  Antenna  Circuit  to  Closed  Circuit. — Close  the 
antenna  circuit  or  secondary  oscillating  circuit.  In  one  of  the  Connect- 
ing wires  take  two  or  three  turns,  making  a  loose  coil  about  3  inches  in 
diameter.  This  coil  is  for  exciting  the  wave-meter;  it  must  be  left  fixed 
and  treated  as  part  of  the  inductance  of  the  secondary  circuit;  although 
its  inductance  is  small  it  will  generally  be  large  enough  to  effect  the  wave- 
length of  the  set  and  so  must  not  be  altered  when  investigating  the  effect 
of  other  changes  in  the  circuit.  It  might  seem  that  the  wave-meter 
should  be  coupled  to  the  secondary  of  the  oscillation  transformer  to  read 
the  wave-length  of  this  circuit,  but  this  must  not  be  done;  the  wave- 
meter  indication  when  excited  by  the  magnetic  field  of  the  oscillation 
transformer  may  lead  to  entirely  incorrect  conclusions.  The  coil  used 
for  exciting  the  wave-meter  will  be  known  as  the  "  search-coil." 


ADJUSTMENT  OF  TRANSMITTING  SET  889 

Tune  the  secondary  to  the  primary  circuit  in  the  following  manner 
with  loose  coupling:  Vaiy  the  number  of  turns  used  in  the  secondary 
until  the  ammeter  shows  maximum  current;  at  this  point  the  second- 
ary and  primary  circuits  are  tuned.  Check  this  by  reading  the  wave- 
length; it  will  be  found  to  be  the  same  as  that  to  which  the  primary 
has  been  adjusted.  Hence  if  the  primary  circuit  of  a  set  is  calibrated 
it  is  not  necessary  to  have  a  wave-meter  to  tune  the  secondary  circuit; 
an  ammeter  in  this  circuit  is  all  that  is  necessary. 

Test  4.  Relation  of  Antenna  Current  to  Turns  of  Secondary  of  Oscil- 
lation Transformer. — To  show  more  exactly  the  effect  of  tuning  on  the 
antenna  current  obtain  a  series  of  readings  between  antenna  current  and 
number  of  secondary  turns,  and  plot  a  curve.  Before  getting  this  series 
of  readings  adjust  the  coupling  of  the  oscillation  transformer  so  that 
with  tuned  circuits  the  ammeter  reads  well  up  on  its  scale.  This  is  to  make 
certain  that  the  maximum  deflection  will  not  exceed  the  range  of  the 
instrument. 

Test  5.  Energy  Distribution  Curves. — With  the  two  circuits  properly 
tuned,  and  tight  coupling  in  the  oscillation  transformer,  couple  the  wave- 
meter  loosely  to  the  search  coil.  Vary  the  setting  of  the  wave-meter 
until  a  maximum  reading  of  the  wave-meter  ammeter  is  obtained ;  increase 
the  coupling  of  the  meter  to  search  coil  until  the  wave-meter  ammeter 
reads  about  one-half  full  scale  value.  Keep  the  adjustment  of  the  wave- 
meter  coupling  constant  while  getting  the  three  runs  indicated  in  the  next 
paragraph. 

Take  a  series  of  readings  of  the  wave-meter  ammeter  for  various  set- 
tings of  the  wave-meter  condenser;  get  enough  points  to  plot  an  accurate 
curve  between  wave-meter  settings  and  ammeter  readings.  This  curve 
shows  the  energy  distribution  of  the  oscillations  in  the  secondary  circuit. 
The  wave-meter  corresponds  to  a  tuned  receiving  set  and  its  indica- 
tions show  how  strong  a  signal  (relatively)  variously  tuned  receiving 
stations  would  receive  from  this  transmitting  set.  Get  similar  energy 
distribution  curves  for  medium  coupling  and  for  loose  coupling. 

It  will  be  found  that  for  tight  coupling  two  distinct  waves  are  gener- 
ated, neither  of  them  being  that  for  which  the  set  is  tuned.  One  of  them 
is  higher  than  the  proper  wave-length  and  one  of  them  is  lower.  The 
amount  by  which  the  two  waves  differ  depends  upon  the  coupling,  the 
difference  diminishing  as  the  coupling  is  weakened ;  for  very  weak  coupling 
they  merge  together. 

Test  6.  Effect  of  Coupling  upon  Antenna  Current  and  upon  Energy 
Radiated  at  Tuned  Wave-length. — Set  the  wave-meter  to  the  tuned  wave- 
length, vary  the  coupling  between  the  primary  and  secondary  of  the 
oscillation  transformer,  and  read  the  antenna  ammeter  and  the  wave- 
meter  ammeter  for  various  values  of  coupling.  It  will  generally  be 


S:;0  EXPERIMENTS  WITH  RADIO  CIRCUITS  [CuAp/XII 

found  that  the  antenna  current  continually  rises  as  the  coupling  is  in- 
creased, but  the  amount  of  energy  radiated  at  the  true  wave-length  of  the 
set  (indicated  by  the  reading  of  the  wave-meter  ammeter,  the  wave-meter 
being  a  tuned  receiving  set)  will  be  a  maximum  at  some  value  of  coup- 
ling considerably  less  than  the  maximum  obtainable  with  the  set.  This 
is  a  very  important  point;  a  set  should  not  be  adjusted  for  maximum 
antenna  current,  but  to  radiate  a  maximum  power  at  that  wave-length  for 
which  the  set  is  tuned  (and  hence  that  for  which  the  listening  stations  are 
tuned.) 

Test  7.  Conductively  Coupled  Transmitter. — Carry  out  the  tuning 
test  for  a  conductively  coupled  oscillation  transformer,  using  the  primary 
of  the  transformer  for  the  coupler,  and  making  connections  as  in  Fig.  10. 
Adjust  the  primary  to  the  same  wave-length  for  which  the  set  was  adjusted 
in  Test  2,  with  the  antenna  circuit  open.  Close  the  antenna  circuit  and 


FIG.  10. 

adjust  the  turns  included  in  this  circuit  until  the  antenna  ammeter  gives 
a  maximum  indication.  With  this  adjustment  take  an  energy  distribu- 
tion curve  by  means  of  the  wave-meter. 

Test  8.  Adjustment  of  the  Spark  Gap. — Carry  out  the  following 
tests  on  spark  gap  adjustment  with  the  antenna  circuit  open.  Place  a 
suitable  hot-wire  ammeter  in  the  primary  of  the  oscillation  transformer. 
Set  the  gap  to  ^  inch,  and  note  current  and  character  of  sparking;  repeat 
the  gap  settings  of  |,  -f$,  i,  3^,  f  inch.  It  will  be  noted  that  if  the  gap 
is  made  too  short  for  the  voltage  the  set  is  generating  the  spark  will 
change  from  a  white  snappy  spark  to  a  more  or  less  transparent  arc. 
This  is  especially  true  if  the  gap  surfaces  are  rough  and  dirty. 

t  The  arcing  type  of  spark  makes  a  transmitting  set  practically  inopera- 
tive because  of  the  very  small  amount  of  high-frequency  power  general  od 
with  such  a  spark.  If  the  gap  of  a  set  acts  in  this  manner  it  should  first 
be  cleaned  thoroughly  and  then  the  voltage  of  the  set  reduced  or  the  length 
of  the  gap  increased.  It  will  be  noted  in  support  of  this  statement  that 
when  the  gap  has  the  arcing  character  the  reading  of  the  hot-wire  ammeter, 
showing  the  amount  of  high-frequency  current,  is  small  compared  to  the 
reading  when  the  spark  has  the  snappy,  noisy,  and  white  appearance. 


ANTENNA   MEASUREMENTS  891 


QUESTIONS 

1.  A  spark  gap  is  set  to  break  down  at  5000  volts;   the  closed  circuit 
condenser  has  a  capacity  of  .0009  microfarad;    there  are  350  sparks  per 
second.     How  many  watts  of  high-frequency  power  are  generated  in  the 
closed  circuit?     If  60  per  cent  of  this  power  is  transferred  to  the  antenna 
circuit  and  the  effective  resistance  of  the  antenna  is  8  ohms,  what  will 
the  antenna  ammeter  read? 

2.  An  open  spark  set  is  tuned  for  410  meters;   the  coupling  is  30  per 
cent.     What  wave-lengths  are  radiated?     If  the  coupling  is   decreased 
to  8  per  cent  what  two  waves  would  be  radiated?     Would  they  appear 
as  two  waves  with  an  ordinary  receiving  set? 

3.  Calculate  the  decrement  of  your  transmitting  set  for  one  of  the 
adjustments  for  which  an  energy  distribution  curve  was  obtained,  using 
that  curve  showjng  the  purest  radiation.     Assume  the  wave-meter  decre- 
ment is  .03,  if  it  is  not  known. 

4.  From  the  energy  distribution  curve  for  the  tighest  coupling  used 
in  your  experiment  calculate  the  percent  coupling  for  that  adjustment? 

EXPERIMENT  NO.  5 

Object 

To  measure  the  natural  wave-length,  inductance  and  capacity  of  an 
antenna  and  its  variation  with  loading,  etc.  If  time  permits,  to  measure 
antenna  resistance. 

Apparatus 

Large  and  small  antenna,  variable  known  inductance  of  about  4000 
microhenries.  Receiving  coupler,  phones,  and  detectors  to  set  up  aperi- 
odic detecting  circuit,  wave-meter  for  wave-generator.  Variable  known 
condenser  from  about  .001  microforad  to  zero. 

Operation 

Test  1.  To  measure  the  natural  wave-length  of  an  antenna  we  use  two 
other  circuits  coupled  loosely  to  the  antenna  and  so  arranged  that  no  energy 
can  get  directly  from  one  into  the  other. 

The  wave-meter,  used  as  a  wave- generator,  is  coupled  to  the  antenna, 
using  only  oue  or  two  small  turns  in  the  antenna  for  the  coupling.  The 
detecting  circuit  made  up  of  one  or  two  turns  of  the  primary  of  a  coupler 
in  the  antenna  and  a  part  of  the  secondary  coil  (as  little  as  feasible), 
used  with  crystal  detector  and  phone,  forms  the  detecting  circuit. 


892  EXPERIMENTS  WITH  RADIO  CIRCUITS  [CHAP.  XII 

This  detecting  circuit  responds  equally  well  to  all  frequencies,  being 
aperiodic.1  The  antenna  will  absorb  most  energy  from  the  wave-meter 
driver  when  the  natural  period  of  the  antenna  and  that  being  generated 
by  the  wave-meter  are  the  same. 

The  aperiodic  circuit  will,  therefore,  give  a  maximum  of  noise  in  the 
phones  when  the  wave  meter  is  impressing  on  the  antenna  a  wave  of  its 
own  natural  frequency.  This  is  then  read  directly  from  the  wave-meter. 

Carry  out  this  test  for  both  antennae,  using  as  small  an  amount  of 
added  inductance  (for  coupling)  as  is  possible. 

Test  2.  To  measure  the  capacity  of  the  antenna,  measure  its  wave- 
length (by  method  just  described)  when  enough  known  inductance  has  been 
added  in -the  base  of  the  antenna  and  increase  its  wave-length  at  least  four 
times.  Knowing  the  value  of  this  added  inductance  (and  neglecting  the 
inductance  of  the  antenna  itself)  the  capacity  of  the  antenna  is  calculated. 

Knowing  the  capacity  of  the  antenna  and  also  the  natural  wave- 
length (no  added  inductance)  the  inductance  of  the  antenna  may  be  cal- 
culated. 

The  capacity  of  the  antenna  may  then  be  more  accurately  calculated 
by  using  the  total  inductance  (the  known  inductance  added  in  the  base 
plus  the  antenna  inductance).  This  corrected  value  will  generally  check 
the  approximate  value,  obtained  by  neglecting  the  antenna  inductance, 
within  1  or  2  per  cent. 

Test  3.  The  wave-length  of  the  antenna  is  to  be  measured  for  various 
values  of  loading  inductance  and  for  various  values  of  series  condenser, 
exactly  as  was  described  above. 

About  ten  points  should  be  obtained  for  each  curve,  so  selecting  the 
values  of  inductance  and  condenser  that  the  points  obtained  are  uniformly 
distributed  with  respect  to  wave-length. 

If  time  permits  make  the  third  run  by  putting  a  maximum  loading 
in  the  antenna  and  shunt  the  condenser  across  the  loading  coil.  Find 
the  wave-length  of  the  antenna  for  a  very  low  value  of  capacity  shunted 
around  the  inductance  and  take  several  more  readings  of  antenna  wave- 
length as  the  amount  of  shunted  capacity  is  gradually  increased. 

Test  4.  — The  resistance  of  an  antenna  is  obtained  (for  any  given 
wave-length)  b}^  exciting  from  a  sending  set,  having  a  hot-wire  ammeter  in 
the  base  of  the  antenna.  Use  no  more  power  than  is  necessary  to  give  a 
good  deflection  on  the  lowest  range  hot-wire  meter  available.  Now  add  in 
series  with  the  antenna  (at  its  base)  a  non-inductive  resistance  of  sufficient 
value  to  cut  down  the  current  in  the  antenna  to  50  per  cent  its  former 
value,  leaving  the  exciting  circuit  exactly  the  same. 

1  It  may  be  that  the  coil  used  in  the  aperiodic  circuit  has  its  natural  period  in  the 
wave  range  of  the  test;  this  natural  period  may  be  mistaken  for  the  natural  period 
of  the  antenna.  Check  this  by  putting  a  little  extra  inductance  in  the  antenna  circuit 
to  see  if  the  maximum  signal  is  still  found  as  the  same  wave-length. 


ANTENNA  MEASUREMENTS  893 

Neglecting  a  certain  small  correction,  the  value  of  which  depends  upon 
the  ratio  of  the  decrements  of  the  antenna  circuit  and  driving  circuit, 
the  value  of  the  added  resistance  is  just  equal  to  the  antenna  resistance. 
In  case  a  quenched  gap  is  used  in  the  exciting  circuit,  the  value  of  resist- 
ance obtained  should  be  increased  by  about  20  per  cent. 

Another  method  for  getting  the  resistance  is  by  getting  the  decrement 
of  the  antenna  at  various  wave-lengths,  using  quenched-spark  excitation. 
The  resistance  is  then  obtained  by  the  relation 


5=wRVC/L. 

If  C  and  L  are  not  known  the  decrement  may  be  obtained  after  a  small 
non-inductive  resistance  has  been  added  in  the  base  of  the  antenna.  This 
combined  with  the  decrement  obtained  before  the  addition  of  resistance, 
will  give  the  antenna  resistance  even  if  L  and  C  are  not  known. 

The  tests  outlined  above  are  for  damped-wave  excitation;  the  results 
of  the  test  should  be  checked  by  measurements  with  continuous-wave 
excitation  after  Ex.  11  has  been  carried  out. 

QUESTIONS 

1.  Why  is  it  necessary  to  use  few  turns  in  the  coupling  coils,  when 
measuring  natural  wave-length?     How  could  you  tell   (approximately) 
the  natural  wave-length  of  a  ship's  antenna?    About  how  much  is  the 
capacity  of  a  ship's  antenna? 

2.  How  many  microhenries  of  inductance  would  you  add  in  the  base 
of  such  an  antenna  to  increase  the  wave-length  to  1000  meters?   to  2500 
meters? 

3.  Using  the  same  width  spreader,  how  much  might  the  capacity  of 
a  4-wire  aerial  be  increased  by  increasing  the  number  of  wires  to  eight? 
Explain. 

4.  Would  the  capacity  of  a  ship's  aerial  change  as  coal  is  taken  on 
board?    Why?    How  much?     How  much  would  such  a  change  alter  the 
natural  wave-length  of  the  aerial? 

5.  Why  are  aerials  excited  from  spark  transmitters  generally  operated 
at  a  wave-length  greater  than  the  natural  wave-length? 

6.  Of  what  two  general  components  is  the  total  resistance  of  antenna 
made  up? 

7.  How  do  these  vary  with  the  wave-length  radiated  from  the  antenna? 

8.  Explain  the  difference  between  the  shape  of  resistance  curves  of 
a  land  station  and  a  ship  station? 

9.  If  a  land  station  shows  a  high  ground  resistance,  how  would  you 
attempt  to  remedy  it?     Why  is  a  high  ground  resistance  objectionable? 

10.  Show  by  sketches  the  distribution  of  current  and  voltage  in  an 
antenna  for  the  three  cases,  first,  antenna  by  itself;  second,  antenna  with 
loading  coil  in  base;  third,  antenna  with  series  condenser  in  base. 


894  EXPERIMENTS  WITH   RADIO   CIRCUITS  [CHAP.  XII 

11.  Explain  how  the  series  condenser  cuts  down  the  natural  wave- 
length of  an  antenna. 

12.  What  is  the  effect  on  the  antenna  resistance  of  adding  loading 
coil  in  base  of  antenna  and  also  of  adding  series  condenser? 

13.  How  will  the  decrement  of  an  antenna  vary  as  the  amount  of 
loading  inductance  is  increased? 

14.  What  is  likely  to  happen  to  a  series  condenser  in  the  base  of  an 
antenna?     Why?     How  may  it  be  prevented? 

15.  In  what  part  of  a  ship's  antenna  is  the  current  a  maximum? 

EXPERIMENT  NO.  6 

Object 

To  determine  the  continuous  current  characteristics  of  a  three-electrode 
tube,  using  a  tube  suitable  for  receiving  and  amplifying  radio  signals. 
Free  grid  potential.  Effect  of  low  plate  voltage  or  low  filament  current 
on  the  characteristics  of  the  tube.  Effect  of  reversed  plate  battery  or 
reversed  filament  battery. 

Apparatus 

One  vacuum  tube  (receiving  type,  as  for  instance,  the  Western  Electric 
Co.'s  VT-1,  or  General  Electric  Co.'s  VT-11). 

Vacuum  tube  receptacle. 

Two  dry  cells  (to  be  used  for  grid  potential). 

Ammeter  (for  filament  current). 

Milliameter  (for  plate  current). 

Micro-ammeter  (for  grid  current). 

Potentiometer  (should  be  of  high  resistance). 

Voltmeter  (for  reading  plate  voltage). 

Low  range  voltmeter.  (For  reading  grid  voltage.  If  voltmeter  for 
measuring  plate  voltage  is  equipped  with  low-range  scale,  this  instrument 
will  not  be  required.) 

Rheostat  for  filament  circuit. 

Dry  battery  for  plate  circuit  (about  40  volts). 

Storage  battery  (for  filament  circuit). 

Operation 

Test  1.  Tube  Characteristic  under  Normal  Conditions  of  Plate 
Voltage  and  Filament  Current. — Grid  voltage  vs.  plate  current  and  Grid 
voltage  vs.  Grid  current  curves  should  be  plotted  for  each  of  the  tests 
indicated,  plotting  current  on  the  Y  axis. 


THE   THREE-ELECTRODE   VACUUM   TUBE  895 

Connect  the  tube  in  accordance  with  Fig.  11  with  the  negative  side 
of  the  filament  as  the  common  junction.  With  plate  voltage  about  20 
volts,  filament  current  =  1.1  ampere, 
vary  grid  potential  from  +2  to  —2 
volts  in  steps  of  0.2  volt,  and  read 
plate  current  and  grid  current  for 
each  adjustment  of  grid  voltage. 

Test  2.  Free  Grid  Potential 
under  Normal  Conditions  of  Plate 
Current. — Determine  the  free  grid  FIG.  11. 

potential  by  reading  the  plate  cur- 
rent with  grid  entirely  disconnected  from  the  rest  of  the  circuit.     From 
this    reading  of  the   plate   current   and   the   tube   characteristic   curve 
obtained  in  Test  1,  the  free  grid  potential  may  be  obtained. 

Test  3.  Tube  Characteristic  with  Reduced  Plate  Voltage. — Repeat 
Tests  1  and  2,  using  about  half  plate  voltage,  filament  current  =  1.1  ampere. 

Test  4.  Tube  Characteristic  with  Reduced  Filament  Current.— 
Repeat  Tests  1  and  2,  using  normal  plate  voltage,  filament  current  =0.8 
ampere. 

Test  5.  Tube  Characteristic  under  Normal  Conditions  of  Plate  Volt- 
age and  Filament  Current  with  Plate  Battery  Reversed. — Repeat  Tests 
1  and  2  with  plate  battery  reversed. 

Test  6.  Tube  Characteristic  under  Normal  Conditions  of  Plate  Voltage 
and  Filament  Current  with  Filament  Battery  Reversed. — Repeat  Tests 
1  and  2  with  filament  battery  reversed,  the  positive  side  of  filament  now 
being  the  common  junction. 

QUESTIONS 

1.  What  is  the  normal  resistance  of  the  plate  circuit  of  the  type  of  tube 
used  in  this  experiment? 

2.  What  is  meant  by  the  space  charge  in  a  vacuum  tube  and  what 
is  the  effect  of  the  grid  potential  upon  its  action? 

3.  What  effect  does  a  low  plate  voltage  have  upon  the  characteristic 
curves  of  a  tube?     What  effect  does  a  low  filament  current  have? 

4.  What  is  the  effect  upon  the  characteristic  curves  of  a  tube  of  using  as 
the  common  junction  the  positive  side  of  the  filament  instead  of  the  negative? 

EXPERIMENT  NO.  7 
Object 

Study  of  the  connections  and  use  of  the  three-electrode  vacuum  tube  as 
a  detector  of  high-frequency  damped  waves  with  and  without  suitable 
grid  condenser.  Effect  of  the  grid  condenser  leak.  Effect  of  using  too 


896  EXPERIMENTS  WITH   RADIO   CIRCUITS  [CHAP.  XII 

large  or  too  small  a  grid  condenser.  Effect  of  filament  current  and  plate 
voltage  upon  the  detector  action  of  the  tube.  Effect  of  reversed  plate 
battery  or  reversed  filament  battery.  Comparison  of  the  vacuum  tube 
and  rectifying  crystal  as  detectors. 

Apparatus 

Vacuum  tube  (similar  to  that  used  in  Experiment  No.  6). 

Vacuum  tube  receptacle. 

Storage  battery  for  filament  circuit. 

Dry  battery  for  plate  circuit  (about  40  volts). 

Two  dry  cells  for  buzzer  circuit. 

Ammeter  for  filament  circuit. 

Voltmeter  for  measuring  plate  voltage. 

Phones. 

Buzzer  and  rheostat. 

Two  fixed  inductances  (about  50  and  150  microhenries). 

One  fixed  condenser  for  buzzer  circuit  (about  .002  microfarad). 

One  fixed  condenser  for  shunting  phones  (about  .005  microfarad). 

Three  fixed  condensers  for  grid  circuit  (about  .005,  .0001  and  1  micro- 
farad) . 

Three  leak  resistances  for  grid  circuit  (about  2  megohms,  50,000  ohms 
and  10,000  ohms). 

One  variable  condenser  (about  .001  microfarad  maximum  capacity). 

One  crystal  rectifier. 

One  filament  circuit  rheostat. 

Two  D.  P.  D.  T.  switches  (one  to  be  a  reversing  switch). 

One  S.  P.  S.  T.  switch. 

Operation 

Caution. — In  making  the  tests  indicated  below,  it  is  important  that 
the  receiving  circuit  be  excited  only  by  the  high-frequency  oscillations  gen- 
erated by  the  buzzer-wave  generator.  If  the  receiving  circuit  is  placed 
near  to  the  buzzer  leads,  which  are  carrying  pulsating  current  of  audible 
frequency,  current  of  this  frequency  will  be  induced  directly  into  the 
receiving  circuit,  and  so  heard  in  the  phones.  The  signal  thus  received 
cannot  be  tuned  out  and  may  result  in  wrong  conclusions.  It  is,  there- 
fore, important  that  the  buzzer  leads  be  short  and  kept  remote  from  the 
receiving  circuit. 

If  an  audibility  meter  is  available  it  may  be  used  in  connection  with  the 
phonfis,  and  its  indications  may  be  used  instead  of  varying  the  coupling" 
between  receiving  circuit  and  buzzer  generator.  The  audibility  meter 
must  be  of  the  constant  impedance  type. 


VACUUM  TUBE  AS  DETECTOR 


897 


Test  1.  Connections  and  Adjustment  of  Crystal  Rectifier. — Connect 
up  the  apparatus  as  indicated  in  Fig.  12,  and  adjust  the  buzzer  to  give 
a  clear  musical  note.  With  close  coupling  adjust  crystal  until  a  clear 
signal  is  heard  in  the  phones.  Keeping  the  circuit  tuned  loosen  coupling 
until  signal  is  just  audible  and  yet  distinct,  and  note  distance  between 
the  secondary  and  primary  coils. 

Test  2.  Detector  Action  of  Tube ;  All  Conditions  Normal. — The 
positive  side  of  the  filament  battery  should  be  connected  to  the  common 
junction.  With  plate  voltage  and  filament  current  adjusted  to  normal 
value,  and  grid  condenser  =  100  micro-microfarads,  grid  leak  of  two 
megohms,  connect  tube  to  receiving  circuit,  retune  the  circuit  if  necessary, 
and  again  vary  distance  between  the  primary  and  secondary  until  a  signal 
of  same  strength  as  in  Test  1  is  obtained.  Note  the  greater  sensitiveness 




(Buzzer  generator  mounted 
on  board 


of  the  tube  as  compared  to  the  crystal  detector,  as  indicated  by  the  greater 
separation  between  the  primary  and  secondary  coils. 

Test  3.  Detector  Action  of  Tube;  All  Conditions  Normal,  Plate 
Battery  Reversed. — Repeat  Test  2  with  plate  battery  reversed. 

Test  4.  Detector  Action  of  Tube;  All  Conditions  Normal,  Filament 
Battery  Reversed. — Repeat  Test  2  with  filament  battery  reversed.  Neg- 
ative side  of  battery  now  connected  to  common  junction. 

Test  5.  Detector  Action  of  Tube;  Plate  Battery  Voltage  Reduced, 
all  Other  Conditions  Normal. — Repeat  Test  2  with  plate  voltage  reduced 
to  about  50  per  cent  of  normal  value. 

Test  6.  Detector  Action  of  Tube;  Filament  Current  Reduced,  All 
Other  Conditions  Normal. — Repeat  Test  2  with  filament  current  reduced 
to  about  75  per  cent  of  normal  value. 

Test  7.  Detector  Action  of  Tube  with  Different  Grid  Condenser 
Capacities  and  All  Other  Conditions  Normal. — Repeat  Test  2  using 
grid  condenser  capacities  of  1  microfarad,  5000  micro-microfarads,  100 
micro-microfarads,  0,  and  short-circuit  across  grid  leak. 


898  EXPERIMENTS  WITH  RADIO  CIRCUITS  [CHAP.  XII 

Test  8.  Detector  Action  of  Tube  with  Different  Grid  Leak  Resist- 
ances, All  Other  Conditions  Normal.— Repeat  Test  2  using  grid  leak 
resistances  equal  to  2  megohms,  50,000  ohms,  12,000  ohms,  0  ohm,  and 
infinite  resistance  (open  circuit). 

Test  9.  Detector  Action  of  the  Tube  without  a  Grid  Condenser  under 
Different  Conditions  of  Plate  Voltage  and  Filament  Current. — Try  dif- 
ferent values  of  plate  voltage  and  filament  current  to  see  if  good  recti- 
fication may  be  obtained  without  the  grid  condenser.  When  best  adjust- 
ment has  been  found  note  sensitiveness  as  compared  with  that  of  Test  2. 

QUESTIONS 

1.  When  no  grid  condenser  is  used,  why  is  it  difficult  to  find  a  good 
rectifying  adjustment  of  the  tube? 

2.  Why  would  the  tube  detect  poorly  when  a  grid  condenser  is  used 
without  a  leak  resistance,  assuming  no  leak  in  the  tube? 

3.  Why  does  a  grid  condenser  with  suitable  leak  make  the  rectifying 
action  of  the  tube  certain  for  a  wide  range  of  values  of  plate  voltage  and 
filament  current? 

4.  A  certain  tube  with  grid  condenser  and  leak  rectifies  well  when  the 
group  frequency  of  the  incoming  waves  is  120;    it  rectifies  very  poorly 
when  the  group  frequency  is  1000?     Explain. 

EXPERIMENT  NO.  8 

Object 

To  determine  (a)  the  geometric  amplifying  factor  GUQ)  of  the  tube  and 
its  variation  with  filament  current  and  plate  voltage;  (6)  the  amplifying 
factor  (M),  which  represents  the  true  amplification  obtained  when  the 
output  circuit  of  the  tube  is  loaded,  and  its  variation  with  external  resist- 
ance in  the  plate  circuit;  (c)  the  internal  plate  circuit  resistance  (Rp)  of 
a  three-electrode  vacuum  tube  and  its  variation  with  filament  current 
and  plate  voltage. 

Apparatus 

Vacuum  tube  (similar  to  that  suggested  for  experiment  No.  6). 

Vacuum  tube  receptacle. 

Storage  battery  for  filament. 

Source  of  high-frequency  current.  (About  1000^.  Source  should 
be  ungrounded.  An  oscillating  tube  generator  may  be  conveniently 
used  or  a  small  alternator.) 

Plate  battery  '(40-volt  dry  battery). 

Phones. 


DKTKKMINATION    OF   TUBE   CONSTANTS 


Variable  resistance  R  (from  0  to  20,000  ohms).  A  plug  box  resistance 
is  suitable. 

Grid  circuit  battery  (five  or  six  dry  cells  in  series). 

Potentiometer  (to  consist  of  two  plug  resistance  boxes  connected  in 
series — r\  and  r2). 

Hot-wire  milliammeter  (to  be  connected  in  series  with  potentiometer) . 


Operation  l 

Throughout  the  following  tests   (with  exception  of  test  No.   1   (d)) 
the  grid  voltage  should  be 
adjusted  to  a  certain  value 
this 


and  held  constant  at 
value.  This  value  may  be 
arbitrarily  chosen,  although 
it  is  desirable  to  make  EC 
of  that  value  which  has 
been  found  to  give  the  best 
performance  with  the  tube, 
e.g.,  for  reception  or  ampli- 
fication. 

Test  1.  —  Determination 
of  M. 

(a)  With    normal    fila- 

ment current  and  plate  voltage,   open  switch  S,  and  adjust  r\,  and  r* 
until  no  sound  is  heard  in  the  phones.     Under  these  conditions: 


FIG. 


where  i  =  the  audio-frequency  current  through  r\  and  r*,  therefore, 


Since  r^  and  ri  are  known,  ^o  is  thus  readily  determined.2 

(b)  Repeat  the  above  determination  holding  the  filament  current  con- 
stant at  normal  value  and  varying  the  plate  voltage  in  fixed  steps. 

(c)  Repeat  the  above  determination,  holding  the  plate  voltage  con- 
stant at  normal  value  and  varying  the  filament  current  in  fixed  steps. 

(d)  Repeat,  holding  plate  voltage  and  filament  current  normal  and 
varying  Ec,  the  grid  voltage  through  as  wide  range  as  convenient- 

Plot  the  readings  taken  in  runs  fe,  c,  and  d. 

1  The  student  should  refer  to  Chapter  VI  for  detailed  definitions  of  no,  /x  and  rp 
and  explanation  of  their  variation  and  significance. 

2.  The  a.c.  voltage  impressed  on  the  grid,  i.e.,  the  IR  drop  across  ri,  should  be  only 
a  small  fraction  of  a  volt  in  this  test,  otherwise  the  balance  obtained  will  not  be  good 
One-tenth  of  a  volt  on  the  grid  should  be  sufficient. 


900  EXPERIMENTS  WITH  RADIO  CIRCUITS          [CHAP.  XII 

Test  2.  —  Determination  of  /*. 

(a)  With  switch  S  closed  and  R  set  at  the  value  at  which  p  is  to  be 
measured,  vary  r^  or  r\  until  no  note  is  heard  in  the  phones.  Under  this 
condition  the  alternating  voltage  drop  across  R  is  equal  to  the  alternating 
voltage  drop  across  r^  ',  or 

ipR=ir2 
and 

7*2 


(6)  Repeat  test  (a)  with  various  values  of  R  and  plot  results  obtained. 

NOTE:  As  R  is  increased  En  must  be  increased  to  keep  Ep  at  its  rated 
value  (Ep  represents  the  voltage  impressed  between  plate  and  filament). 
To  do  this,  note  what  plate  current  flows  when  R  is  made  equal  to  0  and 
Eb  is  at  rated  value  for  the  tube.  Then  keep  Ip  at  this  value  by  increasing 
Eb  as  R  is  increased. 

Eg  must  be  kept  small  and  should  not  exceed  0.1  volt.  To  make  sure 
of  this,  the  milliammeter  A  is  connected  in  series  with  the  potentio- 
meter. From  its  indications  and  the  known  value  of  r\,  the  value  of  Ea 
(  =ir\)  is  readily  obtained. 

Test  3.  —  Determination  of  the  internal  resistance  (Rp)  of  the  tube. 

(a)  With  normal  values  of  filament  current  and  plate  voltage  close 
switch  S.  Adjust  potentiometer  resistance  so  that  r\=T2  and  vary  R 
until  no  note  is  heard  in  the  phones.  Under  this  condition 


where  MO  is  known  from  the  results  obtained  in  Test  1. 

(6)  Repeat  test  (a)  using  various  values  of  plate  voltage,  holding  the 
filament  current  constant  at  normal  value. 

(c)  Repeat  test  (a)  using  various  values  of  filament  current,  holding 
the  plate  voltage  constant  at  normal  value. 

In  case  it  is  not  feasible  to  get  a  balance  with  r\  =  r^.  then  a  suitable 
ratio  of  r\  —  r<z  may  be  chosen,  in  which  case  we  have: 


The  results  of  tests  6  and  c  should  be  plotted. 
EXPERIMENT  NO.  9 

Object 

To  measure  the  power  output  of  an  oscillating  tube  generator  (with 
separate  excitation)  and  its  variation  with  plate  voltage,  filament  current, 
excitation  and  plate  circuit  external  resistance. 


TRIODE  AS   CONVERTER 


901 


This  test  may  be  carried  out  at  radio  frequencies  or  at  audio-frequencies 
(in  fact  60-cycle  excitation  may  be  used).  The  values  given  for  the  supply 
voltage,  resistances,  etc.,  are  made  suitable  for  one  of  the  smaller  tubes 
mentioned  below. 


Apparatus 

Vacuum  tube.  (For  these  tests  a  power  tube  should  preferably  be 
used.  The  Western  Electric  Company,  VT-2  or  General  Electric  Com- 
pany, VT-12  or  14  would  be  suitable.  Still  better  is  a  larger  tube,  such 
as  the  G.  E.  type  P  or  type  U  pliotroh.) 

Vacuum  tube  receptacle. 

Dry  battery  for  grid  circuit  (about  20  volts) . 

Source  of  alternating  voltage  for  exciting  grid  circuit.  (This  may  be 
conveniently  obtained  by  means  of  another  oscillating  tube  circuit.) 

Ammeter  for  filament  circuit. 

Rheostat  for  filament  circuit. 

D.c.  milliammeter  for  grid  circuit  (E). 

D.c.  milliammeter  for  plate  circuit  (A). 

Hot-wire  milliammeter  for  plate  circuit  (Af). 

Plate  battery  or  d.c.  generator  (since  the  normal  plate  voltage  will 
be  about  300  volts,  the  generator  would  probably  be  most  convenient). 

Shunting  condenser  for  plate  battery  and  ammeter  (about  1  micro- 
farad) . 

High  value  fixed  inductance  for  plate  circuit.     This  must  be  sufficiently 

large  to  give,  at  the  fre-  . — . , 

quency   used,   an   impe-  i © w**  _/AV- 

dance   several   times   as  A 

large  as  the  Rp  of   the 
tube  used. 

Condenser  for  load 
circuit  (should  have  such 
capacity  as  will  make 
its  reactance  small  com- 
pared to  the  tube  re- 
sistance at  the  frequency 
used). 

Variable  non-inductive  resistance  for  load  circuit.  This  should  be 
adjustable  in  steps  and  should  have  a  maximum  value  two  or  three  times 
as  large  as  the  a.c.  resistance  of  the  plate  circuit  (output  circuit)  of  the 
tube  used. 


FIG. 


902  EXPERIMENTS   WITH   RADIO   CIRCUITS  [CHAP.   XII 


Operation 

In  all  of  the  tests  outlined  below  care  must  be  exercised  that  the 
amount  of  power  expended  on  the  plate  or  grid  is  not  greater  than  the 
safe  rating  for  the  tube  used. 

Part  I. — The  action  of  the  tube  will  first  be  investigated  with  the  plate 
circuit  untuned  since  this  is  the  easier  circuit  to  manipulate.  The  large 
value  of  inductance  should  be  inserted  in  the  plate  circuit  during  the 
following  tests. 

Test  1. — With  suitable  values  of  E0l  Ecl  and  R,  and  with  Ev  normal, 
note  the  output  of  the  tube  and  its  variation  as  the  filament  current  is 
varied,  plotting  your  results  in  the  form  of  a  curve.  A  proper  value  for 
R  makes  it  equal  to  the  normal  value  of  Rp. 

Test  2.  Repeat  Test  1,  varying  the  plate  voltage  instead  of  the  fila- 
ment current. 

Test  3. — Repeat  Test  1,  varying  E0  instead  of  the  filament  current. 
(In  this  test  Ec  must  be  varied  so  as  to  get  maximum  output  at  each 
setting  of  Ea,  without,  however,  exceeding  the  safe  rating  of  the 
tube.) 

Test  4. — With  all  conditions  normal,  determine  the  variation  in  out- 
put of  the  tube,  as  the  resistance  (R)  in  the  output  circuit  is  varied. 

In  all  of  the  foregoing  tests  the  high-frequency  power  in  the  output 
jircuit  is  given  by 

P=i2R 

vvhere  i  is  the  current  measured  by  the  ammeter  A'.  Due  to  the  high 
impedance  of  L  to  high-frequency  currents,  it  may  be  reasonable 
assumed  that  practically  no  high-frequency  current  passes  through  this 
branch. 

Part  II. — The  characteristics  of  the  generator  when  using  a  tuned- 
plate  circuit  will  next  be  investigated.  The  high  inductance  should  there- 
fore be  replaced  by  the  low  inductance  to  permit  tuning  the  parallel  cir- 
cuit LC  to  radio  frequencies.  A  suitable  low  inductance,  such  that  the 
capacity  used  in  parallel  with  it  will  permit  tuning  (parallel  resonance) 
to  the  frequency  used  for  grid  excitation. 

Test  1. — With  all  conditions  normal,  e.g.,  Ep,  //,  Ec  of  proper  value, 
and  Eg  held  fixed  at  a  certain  value,  find  the  effect  on  the  output  of  the 
tube  of  tuning  or  of  not  tuning  the  output  circuit  to  the  input  frequency, 
using  a  low  value  of  /*'. 

1  EC  should  be  held  constant  at  some  value  which  has  previously  been  found  to  be 
most  suitable  for  the  tube  when  acting  as  a  generator  with  all  conditions  normal.  This 
will  generally  be  about  80  per  cent  of  the  maximum  value  of  the  excitation  voltage. 


SELF-EXCITING   POWER   TUBE  903 

Test  2. — With  the  plate  circuit  tuned  arid  all  conditions  normal, 
determine  the  variation  in  output  with  variation  in  R',  calculating  for 
each  value  of  R'  the  load  circuit  resistance  as  follows: 

tf'load  circuit  =  £  g  (§66  page  72), 

where  L  =  inductance  in  henries; 

C  =  capacity  in  farads ; 
R  =  actual  resistance  in  the  oscillating  circuit. 

Test  3. — With  the  load  circuit  adjusted  for  maximum  output,  find 
the  effect  of  varying  Ec,  both  above  and  below  its  normal  value. 
Plot  curves  showing  the  results  obtained. 

EXPERIMENT  NO.  10 

Object 

Study  of  the  power  tube  as  applied  to  a  typical  oscillating  circuit,1 
such  as  might  be  applicable  to  a  radio  telephone  set.  Effect  of  the  plate 
inductance,  the  condenser  in  series  with  the  antenna,  the  resistance  in 
the  oscillating  circuit,  the  degree  of  coupling  of  the  plate  to  the  oscillating 
circuit,  the  plate  voltage,  the  filament  current,  the  grid  condenser,  the  grid 
leak,  and  the  grid  potential. 

Apparatus 

Vacuum  tube  (similar  to  that  used  in  Experiment  No.  9). 

Vacuum-tube  receptacle. 

Ammeter  for  filament  circuit. 

Rheostat  for  filament  circuit. 

Plate  battery  or  d.c.  generator  (about  300  volts). 

Ammeter  for  plate  circuit. 

Condenser  for  shunting  plate  battery  and  ammeter  (about  1  micro- 
farad) . 

Hot-wire  ammeter  for  antenna  circuit  (may  conveniently  be  a  galvanom- 
eter and  thermo-couple  with  a  maximum  range  of  about  0.5  ampere). 

Wave-meter  of  suitable  range. 

Dummy  antenna.  (The  constants  of  this  antenna  are  arbitrarily 
chosen.  A  representative  one  would  be: 

L  =  40  microhenries 

C=400  micro-microfarads  (mica) 

R  =  8  ohms.) 

1  The  circuit  which  is  investigated  in  this  experiment  is  discussed  on  page  561  et  seq. 
and  the  student  should  thoroughly  review  the  theory  and  principles  of  operation  as 
given  there,  before  attempting  to  perform  the  tests  specified. 


904 


EXPERIMENTS  WITH   RADIO  CIRCUITS 


[CHAP,  XII 


Special  low  resistance  inductance  (L),  variable  in  about  12  equal 
steps,  for  oscillating  circuit  (total  inductance  may  be  about  2000  micro- 
henries). 

Special  condenser  (Ci),  variable  in  twelve  equal  steps,  for  oscillating 
circuit.  (Maximum  capacity  may  be  approximately  3000  or  4000  micro- 
microfarads.)  This  condenser,  the  same  as  C  above,  should  have  negligible 
losses,  preferably  made  with  mica. 

Variable  plate  circuit  inductance  (maximum  value  about  5000  or 
10,000  microhenries). 

Grid  circuit  battery  (about  20  volts,  with  grid  to  be  made  negative). 

Various  grid  condensers  (from  100  micro-microfarads  to  1  microfarad). 

Various  grid  leak  resistances  (from  12,000  to  2,000,000  ohms). 

Resistance  for  insertion  into  oscillating  circuit  (about  50  ohms). 

All  of  above  values  are  suitable  for  a  VT-2  or  VT-14  tube  and  the 
result  obtained  indicate  the  behavior  of  one  of  these  tubes  when  used  for 
signaling  between  aeroplanes  and  similar  service. 

Operation 

Test  1.  Adjustment  of  Plate  Inductance. — Make  connections  as  in 
Fig.  15,  place  the  coupling  contact  M  at  D  and  the  wave-length  contact 

L^f*  5000  #  h 


VJSk, 


Condenser  with 
about  12  steps 


FIG.  15. 


H  at  the  third  step  away  from  D,  use  C,=500  wf,  #ff  =  12,000  ohms, 
Ci  =  1200  MM/-  Vary  the  plate  inductance  Lp,  from  its  minimum  to  its 
maximum  value  and  read  A  and  Av  for  each  point  on  the  inductance  Lp. 
Note  that  the  circuit  can  be  made  to  oscillate  for  a  limited  range  of  values 
of  Lp,  and  that  when  it  starts  to  oscillate  the  plate  current  decreases. 
Note  the  value  of  Lp.  giving  maximum  current  in  the  oscillating  circuit, 
and  use  it  in  the  following  tests. 

Test  2.  Effect  of  the  Condenser  in  Series  with  the  Antenna. — With 
all  other  adjustments  as  in  Test  1  vary  the  capacity  Ci  in  series  with  the 
antenna  from  50  wf  to  3200  wf  in  the  following  steps:  50,  100,  200, 


SELF-EXCITING   POWER   TUBE  905 

400,  800,  1200,  1600,  2000,  2400,  2800,  3200,  arid  read  A,  also  measure 
the  wave-length.  Do  not  increase  C\  beyond  the  point  where  the  circuit 
refuses  to  oscillate.  Note  that  the  circuit  cannot  be  made  to  oscillate 
for  certain  values  of  Ci,  also  that  the  value  of  C\  affects  the  wave-length. 
Note  the  value  of  C\  which  gives  the  maximum  current  in  the  oscillating 
circuit  and  use  it  in  the  following  tests. 

Test  3.  Effect  of  High  Resistance  in  the  Oscillating  Circuit. — With 
all  other  adjustments  as  in  Test  2  introduce  a  resistance  of  50  ohms  in 
the  oscillating  circuit  and  note  A.  Compare  this  reading  of  A  with  that 
obtained  in  Test  2  for  best  adjustment  of  Ci. 

Test  4.  Effect  of  Shifting  the  Wave-length  Contact  H—  With  all 
other  adjustments  as  in  Test  2  shift  the  wave-length  contact  H  from 
point  D  towards  K  in  steps,  and  note  the  step  number,  the  reading  of  A, 
and  also  measure  the  wave-length.  Note  that,  although  this  is  primarily 
a  wave-length  adjustment,  yet  the  coupling  of  the  plate  circuit  to  the 
oscillating  circuit  is  also  varied  and  hence  the  current  in  the  oscillating 
circuit  is  varied. 

Test  5.  Effect  of  Shifting  the  Coupling  Contact  M—  With  all  other 
adjustments  as  in  Test  2  shift  the  coupling  contact  M  from  D  towards 
K  in  steps  and  note  the  step  number,  the  reading  of  A  and  also  the  wave- 
length. Note  that  when  the  coupling  contact  is  moved  about  half  way 
down,  the  tube  stops  oscillating.  The  adjustment  for  this  test  is  primarily 
a  coupling  adjustment,  and  should  only  affect  the  current  in  the  oscillating 
circuit,  the  wave-length  being  but  slightly  affected. 

Test  6.  Effect  of  Plate  Voltage.— With  all  other  adjustments  as  in 
Test  2  vary  the  plate  voltage  from  its  normal  value  both  up  and  down 
and  note  A.  Be  careful  not  to  exceed  the  safe  plate  voltage  and  watts. 

Test  7.  Effect  of  Filament  Current.— With  all  other  adjustments 
as  in  Test  2  decrease  the  filament  current  in  steps  from  its  normal  value 
to  1.0  ampere  and  note  A.  Note  that  A  decreases  with  decreasing  fila- 
ment current. 

Test  8.  Effect  of  Value  of  Grid  Condenser. — With  all  other  adjust- 
ments as  in  Test  2  make  the  grid  condenser  Cg  100  ntf,  500  wf,  5000 
wf,  1.0  M/,  and  note  A  and  Ap.  Note  the  best  value  of  Cg. 

Test  9.  Effect  of  Value  of  Leak  Resistance.— With  all  other  adjust- 
ments as  in  Test  2  make  the  value  of  the  leak  resistance  R0  infinite  (open 
circuit),  2  megohms,  50,000  ohms,  10,000  ohms,  and  zero  and  read  A  and 
A p.  Note  the  best  value  of  Rg\  Try  the  effect  of  putting  a  high-frequency 
choke  coil,  of  variable  inductance  in  series  with  the  normal  value  of  grid 
leak  resistance. 

Test  10.  Effect  of  Holding  the  Grid  at  Different  Negative  Potential.— 
With  all  other  adjustments  as  in  Test  2  vary  the  e.m.f.  in  series  with  the 
leak  resistance  from  zero  to  30  volts  in  several  steps  and  read  A  and  Av. 


906  EXPERIMENTS  WITH  RADIO  CIRCUITS  [CHAP.  XII 

Note  that  as  this  e.m.f.  is  increased  the  reading  of  A  may  decrease  some- 
what, but  the  reading  of  Ap  decreases  much  more. 

1.  Why  is  it  that  in  Test  1  too  low  an  inductance  in  the  plate  circuit 
will  prevent  the  tube  from  oscillating? 

2.  Why  is  it  in  Test  2  either  too  low  or  too  high  a  value  of  Ci  will 
prevent  the  tube  from  oscillating? 

3.  From  your  results  of  Experiments  9  and  10  what  is  the  effect  of 
holding  the  grid  at  various  negative  potentials  upon  the  output  and 
efficiency  of  the  tube? 

EXPERIMENT  NO.  11 
Object 

To  measure  the  high-frequency  resistance  of  a  simple  radio  circuit 
and  to  determine  the  variation  of  this  resistance  with  change  in  frequency.1 

Apparatus 

Standard  inductance  whose  inductance  is  practically  independent 
of  frequency  (about  500  microhenries). 

Standard  variable  condenser  whose  capacity  is  practically  independ- 
ent of  frequency  (about  0— .005  microfarad).  (An  oil-filled  condenser 
is  most  desirable  due  to  the  large  capacities  obtainable  and  decreased 
losses.) 

Hot-wire  ammeter,  of  low  range. 

Known  resistance  R,  which  does  not  vary  with  frequency;  radio 
cable  of  German  silver  strands  is  most  suitable  for  this. 

Source  of  undamped  high-frequency  current  whose  frequency  may 
be  varied  from  perhaps  50,000  to  300,000  cycles  per  second.  (The  oscil- 
lating tube  circuit  considered  in  Experiment  No.  10,  or  its  equivalent, 
may  be  conveniently  used  for  this  purpose.) 

Wave-meter. 

Operation 

NOTE:  When  making  the  following  tests,  it  is  important  to  have 
sufficient  power  generated  by  the  tube  and  transferred  to  the  test  circuit 
so  that  the  currents  will  be  reasonably  large  and  easily  read  on  the  hot- 
wire ammeter.  This  will  aid  in  minimizing  the  errors  involved  in  the 
measurement,  the  accuracy  of  which  depends  largely  on  the  precision 
with  which  the  current  is  measured.  It  is  also  necessary  to  keep  E, 
the  e.m.f.  induced  in  the  test  circuit,  constant  in  value  throughout  the 
measurements. 

1  The  student  is  referred  to  Bulletin  No.  74,  published  by  the  Bureau  of  Standards, 
pages  180-187,  for  a  complete  treatment  and  discussion  of  these  measurements. 


RESISTANCE  MEASUREMENT  AT  HIGH  FREQUENCY 


907 


Where  tuned  circuits  are  specified,  particular  care  should  be  taken  to 
insure  the  resonant  condition  being  actually  obtained;  otherwise  con- 
siderable error  will  be  introduced  into  the  results. 

Test  1. — Determine  the  resistance  of  the  circuit  containing  L,  C, 
and  the  ammeter  by  means 
of  the  "  resistance  varia- 
tion "  method,  connections 
to  be  made  as  shown  in 
Fig.  16. 

Set  the  variable  con- 
denser C  to  some  certain 
value  and  with  the  known 
resistance  R  omitted  from 

the  circuit  vary  the  constants  of  the  exciting  tube  circuit  until  resonance 
is  obtained  as  indicated  by  a  maximum  reading  on  the  hot-wire  ammeter. 
Under  this  condition: 


To  Source  of 

Undamped 

'  High  Efficiency 

Power 


FIG.  16. 


/--=. 
1    R; 


(i) 


where  E  is  the  e.m.f  .  introduced  into  the  circuit  by  induction  in  the  coil  L. 
Then  insert  the  known  resistance  R  into  the  circuit  as  shown,  and 
slightly  re-tune  the  circuit,  if  necessary;    again  note  the  current,  which 
now  equals: 

E 


(The  reading  of  A\,  and  relative  positions  of  L  and  L\  must  be  the  same 
as  when  making  the  previous  measurement.) 

Combining  this  expression  with  Eq.  (1)  we  obtain  the  value  of  cir- 
cuit resistance  (Rx)  as: 

o       R 

/i/x  —    j 

IT1 

Measure  the  wave-length  of  the  set  to  get  the  frequency. 

Test  2.  —  Determine  the  resistance  of  the  circuit  for  the  same  frequency 
as  in  Test  1,  using  the  "  reactance  variation  "  method,  using  the  same 
connections  as  above,  without  the  extra  resistance. 

Carry  out  the  first  step  specified  in  Test  1,  setting  the  variable  con- 
denser to  the  same  value  of  capacity  and  carefully  adjusting  the  exciting 
source  until  tuned  conditions  are  obtained.  As  before: 


Then  insert  reactance  in  the  circuit  by  changing  the  setting  of  the 
variable  condenser  until  a  considerable  change  in  the  current  has  taken 


908  EXPERIMENTS  WITH  RADIO  CIRCUITS  [CHAP.  XII 

place.     (Be  sure  that  the  current  through  the  primary  exciting  coil  is 
not  changed  during  this  adjustment;   if  it  does  vary,  as  indicated  by  a 
hot-wire  ammeter  in  the  tube  circuit,  the  proper  adjustment  should  be 
made  to  hold  it  constant.) 
Under  the  new  condition: 


Combining  (I/)  and  (3)  we  obtain: 


In  this  case: 

and  Rx  = 

L  being  known,  Cr  and  C\  can  both  be  readily  determined  by  noting  the 
resonant  frequency  of  the  circuit  and  then  determining  this  frequency 
by  wave-meter. 

The  resistance  of  the  circuit  (Rx)  as  obtained  by  this  test  should 
check  the  result  of  the  previous  measurement  since  all  circuit  apparatus 
and  the  frequency  has  remained  the  same. 

Test  3. — Determine  the  resistance  at  eight  or  ten  different  frequencies 
from  50,000  up  to  300,000  cycles  per  second,  using  either  of  the  two  methods 
just  outlined. 

Plot  the  results  in  the  form  of  a  curve,  using  frequencies  as  abscissae 
and  the  corresponding  resistance  as  ordinates. 

EXPERIMENT  NO.  12 

Object 

Study  of  the  oscillating  tube  receiving  circuit;  methods  of  detecting 
when  a  tube  circuit  is  oscillating  by  indication  of  the  plate  current  ammeter 
and  by  phone  indication;  effect  of  the  degree  of  coupling,  the  oscillating 
circuit  capacity,  the  oscillating  circuit  resistance,  the  plate  voltage  and 
filament  current,  upon  the  oscillations;  periodic  phone  clicks  produced 
in  the  oscillating  tube  circuit  with  grid  condenser  with  improper  adjust- 
ments; use  of  the  oscillating  tube  circuit  for  the  reception  of  continuous- 
wave  signals;  use  of  the  regenerative  action  of  the  tickler  coil  for  the 
amplification  of  damped-wave  signals. 

Apparatus 

Vacuum  tube  (similar  to  that  used  in  Experiment  No.  6). 
Vacuum-tube  receptacle. 


OSCILLATING   TUBE  AS  RECEIVER 


909 


Storage  battery,  ammeter,  and  rheostat  for  filament  circuit. 

Dry  battery  for  plate  circuit  (about  40  volts). 

Galvanometer  or  sensitive  milliammeter  for  plate  current. 

Voltmeter  for  plate  voltage. 

Phones. 

Variable  condenser  (C)  for  oscillating  circuit  (one  with  a  maximum 
capacity  of  about  1000  micro-microfarads  would  be  suitable). 

Coupler  (an  ordinary  receiving  coupler  may  be  conveniently  used,  the 
primary  or  "  tickler "  coil  having  about  500  microhenries  while  the 
secondary  may  have  about  4000  microhenries). 

Resistance  to  introduce  into  oscillating  circuit  (about  50  ohms). 

Shunting  condenser  for  phones,  plate,  battery  and  ammeter  (about 
.005  microfarad). 

Grid  condensers,  similar  to  those  specified  in  Experiment  No.  7  (about 
.005,  .0001  and  1  microfarad  in  capacity). 

Grid  leak  resistances,  similar  to  those  specified  in  Experiment  No.  7 
(about  2  megohms,  50,000  and  10,000  ohms). 

Source  of  continuous  high-frequency  oscillations  (see  Experiment  No. 
10  for  tube  circuit  which  m&y  be  used  for  this  purpose) . 

Source  of  damped  high-frequency  oscillations  (use  buzzer  wave  gen- 
erator). 


Operation 

Test  1. — Effect  of  the  beginning  of  oscillations  upon  the  plate  current 
and  upon  the  phones  when  no  grid  condenser  is  used. 

Make  connections  as  in  Fig.  17.  Make  the  plate  voltage  and  filament 
current  normal.  Set  for  the  weakest  coupling  possible  between  the  tickler 
and  the  oscillating-circuit  induct- 
ance. This  is  done  by  using  very 
few  turns  for  the  tickler  coil  and 
having  the  two  coils  of  the  coupler 
as  far  apart  as  possible.  In  case 
one  of  the  coils  of  the  coupler  re- 
volves, weakest  coupling  is  had 
when  the  two  coils  are  at  right 
angles.  Set  the  condenser  in  the 
oscillating  circuit  at  10  per  cent  of 
its  maximum  value;  now  increase  FlG-  17- 

the     coupling    by    bringing     the 

movable  coil  more  and  more  within  the  field  of  the  fixed  coil,  and 
note  any  change  in  the  plate  current  and  noise  in  the  phones.  When 
the  coupling  reaches  a  certain  critical  value,  oscillations  will  start, 


910  EXPERIMENTS  WITH  RADIO  CIRCUITS  [CHAP.  XII 

providing  the  two  coils  of  .the  coupler  have  the  proper  relative  polari- 
ties. The  starting  of  the  oscillations  produces  a  sudden  change  in 
the  plate  current  and  a  resultant  noise  in  the  phones;  this  noise  has 
a  peculiar  quality,  something  like  the  plucking  of  a  rubber  band,  and  is 
sometimes  difficult  to  detect. 

In  case  no  indication  of  oscillation  occurs,  even  when  the  coils  of  the 
coupler  are  close  together,  increase  the  number  of  turns  in  the  tickler 
coil.  If  the  circuit  still  refuses  to  oscillate,  it  is  almost  certain  that  the 
relative  polarity  of  the  two  coils  of  the  coupler  is  incorrect,  in  which  case 
reverse  the  connections  to  either  coil  and  repeat  the  test,  noting  the  phone 
click  at  the  beginning  of  the  oscillations,  also  the  plate  current  before 
and  after  the  oscillations  have  started. 

Repeat  the  test  with  normal  plate  voltage  and  a  filament  current  of 
about  75  per  cent  of  normal,  and  again  with  normal  filament  current 
and  a  plate  voltage  of  about  75  per  cent  normal. 

Test  2. — Effect  of  the  beginning  of  oscillations  upon  the  plate  current 
and  upon  the  phones  when  a  grid  condenser  and  suitable  leak  resistance 
are  used. 

In  the  circuit  of  Fig.  17  introduce  a  grid  condenser  of  100  wf  and 
a  grid  leak  resistance  of  2  megohms  and  repeat  Test  1  with  normal  plate 
voltage  and  filament  current;  also  with  normal  plate  voltage  and  reduced 
filament  current,  and  with  reduced^ plate  voltage  and  normal  filament 
current. 

Test  3. — Oscillating  condition  as  indicated  by  the  "  finger  test  "  when 
no  grid  condenser  is  used. 

With  all  adjustments  as  in  Test  1  increase  the  coupling  until  oscil- 
lations start.  After  the  oscillating  condition  has  been  reached  the  phones 
are  quiet;  they  do  not  indicate  the  presence  of  the  oscillations.  The 
oscillating  condition  may,  however,  be  tested  for  as  follows:  With  the 
thumb  on  the  common  junction  of  filament  and  grid  circuits  touch  the  grid 
with  one  finger;  this  should  give  a  click  in  the  phones.  Take  the  finger 
off  from  the  grid,  and  the  phones  should  give  a  click.  Now  reverse  the 
connections  to  the  tickler  so  that  the  circuit  does  not  oscillate,  and  try 
the  "  finger  test  "  as  before;  it  will  be  noted  that  no  click  is  heard  in  the 
phones  either  when  the  finger  is  placed  on  the  grid  or  when  removed 
from  it. 

Test  4. — Oscillating  condition  as  indicated  by  the  "  finger  test  "  when 
a  grid  condenser  and  leak  are  used. 

Repeat  Test  3  after  introducing  a  grid  condenser  of  100  wf  and  leak 
resistance  of  2  megohms.  Note  that  when  the  circuit  is  oscillating  a  click 
is  heard  in  the  phones  both  when  the  finger  is  placed  on  the  grid  and  when 
removed  therefrom. 

On  the  other  hand,  when  the  circuit  is  not  oscillating,  although  a 


OSCILLATING   TUBE   AS   RECEIVER 


911 


click  is  heard  when  the  finger  touches  the  grid,  it  will  be  found  that  there 
is  little  or  no  click  when  the  finger  is  removed;  this,  however,  may  not 
always  be  the  case,  and  the  finger  test  in  this  case  is  not  reliable. 

Repeat  the  "  finger  test  "  both  with  and  without  grid  condenser  suf- 
ficiently to  become  convinced  of  the  following  summary  of  facts : 


Condition  of  Circuit. 

Finger  Placed  on  Grid. 

Finger  Removed. 

No  grid  condenser  and  no  oscillations  .  .  . 
No  grid  condenser  and  with  oscillations  .  . 
With  grid  condenser  and  no  oscillations  .  . 
With  grid  condenser  and  oscillations.  .  .  . 

No  click 
Click 
Click 
Click 

No  click 
Click 
Very    likely  to   click 
Click 

Check  up  the  points  listed  in  the  above  table  which  are  borne  out 
by  experiment. 

Test  5. — Effect  of  a  high  resistance  in  the  oscillating  circuit  upon  the 
coupling  necessary  to  produce  oscillations. 

With  all  other  conditions  as  in  Test  1,  find  the  position  of  the  movable 
coil  of  the  coupler  necessary  to  start  oscillations  and  note  it.  Introduce 
50  ohms  in  the  oscillating  circuit  and  repeat  the  test. 

For  this  test,  as  well  as  the  two  following,  the  two  coils  of  Fig.  17 
should  be  in  the  form  of  a  vario-coupler,  the  values  of  M  of  which  are 
known  for  the  various  settings. 

Test  6. — Effect  of  the  value  of  the  capacity  in  the  oscillating  circuit 
upon  the  coupling  necessary  to  produce  oscillations. 

With  all  other  adjustments  as  in  Test  1,  note  and  record  the  position 
of  the  movable  coil  of  the  coupler  necessary  to  start  oscillations  with 
oscillating  circuit  condenser  set  at  100  per  cent,  60  per  cent,  and  10  per 
cent  of  its  maximum  value.  Note  that  the  smaller  the  capacity  of  the 
oscillating  circuit  the  easier  it  is  to  start  oscillations  as  indicated  by  ,the 
weaker  coupling  needed. 

Test  7. — Effect  of  low  plate  voltage  or  low  filament  current  upon  the 
coupling  necessary  to  produce  oscillations. 

With  all  other  adjustments  as  in  Test  1,  note  and  record  the  position 
of  the  movable  coil  of  the  coupler  necessary  to  start  oscillations  for  the 
following  conditions: 

Plate  voltage  =  normal  value.    'Filament  current  =  normal  value. 
Plate  voltage  =  normal  value.     Filament  current  =75%  normal  value. 
Plate  voltage  =75%  normal  value.     Filament  current  =  normal  value. 

Test  8.  Periodic  Phone  Clicks  when  Grid  Condenser  is  Used. — With 
normal  plate  voltage  and  filament  current,  grid  condenser  =  100  /////, 
leak  resistance  =2  megohms  and  tight  coupling,  start  with  the  condenser 
in  the  oscillating  circuit  set  at  its  maximum  value,  decrease  it  slowly,  mid 


912  EXPERIMENTS  WITH  RADIO  CIRCUITS  [CHAP.  XII 

note  the  reading  of  condenser  when  periodic  clicks  start.  If  the  peri- 
odicity of  the  clicks  is  high  enough,  a  musical  note  results  and  gives  what 
is  known  as  "  squealing  "'  or  "  singing  "  of  the  tube.  Without  changing 
the  leak  resistance,  determine  the  setting  of  the  oscillating  circuit  con- 
denser necessary  to  start  periodic  clicks  with  tight  coupling  for  the  follow- 
ing values  of  grid  condenser:  1/xf,  5,000  wf,  100  ///*/.  Also  note  the 
frequency  of  the  clicks.  Repeat  the  test  with  constant  grid  condenser 
of  100  nnf  and  grid  leak  resistance  of:  infinity  (open  circuit),  2  megohms, 
50,000  ohms,  10,000  ohms  and  zero. 

Test  9.  Reception  of  Undamped  Wave-telegraphy  by  Means  of  the 
Oscillating  Tube. — Set  the  circuit  oscillating  with  conditions  as  in  Test  1 
and  receive  the  undamped  wave-signal  sent  out  by  an  oscillating  tube 
generator  set  up  as  in  Experiment  10.  (A  small  antenna  should  be  con- 
nected to  the  point  H  on  the  transmitter  and  on  the  receiving  circuit 
as  shown  to  increase  the  energy  received.)  This  is  done  by  adjusting 
the  oscillating  circuit  condenser  until  nearly  in  tune  with  the  transmitter, 
when  a  "  whistle  "  will  be  heard  in  the  phones. 

By  interrupting  the  oscillations  of  the  transmitter,  signals  may  easily 
be  transmitted. 

Test  10.  Regenerative  Action  of  the  Tickler  Coil. — Reception  of 
Damped  Waves. — With  all  other  adjustments  as  in  Test  9,  make  the 
coupling  much  below  that  which  will  start  oscillations,  and  tune  by  means 
of  the  condenser  to  receive  the  damped  wave-signals  sent  out  by  the  source 
of  damped  high-frequency  oscillations.  Note  that  the  reception  takes 
place  when  the  tube  is  not  oscillating.  Gradually  increase  the  coupling, 
continually  retiming  the  receiving  circuit  for  the  incoming  signal  and 
note  the  great  increase  in  the  signal  strength  due  to  the  regenerative 
action  of  the  tickler  coil  as  the  coupling  is  increased.  Too  great  a  coupling 
results  in  oscillations  and  the  musical  quality  of  the  signal  is  spoiled ;  it  is 
therefore  best  to  receive  with  the  circuit  just  out  of  the  oscillating  con- 
dition, when  the  regenerative  action  of  the  tickler  in  amplifying  the 
received  signals  will  be  a  maximum. 

NOTE:  If  poor  signals  are  received  due  to  the  poor  rectification  of  the 
tube,  introduce  normal  grid  condenser  and  grid  leak. 

QUESTIONS 

1.  From  the  results  of  Tests  1  and  2  what  may  the  plate  current  do 
when  oscillations  start  if  no  grid  condenser  is  used,  and  if  a  grid  condenser 
is  used? 

2.  From  the  results  of  your  tests  what  is  the  effect  upon  the  strength 
of  oscillations  of:    loose  coupling,  large  resistance  and  large  capacity  in 
oscillating  circuit,  low  plate  voltage,  and  low  filament  current? 


LOW-FREQUENCY  AMPLIFIER  913 

3.  What  is  the  reason  for  the  singing  of  the  tube  when  a  grid  con- 
denser is  used,  and  how  may  it  be  avoided? 

4.  An  incoming  undamped  wave  signal  of  a  wave-length  of  1000 
meters  is  being  received;   the  inductance  in  the  receiving  oscillating  cir- 
cuit is  400  microhenries;   what  must  the  capacity  be  in  order  to  rocoive 
a  beat  note  of  2000  beats  per  second? 

EXPERIMENT  NO.  13. 

Object 

(a)  Study  of  the  low-frequency  amplifier  equipped  with  inductance 
"repeater."  Investigation  of  the  effect  of  the  value  of  the  inductance 
in  the  plate  circuit  upon  amplifying  power;  effect  of  the  value  of  grid 
condenser  and  grid  leak  resistance  upon  amplifying  power:  and  effect  of 
plate  voltage  and  filament  current. 

(6)  Study  of  the  low-frequency  amplifier  equipped  with  transformer 
"  repeater." 

Apparatus 

Two  vacuum  tubes  (similar  to  the  tube  investigated  in  Experiment 
No.  6). 

Two  vacuum-tube  receptacles. 

Storage  battery,  ammeters  and  rheostat  for  filament  circuit. 

Dry  battery  for  plate  circuit  (about  40  volts). 

Voltmeter  for  measuring  plate  voltage. 

Phones. 

Buzzer  wave  generator.  (This  is  exactly  similar  to  the  equipment 
described  in  Experiment  No.  7,  to  be  mounted  on  a  small  board  to  permit 
the  whole  circuit  to  be  readily  moved.) 

Variable  tuning  condenser  C  (about  .001  microfarad  maximum  value). 

Fixed  inductance  L  (about  150  microhenries). 

Fixed  inductance  for  Test  4.  (Secondary  of  receiving  coupler  having 
about  4  millihenries  inductance  would  be  suitable.) 

Grid  condensers  (Test  6).  (.0001,  .0005,  .005  and  1.0  microfarad 
would  be  suitable.  These  condensers  have  already  been  used  in  previous 
experiments.) 

Grid  leak  resistances  (Test  7).  (50,000  ohms  and  2  megohms  resist- 
ances may  be  used.) 

D.  P.  D.  T.  switch. 

Crystal  detector  (for  use  in  Tests  9  and  10). 

Shunting  condenser  for  plate  circuit  (about  .01  microfarad). 

Grid  condenser  and  leak  resistance  for  receiving  tube  grid  circuit  (to 
be  normal  value  for  the  tube:  .0001  microfarad  and  2  megohms  would 
probably  be  satisfactory). 


914 


EXPERIMENTS  WITH  RADIO  CIRCUITS 


[CHAP.  XII 


Grid  condenser  and  leak  resistance  for  amplifying  tube  grid  circuit 
(.0005  microfarad  and  1  megohm  respectively). 

Low  air-core  inductance  (about  3000-5000  microhenries). 

Iron  core  inductance  for  "  repeating."  (An  inductance  of  10  to  15 
henries  is  required.  This  may  be  obtained  in  the  form  of  an  iron-cored 
and  iron-shielded  inductance  wound  with  very  fine  wire,  the  whole  being 
about  4  inches  long  and  1J  inches  in  diameter.  The  d.c.  resistance  will 
be  about  2000  ohms.) 

Two  iron-cored  transformers  for  "  repeating  "  (Tests  9  and  10).  (Suit- 
able transformers  may  be  obtained  which  are  contained  in  a  case  about 
3X3X2  inches.  The  inductance  of  the  primary  and  secondary  windings 
is  about  3  and  30  henries  respectively,  and  the  turn  ratio  3.2. 

Operation 

Test  1.  Connection  of  a  Tube  Detector  and  Single-stage  Low-fre- 
quency Amplifier  with  Inductance  Repeater. — Make  connections  as  per 
Fig.  18.  Use  for  G  a  high-inductance  coil  of  about  15  henries,  for  K 


Tube  No.  2 


Tube  No.  1 


c_ruttu 


Buzzer  circuit 
secured  on  a  base 


FlG.   18. 


a  500-juju/  condenser,  and  for  M  a  1-megohm  resistance.  Note  that 
tube  No.  1  is  being  used  as  a  detector  of  high-frequency  damped  waves, 
while  tube  No.  2  is  being  used  as  an  amplifier  of  the  low-frequency  currents 
flowing  in  the  plate  circuit  of  tube  No.  1.  The  double-throw  switch 
permits  the  phones  to  be  connected  in  the  plate  circuit  of  the  first  tube 
or  of  the  second  tube.  Make  the  grid  condenser  of  the  first  tube  100  /*/// 
and  the  grid  leak  2  megohms. 

Test  2.  Measurement  of  the  Sensitiveness  of  the  First  Tube  as  a 
Detector. — Connect  the  phones  into  the  plate  circuit  of  the  first  tube, 
make  the  filament  current  and  plate  voltage  normal,  and  by  means  of  the 
variable  condenser  tune  to  the  buzzer  signal.  Move  the  entire  buzzer 
circuit  until  the  distance  between  the  buzzer  circuit  inductance  and  the 
receiving  circuit  inductance  (denoted  by  P  and  S  in  Fig.  18)  is  such  that 


LOW-FREQUENCY  AMPLIFIER 


915 


the  phones  give  a  "  just  audible  "  signal  when  the  two  circuits  are  in  tune; 
note  and  record  the  distance  between  the  two  inductances.  This  dis- 
tance is,  to  a  certain  degree,  a  measure  of  the  sensitiveness  of  the  tube. 

Test  3.  Sensitiveness  of  the  Two  Tubes  with  Normal  Repeating 
Inductance. — Place  phones  into  the  plate  circuit  of  the  second  tube. 
Use  for  G,  K  and  M  (see  Fig.  18)  the  values  specified  in  Test  1.  With 
all  other  conditions  normal,  measure  the  distance  P-S  necessary  to  make 
the  signal  just  audible. 

Test  4.  Sensitiveness  of  the  Two  Tubes  with  Low  Repeating  Induc- 
tance.— Use  for  G  the  low  air  core  inductance,  and  repeat  Test  3  with  all 
other  conditions  the  same  as  in  Test  3. 

Test  5.  Sensitiveness  of  the  Two  Tubes  with  Resistance  Repeater. — 
Use  for  G  a  50,000-ohm  resistance  and  repeat  Test  3  with  all  other  con- 
ditions the  same  as  in  Test  3. 

Test  6.  Effect  of  the  Grid  Condenser  of  the  Second  Tube  upon 
Amplification. — With  all  other  conditions  as  in  Test  3,  measure  the  sen- 
sitiveness of  the  two  tubes  for  values  of  the  capacity  in  the  grid  of  the 
second  tube  of  100  MM/,  500  MM/,  5000  MM/,  and  1.0  M/- 

Test  7.  Effect  of  the  Grid  Leak  Resistance  of  the  Second  Tube  on 
Amplification. — With  all  other  conditions  as  in  Test  3,  measure  the  sen- 
sitiveness of  the  two  tubes  for  values  of  the  leak  resistance  M  (see  Fig.  18) 
of  infinity,  2  megohms,  50,000  ohms,  and  zero. 

Test  8.  Effect  of  Low  Plate  Voltage  or  Low  Filament  Current  upon 
Amplification. — With  all  other  conditions  as  in  Test  3,  measure  the  sen- 
sitiveness of  the  two  tubes  with  plate  voltage  about  75  per  cent  of  normal 
and  normal  filament  current;  also  with  normal  plate  voltage  and  reduced 
filament  current. 

Test  9.  Connections  of  a  Low-frequency  Amplifier  with  Transformer 
Repeater. — Make  connections  as  in  Fig.  19.  Note  that  the  rectifying 


-nrw  j 


Board 


FlG.  19. 


will,  in  this  case,  be  done  by  the  crystal  and  the  amplifying  by  the  step- 
up  transformers  and  by  the  tubes. 


910  EXPERIMENTS  WITH  RADIO  CIRCUITS  [CHAP.  XII 

Test  10.  Sensitiveness  of  the  Low-frequency  Amplifier  with  Trans- 
former Repeater. — Use  normal  filament  current  and  plate  voltage.  Dis- 
connect the  primary  of  transformer  1,  and  in  its  place  connect  the  phones; 
measure  the  sensitiveness  of  the  crystal  detector  alone.  Reconnect  the 
primary  of  transformer  1,  and  connect  the  phones  in  place  of  the  primary 
of  transformer  2;  measure  the  sensitiveness  of  the  combination  of  crystal 
detector,  transformer  1,  tube  1.  Again  reconnect  the  primary  of  trans- 
former 2,  and  connect  the  phones  in  the  plate  circuit  of  the  second  tube; 
measure  the  sensitiveness  of  the  combination  of  crystal  detector  and  two- 
stage  amplifier. 

NOTE  :  In  the  foregoing  tests  the  relative  sensitiveness  of  the  various 
arrangements  may  be  obtained  by  shunting  the  telephones,  instead  of  by 
separating  P  and  S;  the  shunt  used  should  be  of  the  "  constant  impe- 
dance "  type. 

QUESTIONS 

1.  In  the  diagram  of  Fig.  18,  what  is  the  object  of  the  following? 

(a)  The  condenser  and  leak  resistance  in  the  grid  circuit  of  the 

first  tube. 
(6)  The  inductance  (G)  in  the  plate  circuit  of  the  first  tube. 

(c)  The  condenser  (C")  in  the  plate  of  the  first  tube. 

(d)  The  condenser  (K)  and  leak  resistance  (M)  in  the  grid  of  the 
second  tube. 

2.  From  your  results  of  Test  4,  what  is  the  effect  upon  amplification 
of  a  low  repeating  inductance?    From  the  results  of  Tests  3  and  5,  how 
does  resistance  repeating  compare  with  inductance  repeating? 

3.  From  the  results  of  Tests  6  and  7,  what  are  the  best  values  of  the  I 
grid  condenser  and  grid  leak  resistance  for  the  second  tube? 

4.  From  your  results,  how  does  the  two-tube  low-frequency  amplifier 
with  transformer  repeater  (Test  10)  compare  with  the  two-tube  detector 
and  low-frequency  amplifier  with  inductance  repeater? 

EXPERIMENT  NO.  14 

Object 

Study  of  the  radio-telephone  transmitter  and  receiver,  utilizing  equip- 
ment giving  a  range  of  transmission  of  20  to  30  miles.  The  apparatus  is 
small,  of  light  weight,  and  readily  portable,  and  has  found  a  wide  applica- 
tion for  establishing  communication  in  military  aeronautics.  Investi- 
gation of  the  effect  of  improper  adjustment  of  the  voltage  of  the  grid 
of  the  modulating  tube  and  of  the  modulating  inductance. 


RADIO  TELEPHONE   SET  917 

Apparatus 

1.  The  Receiver. — The  receiver  consists  of  a  detecting  and  amplifying 
tube  connected  as  shown  in  Fig.  20.     This  circuit  is  identical  to  that 
illustrated  in  Fig.  18,  Experiment  13,  and  the  apparatus  required  is  as 
previously  specified.     The  D.  P.  D.  T.  switch  is  omitted,  or  may  be  con- 
sidered permanently  thrown  to  the  right  (for  amplifying  action)  in  Fig.  18. 
The  several  capacities  and  grid  leaks  should  have  approximately  the  values 
indicated  in  the  diagram. 

2.  The  Transmitter. — The  oscillating  tube  generator  and  its  associated 
circuit  is  identical  to  that  studied  in  Experiment  10,  and  much  of  the 
equipment  specified  in  that  experiment  may  be  utilized.     For  the  modu- 
lator element  the  following  additional  apparatus  is  required  and  used 
as  indicated  in  Fig.  21. 

Vacuum  tube  and  receptacle  (similar  to  the  oscillator,  as  specified  in 
Experiment  10). 

Ordinary  telephone  transmitter. 

Dry  cells  for  telephone  transmitter  local  circuit  (five  No  6  dry  cells 
should  give  satisfactory  results). 

S.  P.  S.  T.  switch  for  transmitter  circuit. 

Step-up  audio-frequency  transformer  for  coupling  transmitter  circuit 
to  modulator  grid  circuit.  (This  transformer  measures  about  3X3X2^ 
inches  and  is  of  the  closed  iron  core  type.  The  inductance  of  the  primary 
and  secondary  windings  would  be  about  .04  and  160  henries  respectively, 
the  resistance  of  the  primary  is  2  ohms  while  the  turn  ratio  is  approxi- 
mately 60.) 

Grid  battery  for  modulator  tube  (about  40  volts). 

"  Modulating  "  inductance.  (This  is  a  high  inductance  having  between 
1  and  2  henries.  The  coil  is  about  2|  inches  high  and  1 J  inches  in  diam- 
eter, has  an  iron  core  and  is  assembled  within  a  surrounding  soft  iron 
shield.  The  d.c.  resistance  will  be  about  90  ohms.) 

Low  inductance.  (The  inductance  may  be  any  value  which  may  be 
available  as  long  as  it  is  considerably  less  than  the  preceding  inductance 
which  represents  the  "  normal  "  value.) 

Antennae  for  transmitter  and  receiver.  (These  are  easily  made,  each 
consisting  of  20  or  30  feet  of  wire  well  insulated  and  supported  from  the 
ceiling  of  the  laboratory,  above  the  apparatus.  The  "  lead  in  "  wire  may 
consist  simply  of  a  voltmeter  lead  clipped  onto  this  horizontal  wire  and 
properly  connected  to  the  circuit  beneath.) 

Operation 

Before  proceeding  with  the  tests  indicated  below,  the  student  should 
review  thoroughly  the  theory  of  action  of  the  above  circuits,  as  described 
in  Chapters  VIII  and  XL 


918 


EXPERIMENTS   WITH   RADIO   CIRCUITS 


[CHAP.  XII 


Test  1.  Connections  of  the  Transmitting  and  Receiving  Radio- 
phone Circuits. — Connect  the  transmitting  circuit  according  to  Fig.  21 
and  the  receiving  circuit  according  to  Fig.  20.  Note  that  the  trans- 
mitting circuit  consists  of  the  oscillating  tube  circuit  studied  in  Experi- 


Antenna 


150  fth 


ment  10  and  in  addition  a  modulating-tube  circuit.  The  receiving  circuit 
consists  of  .a  three-electrode  tube  detector  and  a  single-stage  amplifier 
with  inductance  repeater. 

Test  2.    Transmission  of  Speech  under  Normal  Conditions  of  Modu- 
lating Inductance  and  of  Potential  of  the  Modulating  Tube  Grid. — Use 


FIG.  21. 

for  the  modulating  inductance  an  iron  cored  inductance  of  about  1.3 
henries.  Make  the  grid  potential  of  the  modulating  tube  about  22  volts 
(negative)  and  adjust  the  filament  current  and  plate  voltage  of  all  tubes 
to  the  normal  values.  Start  the  oscillating  circuit  of  the  transmitter 
working,  and  adjust  the  wave-length  to  a  suitable  value  by  adjustment 


RADIO  TELEPHONE  SET  919 

of  the  wave-length  contact  and  of  the  condenser  in  multiple  with  the 
antenna  (Ci).  Now  talk  into  the  telephone  transmitter  with  your  lips 
about  1  inch  from  the  mouth  of  the  transmitter,  while  the  receiving  oper- 
ator endeavors  to  receive  the  speech  by  adjusting  the  variable  condenser 
so  as  to  "  tune  in  "  with  the  transmitting  set.  The  manipulation  of  the 
two  circuits  to  secure  best  results  is  not  simple,  but  the  adjustments 
should  be  persevered  in  until  the  best  transmission  of  speech  of  which 
these  circuits  are  capable  is  obtained.  Be  sure  that  the  circuit  constants 
permit  the  two  circuits  to  be  "  tuned." 

Test  3.  Transmission  of  Speech  under  Abnormal  Conditions  of 
Potential  of  the  Modulating  Tube  Grid. — Repeat  Test  2  after  adjusting 
the  potential  of  the  grid  of  the  modulating  tube  to  —4  volts.  Note  the 
quality  of  the  transmission. 

Test  4.  Transmission  of  Speech  with  Too  Low  a  Modulating  Induc- 
tance.— Repeat  Test  2  after  substituting  for  the  modulating  inductance 
an  inductance  of  very  low  value.  Note  the  quality  of  the  transmission. 

QUESTIONS 

1.  In  the  diagram  of  Fig.  21  what  is  the  purpose  of  the  iron-cored 
inductance  in  series  with  the  plate  battery? 

2.  Why  must   the  potential  of  the   grid  of  the  modulating  tube  be 
adjusted  to  a  certain  value  for  correct  transmission  of  speech? 

3.  What  was  the  quality  of  the  transmission  in  Test  3,  and  why? 

4.  What  was  the  quality  of  the  transmission  in  Test  4,  and  why? 


INDEX 


A 

PAGE 

Adjustment  of  oscillating  detectors,  peculiarities  of 522 

Aerial 694 

Alexanderson  alternator,  construction  and  action  of 594 

Alexanderson's  barrage  receiver 688 

scheme  of  modulation 669 

Alternating  current  supply  for  the  plate  of  a  tube 529 

effective  value  of 17 

wave-shape  of 17 

Alternator,  armature  reaction  of 291 

high  frequency  for  continuous-wave  telegraphy 593 

inductor  type 289 

internal  impedance  of 290 

used  for  spark  transmitter,  action  of 287 

use  of  consequent  poles  in  construction  of 290 

Amplification,  distortionless,  of  a  tube,  conditions  for 572 

Amplifying  factor  of  vacuum  tube,  experimental  determination  of 898 

Ampere-turns 18 

Amplifier,  characteristics  of  three-electrode  tube 570 

classification  of 824-829 

connections  of,  for  reception  of  damped  and  undamped  waves 841 

effect  of  R  and  L  in  plate  circuit  on  action  of 827-829 

fields  of  use  of  radio  and  audio  frequency  types 859 

inductance  repeating 857 

low-frequency,  experimental  study  of 913 

resistance  repeating 849 

stability  of 870 

test  for  quality  of 577 

transformer  repeating 830 

tube  characteristics  for  different  stages 863 

tube  noises  in  operation  of 875 

Amplifiers,  arrangement  of  apparatus  in 876 

Amplifying  power  of  a  tube  as  affected  by  grid  potential  and  plate  circuit  voltage.  575 

average  potential  of  grid 574 

measurement  of 417 

Amplitude  of  vacuum  tube  oscillations  in  the  steady  state. 495 

Antenna,  coil,  as  directional  radiator 711 

receiver 722 

constants,  experimental  determination  of ....  891 

"loading" 760 

921 


922  INDEX 

PAGE 

Antenna,  natural  wave-length  of 751 

pulse  excitation  of  an 780 

radiation,  law  of 730 

reactance 757 

receiving,  current  in 738 

resistance 140,  746 

setting  up  steady  state  in 776 

Antennae,  comparative  merits  of  different  types  of 743 

distribution  of  current  and  voltage  in .   75"),  7(>0,  763 

effective  height  of 716 

for  aeroplanes  and  airships 723 

underwater 726 

ground 729 

simple,  mechanism  of  radiation  by  means  of 694 

various  types  of 713 

Arc  generator  or  converter  (Poulsen)  construction  of 589 

Poulsen,  theory  and  action  of 580 

resistance  of 136 

Armstrong,  E.  H.,  type  of  high  frequency  amplifier  due  to 860 

amplification  measurements  by 518 

Attenuation  of  propagated  waves 196 

Audio  circuit  of  spark  transmitter,  analysis  of  action  of 301 

Austin,  L.  W.,  formula  for  range  of  radio-signal  transmission 357 

Austin's  formula,  analysis  of 200 

for  receiving  antenna  current 196 

Autodyne  method  of  reception  of  continuous-wave  signals 483,  514,  635 

wave-meter.  .                                                                                               .  795 


B 

"Balancing  out"  schemes  for  simultaneous  transmission  and  reception 687 

Baldwin  receiver,  construction  and  action  of 342 

Barrage  receiver 688,  690 

Battery,  polarizing,  function  of,  with  crystal  rectifiers 343 

Beat  frequency,  control  of,  in  reception  of  continuous  wave  signals,  using  hetero- 
dyne method 638 

in  coupled  circuits 246 

receiver  of  continuous  wave  signals 634 

Bellini  and  Tosi  goniometer 767 

Bridge  for  high-frequency  measurements 428 

Buzzer  wave  generator,  use  of 882 


C 

Capacity 29 

electrostatic,  general  discussion  of . . ./  161 

of  conducting,  isolated  sphere  in  air 162 

s    two  flat  circular  parallel  plates  in  air 162 

single  vertical  wire  in  space • 162 

horizontal  wire,  earth  as  other  plate 162 


INDEX  923 

PAGE 

Capacity  of  two  horizontal  overhead  wires  with  respect  to  each  other 164 

wire  antenna 164 

a  multi-plate  condenser 165 

internal,  of  a  two-layer  solenoid 171 

multiple-layer  coil 175 

mutual,  of  two  horizontal  wires 163 

required  in  closed  circuit  of  spark  transmitter,  calculation  of 299 

specific  inductive 31 

Carrier  frequency  for  radio-telephony 649 

values  of,  for  radio-telephony 653 

Chaffee,  E.  L.,  quenched  spark  gap  of 317 

Charged  body 2 

Charges,  bound  and  free 6 

induced 6,  7 

positive  and  negative,  difference  between 8 

Child's  formula  for  plate  current  in  a  two-electrode  vacuum  tube 377 

Circuits  having  resistance  and  iron-core  inductance 53 

with  distributed  capacity  and  inductance,  characteristics  of 107 

Coil  antenna 714,  720,  725 

as  directional  radiator  and  receiver 711,  722 

for  submarines 727 

Condenser,  bridging,  application  of 349 

charge  and  discharge  of 37 

charging  of 29 

discharge,  oscillatory,  frequency  of 212 

through  R  and  L,  criterion  for  oscillations 211 

effect  of  condenser  leakage  on 210 

theory  of 202 

equivalent  series  or  shunt  resistance  of 168 

grid,  in  connection  with  use  of  vacuum  tube  in  self-heterodyne  circuit .  643 

losses  occurring  in 166 

phase  difference  of 171 

special  form  of,  for  wave-meter 792 

variable,  forms  of 165 

Condensers,  construction  of,  for  use  in  spark  transmitters 297 

power,  characteristics  of 169 

Conductor,  constitution  of 364 

Conductors 11 

Consequent  poles,  use  of,  in  radio  alternator 290 

Continuous-wave  generators,  efficiency  of 619 

forms  of 580 

receivers,  action  of 631 

chopper 631 

Goldschmidt  tone  wheel ^  ...  632 

oscillating  vacuum  tube 634 

rotating  plate  condenser -634 

tikker 634 

signals,  reception  of 629 

telegraphy,  advantages  of 188,  578 

use  of  radiophone  transmitting  set  for 627 

transmitters,  methods  of  signaling  with 620 


924  INDEX 

PAGE 

Counterpoise 694,  745 

Coupled  circuits,  amplitude  relations  in  (Chaff ee,  E.  L.) 230 

analysis  of  oscillations  in 226 

determination  of  the  two  frequencies  of  oscillation 227 

form  of  current  in,  if  primary  circuit  is  opened  at  the  right  time .  .    247 

formula  for  damping  factors  and  decrements  of  current  in 237 

wave-length  of  oscillations 231 

frequency  of  beats  in 246 

general  case  of  three 229 

oscillatory  discharge  in  one  circuit  and  non-oscillatory  discharge 

in  the  other -249 

possibility  of  no  beats  without  quenching  gap 248 

shape  and  frequency  of  actual  current  in 238 

vector  representation  of  current  in 242 

oscillatory  circuits,   mechanical  analogue  of 223 

pendulums,  analysis  of  motion  of 225 

Coupling,  capacitive 80,  84,  279 

coefficient  of 27,  79 

conductive 279 

direct 81 

inductive 80 

effect  of  variation  of,  in  tuned  circuits , 103 

of  grid  and  plate  circuits  of  an  oscillating  tube  by  capacity 503 

a  vacuum  tube  by  capacity,  critical  value  of, 

for  oscillations 506 

input  and  output  circuits  of  a  vacuum  tube,  critical  value  of,  for 

oscillations 492 

test  for  detecting  oscillating  condition  of  tubes 520,  522 

various  kinds  of 79 

Critical  coupling  of  oscillating  tube  as  affected  by  condenser  in  series  with  grid.  .  .    518 

Crystal  rectifiers,  characteristics  of 343 

laboratory  investigation  of 882 

Current,  continuous  and  alternating 14 

direction  of  flow  of 11 

distribution  in  conductor  carrying  high-frequency  current 113 

electric,  nature  of 8 

in  a  circuit  containing  resistance  and  a  condenser  in  series 57 

inductance  and  capacity  in  series 58 

with  resistance  only 32,  42 

an  inductive  circuit 32,  45 

a  condenser 55 

coil  receiving  antenna 740 

parallel  circuits 66 

simple  receiving  antenna 738 

vs.  frequency  in  an  inductive  circuit . . 49 

inductively-coupled  circuits 89 

Currents,  decaying,  effect  of,  on  neighboring  circuits 35 

in  a  parallel  resonant  circuit,  oscillogram  of 75 


INDEX  925 

D 

PAGE 

Damped  wave,  current,  voltage  and  energy  in 215 

train,  effective  value  of  current  in 221 

Damping  coefficient,  definition  of 214 

Decrement 62 

effect  of,  on  quality  of  received  speech  in  radio-telephony 678 

measurement  of,  with  wavemeter 801 

Decremeter,  construction  and  uses  of  (Kolster) 809 

'  Detecting  efficiency  of  three-electrode  tube,  measurement  of 465 

tube  requirements 465 

Detection  of  damped  waves  by  means  of  regenerative  tube  circuit 525,  526 

radio  signals,  visual,  audible 336 

undamped  waves  by  means  of  oscillating  vacuum  tube  with  no  grid 

condenser 483,  514 

undamped  waves  by  means  of  oscillating  vacuum  tube  with  grid  con- 
denser     486 

undamped  waves  by  means  of  an  oscillating  tube,  analysis  of 514 

Detector  action  of  three-electrode  tube  with  grid  condenser,  analysis  of 455 

illustrated  by  oscillo- 

grams 462 

of  three-electrode  tube  with  grid  condenser  as  affected  by  fre- 
quency and  decrement  of  signal 461 

vacuum  tube  type 350 

Detectors,  action  of •  •  •   338 

Direction  finders , 766 

elimination  of  "  180°  uncertainty"  in .  .  .  : 772 

incomplete  extinction  of  signals  in 775 

reliability  of 775 

Distance,  transmission  of  radio  telegraphic  signals 357 

Dynatron 534 


E 

Effect  of  high  and  low  grid  excitation  upon  the  form  of  Ep  and  Ip  of  a  separately 

excited  power  tube 541 

high  and  low  load  resistance  upon  the  form  of  Ep  and  Ip  of  a  separately 

excited  power  tube 543 

the  local  oscillations  of  a  tube  detector  of  undamped  waves  upon  strength 

of  signals •   516 

Efficiency,  calculated,  of  a  separately  excited  power  tube  for  various  forms  of 

plate  current 552 

calculated,  of  a  separately  excited  power  tube  for  various  plate  voltages.  552 

measured,  of  a  separately  excited  power  tube 554 

of  a  three-electrode  tube  as  a  detector,  analysis  of 446 

Electric  fields 3 

represented  by  lines 4 

Electricity,  nature  of 1 

Electro-magnetic  waves,  discussion  of 181,  702 

Electro-motive  force 10 

induced .  .  23 


926  INDEX 

PAGE 

Electron  bombardment  in  vacuum  tubes 390 

emission  affected  by  condition  of  hot  surface 307 

from  a  conductor 364 

filament  vs.  filament  current 379 

power  required  for 371 

stream  as  constituting  an  electric  current 698 

Electrons 1 

current  due  to  velocity  of 369 

distribution  of,  near  surface  of  a  hot  metal 368 

emitted  from  a  hot  body,  theoretical  prediction  of  number  of 364 

number  of,  removable  from  an  atom 3 

velocity  of  emission  of,  from  a  hot  metal 368 

Elimination  of  undesired  frequencies  in  oscillating  tube  circuits 512 

Energy  distribution  curve  of  spark  transmitter 325,  331,  799 

undamped  wave  transmitter 800 

of  radiated  electric  and  magnetic  fields 182,  696 

water  particles  in  water  waves 181 

stored  in  a  charged  condenser 31 

magnetic  field 26 

supply  of  spark  transmitter,  forms  of 281 

Evacuation  of  a  vacuum  tube 393 

Excitation  of  spark  transmitter,  forms  of 280 

separate,  for  a  group  of  vacuum  tubes 532 

F 

Fan  antenna 713,  718 

Fence  wire  as  receiving  antenna 730 

Field,   electric,  due  to  an  antenna,  intensity  of 703,  707 

electric,  in  motion 696 

electric,  open  and  closed 5,  699 

magnetic 18 

magnetic,  due  to  an  antenna,  intensity  of 703,  707 

magnetic,  in  motion 696 

magnetic,  open  and  closed 698,  699 

energy  stored  in 26 

induction 182,  703 

radiation 182,  704 

radiated,  at  any  distance  from  an  antenna  consisting  of  a  vertical  wire ....   705 

a  coil  antenna 708 

Fields,  electric 3 

represented  by  lines 4 

Filament  of  a  vacuum  tube,  unequal  currents  in 379,  403 

resistance  of 404 

Filaments  for  vacuum  tubes,  tungsten  and  oxide  coated 400 

Filters,  use  of,  in  amplifiers 864 

"Fleming"  valve 

Fluorescence  in  vacuum  tubes  with  oxide  coated  filaments 392 

"  Freak  "  transmission 200 

Frequency  changers,  application  of  rectifier  elements  to 616 

types  of 608 


INDEX  927 

PAGE 

Frequency  changers,  types  of,  for  tripling  frequency  (Joly) 608 

(Taylor) 611 

for  doubling  frequency  (Epstein- Vallouri) 609 

(Plohl) 610 

losses  of 613 

audio 186 

effect  of  upon  input  capacity  and  conductance  of  a  tube 439 

of  oscillating  tube  current  for  capacity  coupling  of  grid  and  plate  circuits.  506 

an  oscillating  tube,  constancy  of 514 

radio 186 

transformation 607 

tripling,  use  of  wabbling  neutral  for  obtaining 613 

Finger  test  for  detecting  oscillating  condition  of  tubes 520,  522 

G 

Gas  in  tungsten  filament  tubes,  tendency  of,  to  disappear 396 

a  vacuum  tube,  effect  of 390 

detection  of 394 

Generator,  electric 16 

Generators  of  high  frequency,  undamped  waves,  types  of 580 

use  of,  for  power  supply  to  amplifiers 870 

Goldschmidt  alternator,  construction  of 606 

theory  of  action  of 599 

Goniometer,  Bellini  and  Tosi 767 

Grid 381 

action  of,  in  three-electrode  tubes 382 

condenser  for  three-electrode  tube  when  used  as  detector  of  damped  waves .  .   451 

value  of,  for  tubes  used  as  detectors 455,  461 

current  in  well-evacuated  three-electrode  vacuum  tube 399 

normal  potential  of 454 

potential  of  a  three-electrode  tube  when  acting  as  detector  with  grid  condenser  464 

free 402,  410 

Ground  antennae . .  729 


H 

Harmonics,  upper,  effect  of,  in  reception  of  continuous-wave  signals,  using  hetero- 
dyne receiver 639 

Harp  antenna 713 

Heating  of  the  plate  of  a  three-electrode  tube 473 

Heising's  scheme  of  modulation 664,  665 

Heterodyne  reception  of  undamped  waves 483,  517,  635 

"Hysteresis"  in  vacuum  tubes 397 

I 

Impedance,  definition 47 

of  a  branched  circuit  containing  L  and  R  in  one  branch  and  C  and  R 

in  the  other 68 

circuit  containing  L,  R  and  C  in  series 68 


928  INDEX 

PAGE 

Impulse  excitation  of  a  parallel  resonant  circuit 266 

oscillating  circuit 259 

Inductance,  in  grid  and  plate  circuits  of  an  oscillating  tube,  effect  of,  upon  the 

operation  of  tube 570 

mutual,  of  two  single  turns,  coaxial 156 

coaxial,  circular  coils  of  rectangular  cross-section ....  156 

solenoids 157 

of  two  overhead  parallel  wires,  grounded,  at  same  height  from  ground.  157 

between  two  concentric  coils,  as  one  rotates 158 

coaxial  spirals 160 

self-,  discussion  of 143 

of  a  single  straight  vertical  wire  distant  from  all  other  conductors.  144 

circular  turn  of  round  wire 145 

-layer  solenoid  closely  wound 145 

flat  spiral 147 

flat  square  coil 151 

toroidal  coil  of  rectangular  cross-section 149 

circular  cross-section 150 

single-layer  square  coil 150 

multi-layer  coils  of  rectangular  cross-section 152 

two-wire  antennae 157 

variable,  design  of 153 

Induction  coil,  action  of 282 

Inductor  alternator,  action  of 287 

Input  circuit  of  a  tube 421 

capacity  and  conductance  of,  vs.  plate  circuit  resistance. . .  435 

conductance  of,  vs.  filament  current , 429 

plate  voltage 430 

grid  potential 431 

effective  capacity  of 434 

geometrical  capacity  of 432 

negative  conductance  of 437 

resistance  of 428 

used  as  a  detector,  equivalent  of 454 

Insulators 11 

disruptive  strength  of 13 

effect  cf  temperature  on  disruptive  strength  of 13 

Interference,  discussion  of : 191,  193 

Interrupter  action,  requirements  of 282 

/'hammer  break"  type 282 

Interrupters  for  primary  circuit  of  induction  coils,  types  of 287 

lonization,  danger  of,  to  vacuum  tubes 392 

in  vacuum  tubes 390 

Iron-core  coils,  resistance  of 134 


K 

Kenotron 373 

Kenotrons  used  for  rectifying  alternating  current  for  supply  to  plate  of  a  vacuum 

lube : 529 

Kolster,  F.  A.,  decrcrneter,  construction  and  uses 809 


INDEX  U2<) 


L 

PAGE 

"L,"  inverted,  type  of  antenna.  .  .   713,  716,  718 

Leak  resistance  for  three-electrode  tube  when  used  as  detector  of  damped  waves. .  .  451 

value  of,  for  tube  used  as  a  detector 455 

Leyden  jar,  use  of,  in  f-park  transmitter 298,  299 

Limitations  of  transmission  formulae , 744 

"  Loading ' '  an  antenna 760 

Logarithmic  decrement,  definition  of 214 

formula  for 214,  215 

graphs  for  three-electrode  tubes 421 

Loop  antenna  for  submarine 727 

M 

Magnetic  field , 18 

effect  of  iron  in 19 

Marconi,  multi-gap  generator  of  continuous  waves 616 

Mepcury  rectifier 372 

Meters  in  alternating  current  circuits 44 

Microphone,  liquid 656 

transmitter s.  .  .  .  655 

Miller,  J.  M.,  method  for  measuring  /zc  of  a  tube 417 

A.C.  output  resistance  of  a  tube 426 

Modulated  current 649 

wave,  analysis  of 674 

Modulating  frequency 649 

Modulation,  analysis  of 657 

percentage  of 660 

requirements  for 656,  668 

sch  mes  for 661 

Motor,  speed  of,  for  driving  radio  alternator 334 

types  of,  for  driving  radio  alternator 290 

Multiple-tuned  antenna 714,  719 

Multiplex  radio-telephony 680 

Mutual  induction .  .  26 


N 

Natural  period  of  multi-layer  coils 177 

Neutralization  schemes  for  simultaneous  transmission  and  reception 687 

Noises  in  oscillating  tube  detector  circuit 523 


O 

Oscillating  conditions  of  a  tube,  criterions  for 520 

power  tube  circuit,  laboratory  study  of  characteristics  of 903 

tubes  in  multiple 527 

receiving  set  for  radio-telephony 677 

tube  circuits  of  very  high  frequency 511 

receiving  circuit,  laboratory  investigation  of 908 


930  INDEX 

PAGE 

Oscillating  tube  under  conditions  of  oscillating  current  comparable  in  value  with 

plate  current 503 

tube,  use  as  a  continuous  wave  generator 617 

Oscillation  transformer,  construction  of 318 

experimental  investigation  of  power  output 900 

with  oscillating  circuit  in  grid  circuit 510 

vacuum  tube,  adjustment  for  maximum  output 501 

as  a  detector  of  undamped  waves 483 

circuits,  analysis  of 487 

conditions  for  maximum  output  of 471,  497 

efficiency  of 468,  471 

elementary  analysis  of 469 

excitation  of 469 

output  of 471 

uses  of 468 

current  and  power  of,  vs.  exciting  grid  voltage. . .  480 

conditions  necessary  for  self -excitation 478 

Oscillations  of  a  vacuum  tube,  effect  of,  on  grid  and  plate  currents 500 

tube,  effect  of,  upon  plate  current 519 

vacuum  tube  at  other  than  desired  frequency 502,  512 

stability  of 498 

^                                     starting  and  stopping 499 

types  of  (of  arc  generators) 586 

Oscillograph 33 

Oscillatory  circuit,  current  and  voltage  relations  in 213 

excited  by  a  damped  sine  wave,  analysis  of 268 

being    connected   to   a   line   of   alternating   e.m.f., 

theory  of 252 

continuous  voltage,  theory  of 249 

damped  sine  waves,  resonance  curve  of :  . . .  227 

energy  stored  in  inductance,  theory  of 250 

pulse,  analysis  of 259 

condition  of  a  vacuum  tube,  prediction  of,  by  placing  total  resistance 

equal  to  zero 492 

currents  of  a  spark  transmitter,  discussion  of 321 

discharge,  frequency  and  damping  of,  as  affected  by  neighboring  cir- 
cuits   222 

through  a  spark  gap 218 

Output  circuit  of  a  tube 421 

impedance  of  a  tube 423 

resistance  of  a  tube 423 

A.C.,  measurement  of 424 


P 

Phase 42 

of  the  grid  voltage  of  a  self -excited  tube,  possibility  of  variation  of 562 

relation  of  electric  and  magnetic  fields  in  electro-magnetic  radiation 702,  705 

relations,  effect  of,  on  the  possible  power  output  of  vacuum  tube  generator . .  476 
of  voltages  and  current  in  a  vacuum-tube  generator 474,  493 

Pliodynatron 534 


INDEX  931 

PAGE 

Potential  difference 11 

gradient  between  plate  and  filament  of  a  two-electrode  vacuum  tube 377 

Poulsen  arc,  theory  and  action  of 580 

Power,  amount  sent  out  and  received 198 

factor 48 

in  a  circuit  excited  by  pulsating  current 40 

continuous  current  circuit 38 

an  inductive  circuit .' 47 

a  resistance  circuit 43 

transmitted  and  received 198 

used  in  the  plate  of  a  three-electrode  tube 473 

Production  of  current  in  antenna,  methods  for 711 

Protective  equipment  of  spark  transmitter 278 

Pulse  excitation  of  oscillating  circuit 259 

Q 

Quality  of  speech  received  by  radio-telephony  as  affected  by  decrement 678 

Quenched  gap,  construction  of 314 

theory  of  action  of 247 

R 

Radiation 182 

mechanism  of,  by  means  of  simple  antenna 694 

of  light  from  a  hot  filament  compared  to  radiation  from  an  antenna ....  734 

power  from  an  antenna,  law  of 730 

a  coil  antenna,  law  of 735 

resistance 737 

Radio-compass  service   or  ships 771 

Radiophone  sets 684,  692 

Radiophone  transmitting  set,  use  of,  for  undamped  wave  telegraphy 627 

Radio-telephony,  fundamental  idea 189 

Radio-telephone  transmitter  and  receiver,  experimental  study  of 916 

Reactance,  definition 47 

Receiving  circuits  .  .          190 

adjustment  of,  for  damped  wave  signals 350,  882 

for  damped  wave  signals 340 

station,  essential  elements  of  a 189,  336 

Reception  of  undamped  waves  by  means  of  oscillating  tubes 483,  514 

Rectification  by  three-elecrfrode  tube  without  grid  condenser,  as  shown  by  oscillo- 

grams 445 

Rectifying  detectors,  action  of 338 

Resistance 14,  21,  111 

and  reactance  of  the  primary  of  an  inductively-coupled  circuit  as  affected 

by  secondary 93 

effective 40 

high  frequency,  general  concept  of Ill 

laboratory  measurement  of 906 

of  antenna 746 

coils,  effect  of  neighboring  circuits  on 133 


932  INDEX 

frAOK 

Resistance  of  iron-core  coils 134 

spark  and  arc 136 

the  circuits  of  a  three-electrode  tube  and  its  variation 421 

Resonance 60 

curves  for  coupled  circuits 99 

form  of 101 

curve  of  an  oscillatory  circuit  excited  by  damped  sine  waves 272 

in  a  circuit  to  which  another  is  magnetically  coupled 85 

simple  series  circuit,  laboratory  investigation  of 880 

circuits  with  capacitive  coupling 105 

series,  with  varying  capacity 62 

transformer,  definition  of 296 

Resonant  adjustment  of  the  audio  circuit  of  a  spark  transmitter 295 

circuit,  effect  of  periodic  disturbances  in  a 257 

frequencies  in  coupled  circuits 94 

frequency  of  parallel  circuits 78 

multiple  circuit 73 

curves  of  reactances  and  resistance  for 76 

Richardson's  formula  for  electron  emission 365 


S 

Saturation  current 367,  373 

Selectivity,  general  discussion  of 191 

Self -heterodyne  method  of  reception  of  continuous- wave  signals 635 

Self-induction,  coefficient  of 25 

of  a  coil  as  affected  by  presence  of  a  short-circuited  neighboring  coil     28 

Short-wave  condenser,  function  of 278 

Shunting  condenser  used  with  induction  coil,  action  of 283 

Signal,  day  and  night  variation  in  strength  of 197 

seasonal  variation  in  strength  of 198 

selection  of 350 

Signaling  with  high  frequency,  continuous- wave  generators,  methods  of 620 

Simultaneous  radiophone  transmission  and  reception 686 

sending  and  receiving,  essential  elements  required  for 192 

Skid-fin  antenna  for  aeroplanes 724 

Skin  effect,  analysis  of 117 

discussion  of . , 113 

elimination  of 122 

in  coils 125 

Space  charge  in  vacuum  tubes 376,  380 

Spark  gap,  care  of 

Chaffee  type .317 

classification  of,  for  spark  transmitter 309 

non-synchronous  type 313 

open  type,  operating  conditions  of 309 

quenched 247-314 

synchronous  rotating  type,  description  and  operation  of 311 

resistance  of 136 

telegraphy,  definition  of 187 

transmitter,  adjustment  of : 328 


INDEX 

PAGE 

Spark  transmitter,  capacity  and  inductance  required  in  closed  and  open  circuits 334 

description  of 275 

experimental  investigation  of 887 

Specific  inductive  capacity,  table  of  values 167 

Static 193 

Steady  state  in  an  antenna,  setting  up  of 776 

Stone,  J.  S.,  equation  for  spark-gap  resistance 219 

Strays,  classification  of .  .  . " 193 

elimination  of 194 

T 

"T"  antenna 713,  716,  725 

Time  constant  of  an  inductive  circuit 33 

a  condenser  circuit 38 

Telephone  receivers,  construction  and  action  of 340 

impedance  of 839 

Telephony,  radio  multiplex 680 

current  in  transmitting  antenna 648 

receiver 652 

receiving  antenna 650 

field  of  use 646 

principle  of  operation  of  transmitter 647 

receiver 649 

power  required  to  cover  distances 683 

receiving  system  for 673 

sources  of  power  for 654 

transmission  of  speech 651 

Temp  rature,  max  m  m  safe,  for  tungsten  filaments 371 

Transformer,  "open  core,"  description  of 296 

power  for  spark  transmitter 292 

Transformers,  construction  of,  for  low-frequency  amplifiers 839 

Transmission,  distance  of  radio  signal 357 

formulae,  limitations  of 744 

Transient  conditions  in  a  circuit  consisting  of  L,  R  and  C  in  series,  analysis  of ....  252 

current  in  an  inductive  circuit 49 

a  circuit  consisting  of  resistance  and  a  condenser  in  series ....  58 

on  switching  a  resistance  circuit  to  an  A.C.  line 45 

phenomena  in  audio  circuit  of  spark  transmitter,  analysis  of 304 

Transmitter  for  radio-telephony,  best  resistance  for 660 

Transmitters  for  radio-telephony 654 

Tree  as  receiving  antenna 730 

Tube,  three-electrode 381 

as  detector  of  damped  waves 440 

a  source  of  alternating  current 467 

power  converter,  detailed  study  of,  when  self-excited .  .  561 

separately  ex- 
cited    539 

characteristics  of,  with  positive  common  junction  and  with 

negative  common  junction 459 

two-electrode  as  voltage  regulator  for  a  variable  speed  generator 373 

characteristic  curves  of 373 


934  INDEX 

PAGE 

Tube,  vacuum,  two-electrode 371 

Tubes,  limits  of  operation  of 389 

three-electrode,  characteristic  curves  of 401 

for  high  power  telephone  sets 669 

in  radio-telephony 662 

fields  of ,  use  of 387 

hydraulic  model  of 385 

potential  distribution  in .- 382 

relations  between  currents  and  potentials  in 415 

resistance  of  circuits  of,  and  its  variation 421 

various  types  of 388 

with  small  amount  of  gas,  characteristic  curves  of 397 

vacuum,  special  forms  of 534 

"  Tungar  "  rectifier 1 372 

U 

Umbrella  antenna : 713 

Unequal  currents  in  the  filament  of  a  vacuum  tube 379,  403 

Unilateral  connection  of  wavemeter 786 

Unipotentia  emitting  surface  for  a  vacuum  tube 379 

Units  of  electrical  quantities 20 

V 

Vacuum  tube,  experimental  determination  of  amplifying  factor  and  internal  plate 

circuit  resistance 898 

investigation  of  characteristic  curves  of 894 

study  of  its  characteristics  when  used  as  a  detector  of 

damped  waves 895 

generator,  measurement  of  power  output  of 900 

transmitting  sets,  arrangement  of  apparatus  in 645 

use  as  a  detector 350 

Voltage  amplification  factor  of  a  three-electrode  tube 384,  417 

determination  of 417 

W 

Wattmeter 49 

Wave-length 183 

natural,  of  antenna 751 

of  electro-magnetic  radiations 213 

Wave-lengths,  range  of,  for  radio  communication 187 

used  in  spark  telegraphy 356 

Wave-meter,  autodyne  type .795 

devices  and  schemes  for  indicating  resonance 783 

condenser,  special  form  of 792 

crystal  detector  and  phones 785 

hot-wire  ammeter 784 

incandescent  lamp 791 

neon  tube 790 

crystal  detector  and  galvanometer 790 

thermo-couple  and  galvanometer 788 


INDEX  935 

PAGE 

Wave-meter,  experiment  on  uses  of  the 884 

how  to  improvise  a 821 

principle  and  construction  of 781 

use  of,  to  determine  decrement 801 

mutual  inductance  and  coefficient  of  coupling. . .  .  819 

measure  antenna  constants 815 

inductance  and  capacity 814 

wave-length  and  energy  distribution  curves .  .  .   796-798 

Wave  motion,  discussion  of 179 

propagation,  equation  for 183 

velocity  of 184 

Waves,  attentuation  of 196 

damped 186 

electromagnetic,  discussion  of . 181,  702 

transmission  of,  in  water 728 

number  of-,  in  a  tra'n,  formula  for 220 

stationary,  on  antenna 756 

undamped 186 

various  types  of,  used  in  radio  communication 185 

water 179 

Wave-shape  of  alternating  currents 16 

Wave-trains..                                                                                                             .  186 


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